NASA/TM–2014–218535

Mars Entry Atmospheric Data

System Modeling, Calibration, and

Error Analysis

Christopher D. Karlgaard, John Van Norman, and Paul M. Siemers

Analytical Mechanics Associates, Inc., Hampton, Virginia

Mark Schoenenberger, and Michelle M. Munk

Langley Research Center, Hampton, Virginia

October 2014
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NASA/TM–2014–218535

Mars Entry Atmospheric Data

System Modeling, Calibration, and

Error Analysis

Christopher D. Karlgaard, John Van Norman, and Paul M. Siemers

Analytical Mechanics Associates, Inc., Hampton, Virginia

Mark Schoenenberger, and Michelle M. Munk

Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

October 2014
Acknowledgments

The authors are grateful for contributions from Roger Beck, Artem Dyakonov, Noah Favaregh,

Chris Kuhl, Stephen O’Keefe, Jeremy Shidner, and Brady White in the areas of estimator design,

system modeling, wind tunnel data reduction, and calibration. The authors are also grateful to

Karen Bibb, Ron Merski, Matt Rhode, Eric Walker, and Henry Wright for helpful comments and

suggestions.

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not

constitute an offical endorsement, either expressed or implied, of such products or manufacturers by the

National Aeronautics and Space Administration.

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076-1320

443-757-5802
Abstract

The Mars Science Laboratory (MSL) Entry, Descent, and Landing Instrumentation (MEDLI)/Mars

Entry Atmospheric Data System (MEADS) project installed seven pressure ports through the MSL

Phenolic Impregnated Carbon Ablator (PICA) heatshield to measure heatshield surface pressures

during entry. These measured surface pressures are used to generate estimates of atmospheric quantities based on modeled surface pressure distributions. In particular, the quantities to be estimated

from the MEADS pressure measurements include the dynamic pressure, angle of attack, and angle

of sideslip. This report describes the calibration of the pressure transducers utilized to reconstruct

the atmospheric data and associated uncertainty models, pressure modeling and uncertainty analysis, and system performance results. The results indicate that the MEADS pressure measurement

system hardware meets the project requirements.

i
Contents

List of Figures v

List of Tables vi

List of Symbols vii

List of Acronyms ix

1 Introduction 1

2 Atmospheric State Estimation and Surface Pressure Modeling 7

2.1 Least–Squares State Variable Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Nominal Flight CFD Pressure Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Experimentation and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 MEADS Transducer Calibration 14

3.1 Calibration Methodology: General Overview . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Implementation of Calibration Approach for MEADS . . . . . . . . . . . . . . . . . . 15

3.3 Calibration Analysis: Methodology and Assumptions . . . . . . . . . . . . . . . . . . 17

3.4 Analysis of Final Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.5 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Uncertainty Modeling 25

4.1 Hardware System Error Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.1 Port Location Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.2 Sensor Noise and Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.3 Time Tag Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.4 Pressure Leak Rate Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.5 Vibration Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.6 Pneumatic Lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.7 Thermal Transpiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.8 System Calibration and Temperature Uncertainties . . . . . . . . . . . . . . . 47

4.2 CFD Pressure Distribution Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 Port Location Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.2 Grid Refinement and Topology, OML Design Cycle Changes . . . . . . . . . 48

4.2.3 Ablation and Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2.4 Gap Filler Protuberances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2.5 Orifice Induced Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

ii
4.2.6 Uncertainty Term Implementation . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 Error Analysis Results and Sensitivity Studies . . . . . . . . . . . . . . . . . . . . . . 52

5 Conclusions 56

Appendices 57

A Data Reduction Look-Up Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

B Error Analysis Sensitivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

References 80

iii
List of Figures

1.1 Vehicle Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 MEDLI/MEADS Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 MSL Entry, Descent, and Landing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 MSL Nominal Trajectory: Altitude and Mach Number . . . . . . . . . . . . . . . . . 5

1.5 MSL Nominal Trajectory: Dynamic Pressure and Aerodynamic Angles . . . . . . . . 6

2.1 MSL Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 CFD Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Comparison of Mach Number and Dynamic Pressure Along Different Trajectories . . 11

2.4 Variability in MEADS Port 1 Measurements due to Changes in Model Position . . . 13

2.5 Grid Lines and Mach Contours at Bow Shock for Unclustered and Clustered Grids . 13

3.1 Effect of In-Flight Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Temperature Set Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 09-HOL-01 Nominal Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Pressure Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Angle of Attack Error Budget Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 X-Axis Vibration Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.3 Y-Axis Vibration Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.4 Z-Axis Vibration Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.5 Port 5 Pressure: No Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.6 Port 5 Pressure: No Noise (Detail) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.7 Pressure Error Due to Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.8 Port 5 Pressure: 0.5% Full Scale Noise at Maximum Dynamic Pressure . . . . . . . . 32

4.9 Port 5 Pressure: 0.5% Full Scale Noise at Maximum Dynamic Pressure (Detail) . . . 33

4.10 Pressure Error Due to Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.11 Port 5 Pressure: 5% Full Scale Noise at Maximum Dynamic Pressure . . . . . . . . . 34

4.12 Port 5 Pressure: 5% Full Scale Noise at Maximum Dynamic Pressure (Detail) . . . . 34

4.13 Pressure Error Due to Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.14 Port 5 Power Spectral Density: No Noise . . . . . . . . . . . . . . . . . . . . . . . . 35

4.15 Port 5 Power Spectral Density: 0.5% Noise . . . . . . . . . . . . . . . . . . . . . . . 36

4.16 Port 5 Power Spectral Density: 5% Noise . . . . . . . . . . . . . . . . . . . . . . . . 36

4.17 Tube Response: Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.18 Tube Response: Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.19 Nominal Pressure Lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.20 Diameter Sensitivity: Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.21 Diameter Sensitivity: Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

iv
4.22 Port 5 Lag Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.23 Length Sensitivity: Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.24 Length Sensitivity: Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.25 Port 5 Lag Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.26 Thermal Transpiration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.27 Outer Mold Lines Described by Original (Grid a) and Refined (Grid b) CFD Grids . 48

4.28 Pressure Coefficient Disturbance vs. Relative Distance from a Step Discontinuity on

Nose Cap. Flow is From Left to Right. . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.29 Orifice Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.30 Pressure Measurement Errors Along Trajectory . . . . . . . . . . . . . . . . . . . . . 52

4.31 Total Estimation Error: Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.32 Total Estimation Error: Angle of Sideslip . . . . . . . . . . . . . . . . . . . . . . . . 54

4.33 Total Estimation Error: Dynamic Pressure . . . . . . . . . . . . . . . . . . . . . . . 54

B1 Estimation Errors due to Calibration Uncertainty . . . . . . . . . . . . . . . . . . . . 72

B2 Estimation Errors due to Transducer Temperature Uncertainty . . . . . . . . . . . . 73

B3 Estimation Errors due to Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . 73

B4 Estimation Errors due to SSE Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

B5 Estimation Errors due to SSE Temperature Uncertainty) . . . . . . . . . . . . . . . . 74

B6 Estimation Errors due to Port Location Uncertainty . . . . . . . . . . . . . . . . . . 75

B7 Estimation Errors due to Pressure Leak Uncertainty . . . . . . . . . . . . . . . . . . 75

B8 Estimation Errors due to Time Tag Uncertainty . . . . . . . . . . . . . . . . . . . . . 76

B9 Estimation Errors due to Pneumatic Lag Uncertainty . . . . . . . . . . . . . . . . . 76

B10 Estimation Errors due to Thermal Transpiration Uncertainty) . . . . . . . . . . . . . 77

B11 Estimation Errors due to Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

B12 Estimation Errors due to Ablation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

B13 Estimation Errors due to Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . 78

B14 Estimation Errors due to OML Change . . . . . . . . . . . . . . . . . . . . . . . . . 79

v
List of Tables

3.1 Port Assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Calibration Temperature Setpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Pressure Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.4 Flight Transducer Non-Repeatability/Hysteresis Uncertainties . . . . . . . . . . . . . 21

3.5 Flight Transducer Non-Repeatability/Hysteresis Uncertainties . . . . . . . . . . . . . 22

4.1 Vibration Errors, 1σ % Full Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2 Pressure Errors over Trajectory, 1σ % Full Scale . . . . . . . . . . . . . . . . . . . . 30

4.3 Response Model Conditions and Results . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4 Response Model Port Diameter Results . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.5 Response Model Tube Length Results . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.6 Gas Constants for Carbon Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.7 3σ ∆Cp Values for Uncertainty Terms Scaled Over the Trajectory Space . . . . . . . 52

4.8 Error Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.9 Trajectory Average Errors (3σ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

A1 Transducer 020 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 58

A2 Transducer 021 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 59

A3 Transducer 022 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A4 Transducer 023 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A5 Transducer 024 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 62

A6 Transducer 025 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A7 Transducer 026 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A8 Transducer 027 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A9 Transducer 029 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A10 Transducer 030 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A11 Transducer 031 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A12 Transducer 032 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A13 Transducer 034 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A14 Transducer 036 Data Reduction Table . . . . . . . . . . . . . . . . . . . . . . . . . . 71

vi
List of Symbols

as = Speed of sound, m/s

Ac = Tube cross-sectional area

a0, a1, a2 = Transducer calibration coefficients

b0, b1, b2, b0 = Knudsen model coefficients

c0, c1, c2 = Potter model coefficients

C = Sutherland constant

Cp = Pressure coefficient

D = Tube Diameter, in

d

+ = Orifice Reynolds number

F = Calibration coefficient matrix

H = Linearization of pressure distribution model

h = Pressure distribution model, Pa

I = Identity matrix

L = Tube length

Lmax = Maximum leak rate

M∞ = Mach number

P = State covariance

P0 = Input pressure (Laplace domain)

PL = Lagged pressure (Laplace domain)

p = Pressure, Pa

δp = Pressure error, Pa

pˆ = Adjusted pressure, Pa

p ̃ = Quantized pressure measurement, Pa

p ̄ = Saturated pressure measurement, Pa

p∞ = Static pressure, Pa

pt = Total pressure, Pa

p = Pressure measurement vector, Pa

q∞ = Dynamic pressure, Pa

R = Measurement covariance matrix

Rd = Acoustic impedance

Rg = Specific gas constant

R = Pressure ratio, R = p∞/pt

r = Length scale

S = Reference area, m2

s = Laplace variable

T = Gas temperature

T0 = Reference temperature

vii
T1 = Transducer temperature, C

T2 = SSE temperature, C

t = Time, s

V = Voltage

v = Transducer entrapped volume

x = Atmospheric state vector, x = [α, β, p∞, q∞]

T

y = Linearized residual

z = Calibration parameter array, z = [T1, T2, V, a0, a1, a2]

T

α = Angle of attack, rad

αT = Total angle of attack, rad

β = Angle of sideslip, rad

γ = Ratio of specific heats

 = Pressure measurement error vector, Pa

ζ = Lag model damping

ηp = Transducer measurement noise

κ = Knudsen number

λ = Mean free path

μ = Viscosity

μ0 = Reference viscosity

ξ = Calibration coefficient array, ξ = [a0, a1, a2]

T

ρ = Density, kg/m3

σ = Standard deviation

τ = Pneumatic lag time constant, s

τw = Shear stress

Ωz = Covariance of z

ωn = Lag model natural frequency, rad/s

viii
List of Acronyms

AFE = Aeroassist Flight Experiment

CFD = Computational Fluid Dynamics

DOE = Design of Experiments

EDL = Entry, Descent, and Landing

FADS = Flush Air Data System

IFZ = In-Flight Zero

IMU = Inertial Measurement Unit

LAURA = Langley Upwind Relaxation Algorithm

MEADS = Mars Entry Atmospheric Data System

MEDLI = MSL Entry, Descent, and Landing Instrumentation

MSL = Mars Science Laboratory

OML = Outer Mold Line

PICA = Phenolic Impregnated Carbon Ablator

SEADS = Shuttle Entry Air Data System

SSE = Sensor Support Electronics

TPS = Thermal Protection System

UPWT = Unitary Plan Wind Tunnel

ix
Chapter 1

Introduction

This report documents transducer calibration, system error modeling, pressure, pressure uncertainty models and system performance results and uncertainty quantification for the Mars Science

Laboratory (MSL) Mars Entry Atmospheric Data System (MEADS) [1, 2]. MEADS is a sevenport flush air data system (FADS) integrated with the 4.5 m diameter MSL aeroshell, the largest

aeroshell ever flown to Mars [3]. The Mars Science Laboratory entry vehicle was comprised of a

70 degree sphere-cone heatshield and backshell consisting of a stack of three truncated cones. The

forebody was similar to the heatshield geometry developed for the Viking Mars landers. Phenolic

Impregnated Carbon Ablator (PICA) was used for the Thermal Protection System (TPS) material. The backshell configuration was also similar to Viking, with a third cone section added to

accommodate the parachute volume. The MSL vehicle as-built outer mold line is shown in Fig. 1.1.

During most of entry, the capsule used a radial center of mass offset to fly at an angle of attack

(approximately 16 degrees at hypersonic conditions). This attitude produced lift to fly a guided

entry profile, reducing the landing footprint to a much smaller size than any previous Mars mission.

To fly the guided entry, the vehicle carried four pairs of reaction control system jets to perform

maneuvers and damp rates. The four pairs of jets could be fired rapidly in different combinations

to provide control torques about roll, pitch, yaw, or any other axis by modulating the pulses of the

jet.

The MSL heatshield differs from previous Mars mission designs in that the TPS is based upon

a tiled scheme, bonded directly to the aeroshell structure with a room temperature vulcanization

(RTV) sealant. Viewed exteriorly, MEADS surface pressure orifices are holes of approximately 2

mm diameter drilled directly through the PICA TPS tiles. Metallic spools through the carbon

fiber-on-aluminum honeycomb aeroshell structure complete the flowpath from surface orifice to

transducer tube as shown in Figure 1.2(a). MEADS therefore represents somewhat of a departure

from traditional aircraft FADS, or even the Shuttle Entry Air Data System (SEADS) [4–7], where

orifices are precisely machined to relatively small diameters in smooth metallic or nonablating

materials with negligible surface roughness. The MEADS ports are arranged in a cruciform pattern

over the heatshield windside (see Figure 1.2(b)), in locations where the boundary layer is predicted

to remain laminar and aeroheating is predicted to remain relatively low over the expected entry

trajectory [1]. All of the pressure ports are located a minimum of 3-inches from the PICA tile

seams.

Figure 1.3 shows a timeline of the different events along MSL’s entry, descent, and landing

(EDL) trajectory [8]. Note that the event times correspond to the nominal trajectory. Actual

times differed from the nominal event times due to dispersions in the entry time and atmospheric

uncertainties. EDL consists of six major segments: Exo-Atmospheric, Entry, Parachute Descent,

1
SR1134.11

Spacecraft Coordinate Frame

20°

2874.82

4518.16

1295.39 R12.7

R161.8

R134.88

R126.75

+x

+z

+y

22.09°

53.1°

34.43°

33.73°

31°

119° (543.3)

1407.3

924.21

BS-HS

Sep. Plane

BIP: SC z=0.0

.

Figure 1.1: Vehicle Geometry

(a) MEDLI/MEADS Tube Configuration (b) MEDLI/MEADS Pressure Port Locations

Figure 1.2: MEDLI/MEADS Geometry

Powered Descent, Sky Crane, and Fly Away [9]. The Exo-Atmospheric segment begins once the

cruise stage separation command is sent. Once the cruise stage separates, Guidance, Navigation,

2
and Control (GNC) is enabled. Once enabled, the entry body is despun and turned to its entry

attitude. Then, the two 75-kg Cruise Balance Masses (CBMs) are jettisoned to enable aerodynamic

lift.

(a) Cruise Stage Separation to Parachute Deployment (b) Parachute Deployment to Touchdown

Figure 1.3: MSL Entry, Descent, and Landing

The Entry segment starts with the vehicle at the Entry Interface Point (EIP) defined at 3522.2

km from the center of Mars, approximately 540 seconds after cruise stage separation. During the

Entry segment, the vehicle goes through peak heating and peak deceleration, the Reaction Control

System (RCS) controls the lift vector to achieve the desired down-range and cross-range target.

Just prior to parachute deployment, six 25-kg Entry Balance Masses (EBMs) are jettisoned to

eliminate lift and the vehicle rolls to point the Terminal Descent Sensor (TDS) to the ground. This

maneuver is called the Straighten Up and Fly Right (SUFR) maneuver. Figures 1.4 and 1.5 shows

the nominal trajectory over the time period from entry interface to parachute deployment.

The Parachute descent segment starts with the parachute deployment triggered once the vehicle

reached Mach 1.7. Once the vehicle achieves a speed of Mach 0.7, the heat shield is jettisoned and

the TDS starts acquiring the ground. Note that the MEDLI instruments are powered off 10 seconds

prior to heat shield jettison. The command to jettison the backshell and the parachute is issued at

an altitude of 1.6 km and at a velocity of approximately 79 m/s. Just before backshell separation,

the Mars Landing Engines (MLEs) are primed in preparation for the start of the powered descent

segment.

The Powered Descent segment begins at backshell separation. During powered descent, eight

independently throttleable MLEs are actuated, initially to execute a divert maneuver for backshell

avoidance which brings the vehicle to vertical flight at a descent rate of 32 m/s. Once vertical

flight is achieved, a descent at constant velocity to adjust for altitude error at backshell separation

starts. This constant velocity phase is followed by a constant deceleration phase, which reducs the

vehicle’s speed to 0.75 m/s in preparation for the sky crane segment. At this time, the four inboard

MLEs are throttled down to near shutdown (1%) while the four remaining MLEs were throttled

at 50%. The Sky Crane segment starts following issuance of the rover separation command, which

occurrs at an altitude of approximately 18.6 m. The rover is lowered to 7.5 m below the descent

stage. Then, the descent stage continues to descend until post-touchdown is detected.

The Fly Away segment starts after touchdown is sensed. Once the descent stage stops it’s

vertical motion, the bridle and electrical umbilical devices are cut and two of the MLE engines are

throttled up to 100% while the other two engines are at slightly less than 100%. This causes the

descent stage to pitch to 45 degrees. Once the turn maneuver is completed, all four engines are

3
throttled up to 100%. Constant thrust is applied to ensure the descent stage impacts the surface

at least 300 m from the landing point.

MEADS collects pressure data at a rate of 8 Hz over the portion of MSLs entry from atmospheric interface to 10 seconds before heatshield separation, the latter which occurs at a freestream

Mach number of approximately 1.5. As a basic objective, the MEADS hardware is intended to

be capable of furnishing data that, without any additional data sources, can be used to recover

aerodynamic angles and dynamic pressure. Accuracy to within 0.5 degrees in angle of attack and

sideslip are required over portions of the trajectory where freestream dynamic pressures exceed

1750 Pa and 1250 Pa, respectively. Dynamic pressure measurements are required to within 2%

where the freestream value exceeds 850 Pa. Used in combination with inertial measurement unit

(IMU) data and analyzed with Extended Kalman Filter (EKF) methods [10–14], MEADS data will

be used for post-flight reconstruction of vehicle attitude, dynamic pressure, Mach number, atmospheric density, and wind velocity [15]. As MSL is breaking new ground as the first tiled ablator

NASA has flown on an entry vehicle heatshield, MEADS is unique in its distinction as the first

heatshield-integrated FADS to be employed on an extraplanetary mission on an aeroshell larger

than and in an aerothermal environment more extreme than experienced in any previous Mars

mission [16].

This document describes how the uncertainties in the as-built MEADS hardware system and

pressure models contribute to the uncertainties in the reconstructed data. The remainder of this

document is organized as follows. Chapter 2 describes the basic MEADS data processing algorithm,

in which pressure measurements are used in conjunction with a model of the surface pressure

distribution (based on CFD models) to determine the freestream atmospheric conditions (dynamic

pressure, static pressure, angle of attack, and angle of sideslip) using a nonlinear least-squares

algorithm. Also in Chapter 2, the CFD pressure models are described along with some description

of experimental validation.

The MEADS pressure transducer calibration is described in Chapter 3. A basic overview of

the calibration methodology is described, and results from thermal vacuum testing are given along

with an uncertainty analysis. Chapter 4 describes hardware system error modeling and CFD

pressure distribution uncertainty models. These uncertainty models are then utilized in Chapter

4 to quantify how these uncertainties map to uncertainties in the reconstructed air data state.

Concluding remarks are given in Chapter 5.

4
550 600 650 700 750 800

0

20

40

60

80

100

120

140

Altitude [km]

Time [s]

(a) Altitude

550 600 650 700 750 800

0

5

10

15

20

25

30

Mach

Time [s]

(b) Mach

Figure 1.4: MSL Nominal Trajectory: Altitude and Mach Number

5
550 600 650 700 750 800

0

2

4

6

8

10

12

14

16

Dynamic Pressure [kPa]

Time [s]

(a) Dynamic Pressure

550 600 650 700 750 800

−35

−30

−25

−20

−15

−10

−5

0

5

Angle [deg]

Time [s]

Angle of Attack

Angle of Sideslip

Flight Path Angle

(b) Aerodynamic and Trajectory Angles

Figure 1.5: MSL Nominal Trajectory: Dynamic Pressure and Aerodynamic Angles

6
Chapter 2

Atmospheric State Estimation and

Surface Pressure Modeling

The basic MEADS atmospheric state estimation procedure is essentially similar to the Shuttle

Entry Air Data System (SEADS) state estimation described in [4], a point–wise least squares fit of

the surface pressure measurements to the modeled pressure distribution to determine minimum–

variance estimates of the atmospheric states. This algorithm requires a model of the surface pressure

distribution at each port location as a function of the free stream flight conditions. For MSL, this

model consists of tabulated CFD pressure solutions for a range of flight conditions that encapsulate

the expected trajectories. An uncertainty model of the pressure distribution and sensor hardware

is also required for appropriate weighting of the measurements in the least-squares algorithm.

The core of the MEADS pressure model is based on CFD predictions run at representative

nominal Mars entry conditions, while the pressure uncertainty model borrows from off-nominal

Mars entry CFD, wind tunnel experimentation, and CFD simulation of wind tunnel experiments.

Surface pressures are extracted from CFD solutions at the MEADS port locations, which are well

known from flight article laser scan metrology. Comparisons between experimental and numerical

results were to be used to validate computations and model estimates of error in CFD simulations

at flight conditions, however these results are beyond the scope of this report.

2.1 Least–Squares State Variable Estimation

By defining the atmospheric state vector as x = [α, β, q∞, p∞]

T

, p as the vector of N observed

surface pressures, and the pressure model as h(x, t) then the pressure measurement model can be

written compactly as

p = h (x, tk) +  (2.1)

where  is the vector of pressure measurement errors and tk is the measurement sampling time

at time increment k. Definition of the aerodynamic angles is shown in Figure 2.1. The pressure

measurement model can be approximated by means of the truncated series expansion

p ≈ h (x ̄, tk) + H(tk) (x − x ̄) +  (2.2)

where x ̄ is a reference state and H(tk) is the Jacobian matrix

H(tk) = 

∂h

∂x



x=x ̄

(2.3)

7
Figure 2.1: MSL Coordinate System

The problem can be reduced to that of a linear regression problem

y = Hx +  (2.4)

where y = p − h (x ̄, tk) + Hx ̄. By virtue of the Gauss–Markov theorem, the best linear unbiased

estimate of x is the weighted least-squares solution [17],

xˆ =



HT R−1H

−1

HT R−1y (2.5)

where R is the pressure measurement error covariance matrix. Since the original relationship

between the states and the measurement in Eq. (2.1) is nonlinear, the estimation scheme can be

iterated until convergence by successively replacing x ̄ by xˆ, using the converged state estimate

from the previous sampling time (tk−1) as the initial reference state x ̄. The state estimate error

8
covariance matrix Pˆ can then be computed from

Pˆ =



HT R−1H

−1

(2.6)

Note that the atmospheric state vector formulation is not unique. In particular, any two variables from the set of p∞, pt

, q∞, R, and M∞ can be used in the estimator in addition to α and β.

The remaining state variables not used directly in the estimator can be calculated as parameters,

having first estimated the atmospheric state variables. Note that the SEADS algorithm [4] made

use of p∞ and ptin the estimator formulation.

2.2 Nominal Flight CFD Pressure Modeling

The MEADS pressure model is built on CFD solutions from the MSL nominal aerodatabase, computed at points of interest along reference trajectory 05-22 as shown in Fig. 2.2(a). Computations

were carried out with the Langley Upwind Relaxation Algorithm (LAURA) code [18] using a twotemperature thermochemical nonequilibrium gas model representative of the Martian atmosphere

with a freestream composed of 97 percent CO2 and 3 percent N2 by mass. A representative

LAURA solution is shown in Fig. 2.2(b). A total of 8 species (CO2, CO, N2, O2, NO, C, N, O)

were allowable to model the chemical reactions which take place at energetic flow conditions [19].

A super-catalytic wall boundary condition was used, which imposes recombination of species to

freestream composition at the wall so as to yield conservative aeroheating predictions [20]. The vibrational temperature relaxation model of Camac [19] was used throughout, as it has been assumed

more accurate than the Millikan-White model [19], however analysis validating differences between

the models is beyond the scope of this work. Thin-layer Navier-Stokes (TLNS) equations were used

in the computations, a subset of the full Navier-Stokes equations which omits viscous cross terms

and thereby reduces the number of calculations required to converge a solution. Previous work had

shown that differences between solutions computed with the TLNS and full Navier-Stokes equations

were insignificant for the purpose of computing aerodynamics [19]. During a LAURA computation, grids are shock-fitted to the evolving solution with an iterative grid adaptation scheme which

maintains orthogonality and enforces Recell ∼ O(1) at the wall for aeroheating computations. Grid

adaptation cycles are repeated until integrated aerodynamic coefficients are constant to within

three significant figures, after which final numerical convergence is obtained using a line relaxation

algorithm [21]. The nominal aerodatabase runs were computed for the Outer Mold Line (OML)

on a 7-block volume grid with 0.23 million points. During design iterations leading up to the final

flight configuration (designated OML13-F), the flight TPS was changed from a monolithic ablator

design to tiled Phenolic Impregnated Carbon Ablator (PICA) design, changing OML proportions

slightly. Point check cases were run at nominal 05-22 trajectory conditions on a volume grid more

closely describing the flight article heatshield (MSL-OML13F-21806-clean-heatshield.g) with a total of 1.25 million points. Fig. 2.3(a) and (b) show comparisons between point check and nominal

aerodatabase CFD results are used to obtain an estimate of MEADS pressure sensitivity to changes

in the flight article OML, grid topology, and grid refinement.

Numerical solutions at off-nominal flight conditions were used to bound the expected ranges of

MEADS port environments and sensitivities. LAURA solutions from runs utilizing 09-TPS-01 and

-02 trajectory conditions were analyzed, as these particular trajectories were designed for stressing

TPS environments [22]. Cases with simulated gap filler protrusions along reference trajectory 08-

01A were queried for estimates of pressure augmentation factors in the vicinity of step discontinuities

in the heatshield surface. Comparisons between 05-22 and 09-TPS trajectories are shown against

9
(a) Nominal Flight αT and CFD Point Coverage

(b) Representative LAURA Solution

Figure 2.2: CFD Solutions

the current nominal trajectory 12-GAL-01, where t=0 is defined as the point of entry interface,

and curves are plotted over the portion of the trajectory where dynamic pressures exceed 850 Pa.

The CFD database pressures were nondimensionalized using the freestream pressure and dynamic pressure of each solution. The nondimensionalization transforms the forebody pressures into

10
(a) Mach Number

(b) Dynamic Pressure

Figure 2.3: Comparison of Mach Number and Dynamic Pressure Along Different

Trajectories

pressure coefficients, defined as Cp = (p − p∞)/q∞. Modeling the surface pressures in coefficient

form allows the CFD solutions to be used across a wide range of trajectories with different density

and velocity profiles. The data were re-interpolated from the 7 block grid to a single-zone grid of

11
clock and cone angles. This alteration simplifies the interpolation of surface conditions without

the complications of search routines required to handle multiple zones. Each CFD matrix point

consists of a full surface pressure distribution solution, with 37 clock angles in uniform 5 degree increments and 61 cone angles with non-uniform increments. These matrix points can be interpolated

as needed to provide estimates of the pressure distribution at any point on the aeroshell.

The nominal MEADS pressure model is a tabulation of the nondimensional pressure coefficient

Cp at each MEADS port mapped over (M, αT , φ) space, where all data are taken from nominal

Mars entry simulations along the 05-22 trajectory. The dimensionless form is used so that changes

in absolute surface pressure are scaled according to the freestream dynamic pressure for any desired

trajectory. The tables were constructed from LAURA results by extracting surface pressure coefficients from each (M,αT ) solution at the MEADS port locations, then rotating the solution about

the body axis by a roll angle increment and repeating as necessary to fill the desired (α,β) space. As

MSL’s absolute angle of sideslip is predicted not to exceed 1 degree during the portion of nominal

flight where freestream dynamic pressure exceeds 850 Pa, the tables have been constructed for each

(M, αT ) over the range −9 ≤ φ ≤ 9 in 3 degree increments, providing for more than adequate

coverage in β space. For nonlifting flight after balance mass jettison, the tables are constructed

over the entire roll angle range from −180 ≤ φ ≤ 180, using the same 3 degree increments in order

to cover the entire possible range of vehicle attitude. In addition to the surface pressure coefficient,

the magnitude of its gradient was also calculated using an internal Tecplot function and tabulated

for use in the pressure uncertainty model, where it is part of a port location uncertainty expression.

2.3 Experimentation and Simulation

Note that the pressure model utilized for atmospheric state estimation is based entirely on these

tabulated CFD solutions. The CFD modeling approach was validated in air in wind tunnel experiments at Mach numbers of 2.5, 3.5, 4.5, and 10. Residuals between computed and measured

pressures were within the measurement accuracy obtained in the wind tunnel experiments.

Wind-tunnel experiments were conducted in the NASA Langley Research Center (LaRC) Unitary Plan Wind Tunnel (UPWT) with a 6-inch diameter MSL pressure model at Mach numbers

from 2.5 to 4.5. Two tunnel entries were undertaken, one in 2010 and another in 2011. Test 1835

was the first UPWT entry and utilized a single model/sting configuration, whereas the second

entry, test 1855, utilized three model/sting configurations in an attempt to keep the model in the

same region of the test section regardless of angle of attack. Test 1855 data showed significant

variability in pressure measurements due to changes in the model location within the test section,

as shown in Fig. 2.4. Flow surveys show that the UPWT has nonuniform Mach number and flow

angularity throughout the test section, and that these changes can occur over length scales of the

same order as the wind tunnel model diameter [23]. A study of pressure error correction techniques

based on flow survey data were outside the scope of this work.

UPWT experiments were simulated with the LAURA code, using a calorically perfect gas model

with the properties of air. The CAD model from which the test article was made was used as the

surface definition for the computational volume grid, which was composed of 18 blocks and a total

of 0.77 million points. Cases were run over the angle of attack range 0 ≤ α ≤ 32 in 4 deg increments,

at nominal Mach 2.5, 3.5, and 4.5 UPWT conditions, all using a constant temperature (300 K)

viscous wall boundary condition. Grid points were clustered at the bow shock in order to improve

its placement and reduce its apparent thickness, or “smear,” as shown in Fig. 2.5.

Experimentation was carried out in the LaRC 31-inch Mach 10 tunnel using the same 6-inch

diameter model as was used in the UPWT experiments. Experimental results indicated that mea12
Figure 2.4: Variability in MEADS Port 1 Measurements due to Changes in Model

Position

(a) Unclustered (b) Clustered

Figure 2.5: Grid Lines and Mach Contours at Bow Shock for Unclustered and Clustered Grids

sured forebody pressures were extremely sensitive to the model’s location within the test section.

These data are not used in the pressure or uncertainty models, but are useful to illustrate some of

the difficulties and challenges associated with pressure model testing in hypersonic ground facilities, particularly when such experiments are carried out with the intent of validating computations.

Simulations of the Mach 10 experiments were conducted using the LAURA code, using the same

grids, models, and assumptions as the UPWT simulations.

13
Chapter 3

MEADS Transducer Calibration

A calibration of the MEADS fight system was conducted in order to compute input pressure as a

function of voltage and sensor/electronics temperature. The MEADS calibration program carries

two independent calibration efforts. The baseline approach utilizes the industry standard approach

that has a long heritage and is referred to as the traditional method by the MEADS project.

This method was used with great success by the SEADS program [5, 6] and other FADS programs

such as the Aeroassist Flight Experiment (AFE) [24]. The second approach is a proof-of-concept

experiment using a Design of Experiments (DOE) method. This calibration method has never

before been used to calibrate space fight transducers prior to the MEADS program. The DOE

approach is documented in [25, 26] and is not discussed further in this paper.

This chapter describes the calibration approach and the analysis of the final calibration data

using the traditional calibration/analysis approach. The final calibration of the transducers was

preceded by preliminary thermal testing and acceptance testing. This initial testing led to preliminary selection and rankings for both Flight and Flight Spare transducer sets. The result of this

ranking and port assignments are given in Table 3.1.

3.1 Calibration Methodology: General Overview

The traditional calibration approach as applied to a FADS type pressure measurement system is

composed of the collection of pressure transducer performance data and a data analysis process

originally developed in support of the SEADS experiment. This report briefly describes the calibration data collection process and a detailed description of the analysis methodology and assumptions

Table 3.1: Port Assignments

Port Flight Flight Spare

Serial Number Serial Number

1 022 026

2 025 020

3 029 031

4 021 030

5 032 027

6 023 034

7 024 036

14
using final transducer calibration data obtained by the traditional method.

The traditional method acquires a set of input pressure data vs. transducer output Voltage at

various temperatures to define transducer sensitivity (scale factor), non-linearity, and bias (zero

offset) as a function of temperature. The sensitivity and non-linearity data are collected by process

that uses an increasing/decreasing application of pressure over the operating range of the transducer. (In the case of MEADS from zero to 5.5psi.) The number of pressure set points can vary

depending on project requirements. Typically a total of 11-13 pressure points have proven to be

sufficient in previous applications. A series of pressure versus Voltage output data sets (curves)

are obtained at applicable operating temperatures to define the thermal sensitivity of the pressure

sensitivity and zero offset. The number of temperature set points can also vary. Typically five

temperature set points have proven to be adequate.

Other performance characteristics that are determined from the calibration data set are within

test repeatability and pressure/temperature hysteresis. Repeatability is defined here as the amount

of change of a measured reading at the same pressure and conditions over a series of pressure

cycles from zero to full-scale pressure and back to zero again. To ensure no pressure hysteresis is

introduced into repeatability measurements readings are always taken during an increase in pressure

or a decrease in pressure but never a mixture of the two in the implementation of the Traditional

method.

Typically, due to concerns related to the effect of long space missions where severe environments

and test requirements can impact transducer performance, multiple full thermal calibrations are

performed at different stages in the transducer acceptance and test process. These tests then allow

the quantification of any performance variations that might result from time, environment, testing,

and/or operation.

3.2 Implementation of Calibration Approach for MEADS

The MEADS mission and strain gauge pressure transducers configuration resulted in mission specific calibration requirements and a modified Traditional calibration approach. Due to MSL spacecraft constraints the transducer pressure head containing the strain gauge and the electronics were

separated and located in regions on the spacecraft with different thermal environments. Additionally, MEADS required that the transducer performance be maximized at the low-pressure end of

measurement range. As a result each transducer component - pressure head/strain gauge and electronics was calibrated as an independent variable. A thirteen point increasing/decreasing pressure

sequence with a concentration at the lower end of the pressure scale calibration was performed. The

final calibration matrix is shown in Table 3.2. Setpoints T2 - T6 are specific to the electronics while

T7 - T13 are specific to the pressure head strain gauge. Setpoints T11 - T 13 were incorporated to

provide test specific repeatability data due to previous indications relative to transducer thermal

repeatability and hysteresis. All temperature setpoints make use of the same pressure sequence,

given in Table 3.3.

Due to schedule constraints only one set of Traditional calibration data was collected for MEADS

thus the ability to assess and quantify repeatability as a function of time, environmental effects

and operation could not be accomplished.

15
Table 3.2: Calibration Temperature Setpoints

Setpoint Transducer SSE

Number Temperature (deg C) Temperature (deg C)

T1 20 20

T2 -80 60

T3 -80 30

T4 -80 0

T5 -80 -20

T6 -80 -30

T7 -50 0

T8 -80 0

T9 -100 0

T10 -125 0

T11 -100 0

T12 -80 0

T13 -50 0

T14 20 20

Table 3.3: Pressure Sequence

Sequence Number Pressure (psi)

1 0.00

2 0.25

3 0.50

4 1.00

5 2.00

6 3.30

7 4.50

8 5.50

9 3.90

10 2.50

11 1.50

12 0.75

13 0.00

16
3.3 Calibration Analysis: Methodology and Assumptions

The traditional calibration method uses a least-squares fit for each transducer to a model of the

form [6]

p = a0 (T1, T2) + a1 (T1, T2) V + a2 (T1, T2) V

2

(3.1)

where T1 is the pressure transducer temperature, T2 is the SSE temperature, V is the Voltage

output, and p is the pressure. The coefficients a0, a1, and a2 are termed the bias, sensitivity, and

non-linearity, respectively. These coefficients are determined from a least-squares fit of pressure

vs. Voltage at specific temperature setpoints using a simple increasing/decreasing applied pressure

to create the Voltage response. By varying the temperature setpoints, a database of calibration

coefficients can be constructed, and an empirical model developed that uses spline interpolation to

look up the values of these coefficients and functions of the two temperatures.

The specific calculations performed at each temperature setpoint is provided in the following.

First, the matrix F is defined as

F =







1 V1 V

2

1

.

.

.

.

.

.

.

.

.

1 Vn V

2

n





 (3.2)

where n is the total number of pressure points at each temperature setpoint. Similarly, the array

of pressure measurements is written as

p =

h

p1 · · · pn

iT

(3.3)

The coefficient array is written as ξ =

h

a0 a1 a2

iT

. The least-squares estimate of the

coefficient array is given by

ˆξ =



F

TF

−1

F

T p (3.4)

An important byproduct of the least-squares solution is the covariance matrix of the coefficient

estimate, given by

Cov 

ˆξ



= σ

2

c



F

TF

−1

(3.5)

where σc is the Mensor pressure controller accuracy. Along with the values of the calibration

coefficient, the uncertainties in the coefficients are also stored as a function of the two temperatures.

These uncertainties can be used to build a calibration error model to assess system performance.

The total system uncertainty model from the calibration also needs to consider the temperature

uncertainties and hysteresis. To this end, define

z =

h

T1 T2 V a0 a1 a2

iT

(3.6)

It follows from a linear covariance transformation that the total pressure prediction error variance is given by

σ

2

p =



∂p

∂z



Ωz



∂p

∂z

T

+  ̃σ

2

a0 +  ̃σ

2

a1

V

2 +  ̃σ2

a2

V

4

(3.7)

where

Ωz =











σ

2

T1

0 0 0

0 σ

2

T2

0 0

0 0 σ

2

V 0

0 0 0 Cov (xˆ)











(3.8)

17
The quantities  ̃σ

2

a0

,  ̃σ

2

a1

, and  ̃σ

2

a2

account for non-repeatability and hysteresis in the bias, sensitivity, and nonlinearity coefficients in the calibration equation, respectively. These contributions to

the uncertainty model are computed from repeated points in the calibration temperature setpoints.

In summary, the uncertainty predictions include non-repeatability/hysteresis, calibration error,

temperature error, and Voltage error/noise. Note that in this model the temperature uncertainty

due to thermocouple bias and noise are lumped together into the total temperature uncertainty.

The in-flight zero obtained prior to Mars entry has the effect of significantly reducing the

uncertainties in the pressure data. Essentially, the in-flight zero nearly removes the uncertainties

due to bias, but the slope and nonlinearity uncertainties remain, and a small residual bias error

remains due to the slope of the bias curve as a function of temperature, coupled with temperature

uncertainty and noise. An example of the effect of the in-flight zero is shown in Figure 3.1 based on

data from Transducer 022 at temperature setpoint T4 (Transducer temperature -82.9 C and SSE

temperature 9.7 C). Figure 3.1(a) shows the pressure vs. Voltage curve from the calibration data

for the (true) Mensor controller pressure and the estimates pressure with and without the in-flight

zero applied. On this scale, the transducer behaves very linearly with a small correction / bias shift

due to the in-flight zero. Figure 3.1(b) shows the pressure error with and without the correction.

On this scale, a hysteresis loop and the bias correction due to the in-flight zero can be observed.

To develop an uncertainty model, let T

∗

1

and T

∗

2 be the transducer and SSE temperatures,

respectively, and V

∗ be the measured Voltage at the time of the in-flight zero prior to atmospheric

entry. Then the pressure error is

δp = a0 (T

∗

1

, T∗

2

) + a1 (T

∗

1

, T∗

2

) V

∗ + a2 (T∗

1

, T∗

2

) (V

∗

)

2

(3.9)

It follows that the adjusted pressure is given by

pˆ = p − δp (3.10)

By substituting Eq. (3.9) into Eq. (3.10) and linearizing for small temperature errors, the

pressure measurement uncertainty model following the in-flight zero is given by

σ

2

p =



∂a0

∂T1

2

σ

2

n1 +



∂a0

∂T2

2

σ

2

n2 +

"

σ

2

a1 +  ̃σ

2

a1 +



∂a1

∂T1

2



σ

2

b1 + σ

2

n1



+



∂a1

∂T2

2



σ

2

b2 + σ

2

n2



#

V

2

+

"

σ

2

a2 +  ̃σ

2

a2 +



∂a2

∂T1

2



σ

2

b1 + σ

2

n1



+



∂a2

∂T2

2



σ

2

b2 + σ

2

n2



#

V

4

(3.11)

where σn1

, σb1, σn2

, and σb2

are the thermocouple noise and bias uncertainties for temperature

measurements T1 and T2, respectively.

3.4 Analysis of Final Calibration Data

Data from the final calibration of the MEADS/SSE system were analyzed according to the methodology described in the preceding section. The traditional data points collected during the calibration

are shown in Table 3.2. The desired vs. actual temperature setpoints acquired in the calibration

are shown in Fig. 3.2 for the Flight and Flight Spare calibrations. Additional data were collected

for the DOE calibration, which included several “pressure profiles” that attempt to simulate the

pressures during Mars entry. No data were excluded from these datasets, although the ambient test

points were analyzed but are not incorporated into the flight data reduction database since these

points are not within the flight temperature space. No other data was utilized for the purposes of

this calibration report, including ambient performance tests and acceptance testing data.

18
(a) Pressure

(b) Pressure Error

Figure 3.1: Effect of In-Flight Zero

Recall that replications are made involving temperature setpoints (T1,T14) at ambient, (T4,

T8, T12) at -80/0, (T7, T13) at -50/0 and (T9, T11) at -100/0. These replications allow the

repeatability and hysteresis of the transducer to be evaluated. Both the Flight and Flight Spare

19
(a) Flight System

(b) Flight Spare System

Figure 3.2: Temperature Set Points

transducers make use of the same temperature set points in order to enable direct comparisons

between both systems.

The non-repeatability/hysteresis uncertainties were calculated from the repeated temperature

20
Table 3.4: Flight Transducer Non-Repeatability/Hysteresis Uncertainties

Transducer  ̃σ0 Bias  ̃σ1 Sensitivity  ̃σ2 Nonlinearity Within Temp. Between Temp.

Serial Uncertainty Uncertainty Uncertainty Repeatability Repeatability

Number [% FS] [% FS/mV] [% FS/mV2] [% FS] [% FS]

020 0.348 7.98e-3 4.12e-4 0.051 0.347

021 0.838 1.06e-2 6.12e-4 0.060 0.735

022 1.233 7.38e-3 5.81e-4 0.060 1.078

023 0.658 5.04e-3 4.91e-4 0.067 0.573

024 0.470 3.62e-3 3.03e-4 0.042 0.414

025 0.769 8.87e-3 4.03e-4 0.065 0.684

026 0.407 7.50e-3 4.16e-4 0.048 0.407

027 0.225 9.31e-3 6.11e-4 0.042 0.225

029 0.914 5.79e-3 3.50e-4 0.059 0.801

030 0.633 8.23e-3 4.83e-4 0.071 0.613

031 0.428 8.48e-3 6.11e-4 0.064 0.416

032 0.619 9.96e-3 6.75e-4 0.054 0.545

034 0.937 3.35e-2 3.01e-3 0.046 0.960

036 0.945 1.25e-2 9.25e-4 0.040 0.956

setpoints listed above. The results for the transducers are shown in Table 3.4. This table shows

the 1-σ uncertainties in the calibration equation coefficients used in the uncertainty modeling,

with pressure units in percent full scale. It is possible to generate rankings based on any of these

uncertainties, but it is not recommended, since the total system uncertainty is a preferable metric

as it includes all uncertainty sources together. However, several interesting observations can be

made about this data. Namely, transducer 024 has the lowest uncertainty in all three coefficients

among the Flight set. Many transducers from the Flight Spares set (020, 026, 027, and 031) have

slightly better bias uncertainty than 024, but 024 exhibits the best sensitivity and nonlinearity

uncertainty among all transducers. Transducer 034 is an outlier in the sense that its sensitivity

and nonlinearity uncertainties are an order of magnitude larger than all other transducers. Also

shown in these tables are the Within and Between Temperature Repeatability uncertainties. These

uncertainties are utilized by the DOE method and are shown here simply for comparison purposes.

Details on how these uncertainties are calculated can be found in [27]. Interestingly, the between

temperature repeatability trends correlate with the bias uncertainties.

The quadratic calibration equation coefficients were calculated from the least-squares fit to the

pressure/Voltage data across all temperature setpoints in the region of interest to flight data reduction (i.e. T2-T13). Next, the repeated points were averaged together and extrapolations were

conducted, treating the transducer temperature and SSE temperature as independent variables, to

create data tables suitable for 2-Dimensional look-up routines to determine the pressure as a function of Voltage, transducer temperature, and SSE temperature. The look-up tables are tabulated

in Appendix A. For the results described in this document, the Matlab-based griddata routine was

utilized to perform the look-ups, using the cubic interpolation method. The linearizations required

for calculating the uncertainty estimates are computed using a centered divided difference method

with 0.5 deg C temperature perturbations.

The resulting calibration model was utilized to predict the DOE and Pressure Profile data (with

and without the simulated in-flight zero) to asses performance of the model itself as well as the

21
Table 3.5: Flight Transducer Non-Repeatability/Hysteresis Uncertainties

Transducer DOE DOE Profile Profile Profile Profile

Serial Actual Predicted Actual Predicted Actual Predicted

Number RMS Error RMS Error RMS Error RMS Error RMS Error RMS Error

[% FS] [% FS] [% FS] [% FS] [% FS] [% FS]

020 0.385 0.408 0.217 0.404 0.214 0.080

021 0.928 0.805 0.841 0.801 0.229 0.074

022 1.326 1.200 1.316 1.197 0.245 0.067

023 0.660 0.655 0.600 0.654 0.138 0.085

024 0.460 0.459 0.392 0.458 0.110 0.045

025 0.816 0.756 0.750 0.754 0.175 0.045

026 0.705 0.497 0.174 0.497 0.182 0.066

027 0.251 0.266 0.252 0.263 0.194 0.087

029 0.962 0.891 1.008 0.890 0.173 0.079

030 0.630 0.708 0.414 0.707 0.302 0.042

031 0.356 0.470 0.279 0.465 0.196 0.076

032 0.680 0.610 0.677 0.606 0.171 0.049

034 1.277 1.055 0.704 1.038 0.667 0.102

036 0.884 1.039 0.624 1.037 0.467 0.057

uncertainty predictions based on the linear covariance transformations. The results are tabulated

in Table 3.5. These results show that the predicted uncertainties agree with the actual uncertainties

reasonably well. The in-flight zero uncertainty predictions do not match as well as the other cases,

but this difference could be due to how the profiles were executed during the calibration. Further

analysis is required to show this is the case.

Based on these results it is possible to generate rankings of transducer performances based on

the in-flight zero results, which are the most representative of actual system performance. Sorted

in ascending order, the recommended flight system ranking is 024, 023, 032, 029, 025, 021, and

lastly 022. Since the best two transducers are currently assigned to ports 6 and 7, recommendations

were made to re-order the port assignments in order to improve the dynamic pressure and angle of

attack performance. Due to schedule constraints it was not possible to do so.

3.5 Uncertainty Analysis

An analysis of uncertainties from the final calibration data was conducted to examine transducer

performance relative to system requirements of 0.5% accuracy of pressure reading. The analysis

described in this section is based on the 09-HOL-01 nominal trajectory. The nominal port pressures along this trajectory are shown in Figure 3.3. The 850 Pa dynamic pressure boundaries are

indicated, as well as the 5 psi full scale pressure threshold.

The calibration uncertainties along the reference trajectory are shown in Figure 3.4. Note that

the error uncertainties are shown as a percent of reading. These uncertainties include the transducer

calibration uncertainties alone, with all other error sources ignored and the in-flight zero applied.

The errors are based on the 09-HOL-01 nominal trajectory. These curves have been generated

using the expression for the error variance given in Section 3.3 with appropriate terms set to zero.

22
Figure 3.3: 09-HOL-01 Nominal Pressures

The reduced expression is

σ

2

p =



σ

2

a1 +  ̃σ

2

a1



V

2 +



σ

2

a2 +  ̃σ

2

a2



V

4

(3.12)

The error transformed into percent of reading is simply

%Error =



σp

p



× 100 (3.13)

The uncertainty reduces to a constant value at zero pressure due to the limit being a ratio of

two slopes. To a first-order approximation (equating 10 mV to 5 psi), an expression for the error

as a function of pressure is

∆p = 1p + 2p

2

(3.14)

where 1 = 2∆a1 and 2 = 4∆a2. The percent error reduces to

%Error =



σp

p



× 100 = (1 + 2) × 100 = 1001 + 1002p (3.15)

This result indicates that the percent error is a linear function of pressure, reaching a constant

value at zero pressure and maximum value at peak pressure. Note that the percent error results

are less than 0.5% for all transducers except 034 and 036. Transducer 036 has less than 0.5% error

over most of the trajectory but exceeds slightly during the peak dynamic pressure regime. All other

transducers meet the requirement of less than 0.5% error over the entire trajectory.

23
(a) Flight System

(b) Flight Spare System

Figure 3.4: Pressure Errors

24
Chapter 4

Uncertainty Modeling

At the MEDLI project outset, no top-down error budget was formulated to determine the hardware

requirements. To meet the available schedule at the time, analysis or engineering judgment was

used to identify the sources of error that were both (1) expected to contribute significantly to

errors in the returned data, and (2) controllable through manufacturing. The MEADS Level 4

requirements were written to minimize uncertainties in the final data return. The hardware was

then produced, calibrated, and integrated to the Level 4 requirements.

In parallel with MEADS hardware development, an error allocation was devised for the angle of

attack and angle of sideslip data products. This error budget hierarchy is shown in Figure 4.1. The

Level 2 requirement for angle of attack knowledge (PS-372) is +/- 0.5 degrees 3-sigma, shown in the

top box of the hierarchy. The contributors to the uncertainty come from the transducer assembly,

the Sensor Support Electronics, the Aeroshell manufacturing, and the system time latency. Each

box lists the uncertainty requirement on that specific contributor, or the as-built value achieved,

if applicable, and the error in angle of attack that results from that uncertainty. The following

sections explain the analysis that produced these results.

The hierarchy for the angle of sideslip is identical except for the pressure transducer contribution

to the errors; each of the seven transducers is unique, and sideslip takes advantage of the two ports

and transducers that are symmetric about the vehicle centerline.

The impact of individual error sources and the effects of selected failure modes are examined

in this chapter. These error sources include port location knowledge, sensor noise and quantization, telemetry time stamp errors, pneumatic lag, thermal transpiration, and system calibration

uncertainties. Errors due to CFD pressure distribution uncertainties are also described in this chapter. The associated error models are reviewed in the following sections before showing sensitivity

simulation results and the overall error budget results compared to the project requirements.

25
Figure 4.1: Angle of Attack Error Budget Hierarchy

4.1 Hardware System Error Models

4.1.1 Port Location Uncertainties

Errors in the knowledge of the port location after installation are cast as random longitudinal

perturbations at constant clock angle and a random tangential perturbation at constant cone angle.

The errors are specified as uncorrelated zero-mean Gaussian random numbers. The measurement

system is accurate to within 0.04.

4.1.2 Sensor Noise and Quantization

Sensor noise is modeled using the equation

δp = (pmax − pmin) ηp (4.1)

where pmax and pmin are the maximum and minimum pressure range of the sensor system, respectively. The variable ηp is a uniform random variable between ±N/2

n where N is the number of

counts of noise and n is the system effective bit size.

26
Sensor quantization can be modeled using the equation

p ̃ =



pmax − pmin

2

n



Int  p

pmax − pmin 

2

n



(4.2)

Finally, sensor saturation can be modeled as  ̄p = max [min ( ̃p, pmin), pmax].

4.1.3 Time Tag Error

Relative errors in the telemetry time stamp between measurements at different port locations

introduces a distortion effect that corrupts the pressures used as input to the basic data reduction

algorithm. Timing errors include both random and systematic components. The systematic timing

errors can the adjusted in pre-processing of the flight data, leaving only the random error to be

considered in error budgeting. These errors are simulated by first casting a uniform random number

for each port in the range of ±25μs, and then shifting the truth state used to calculate the measured

surface pressures.

4.1.4 Pressure Leak Rate Error

The MEADS pressure transducers cannot be tested with applied pressure once they are mounted on

the MSL aeroshell, since contact with the PICA thermal protection system material is prohibited.

Therefore, the project developed and tested an installation process that minimizes leaks along the

pressure path. Pressure leak analysis is described in 28, 29.

Pressure system leaks can be modeled as a multiplicative loss on the measured pressure at the

transducer relative to the port pressure. Since pressure leaks are a one-sided distribution, the errors

can be reformulated as a two-sided distribution with half the total error by adjusting the pressure

up, assuming the mean value of the leak rate. The adjusted pressure measurement is given by

pˆ =



1 +

Lmax

2



p (4.3)

where Lmax is the maximum expected leak rate, assuming that the leak rate is uniformly distributed.

Following this adjustment, the pressure leak errors are uniformly distributed in the interval

` ∈ U −

Lmax

2

,

Lmax

2



(4.4)

It then follows that the simulated pressure errors due to leaks are given by

pˆ = (1 + `) p (4.5)

4.1.5 Vibration Error

Tests were performed to assess pressure error due to vibration during EDL. The tests were performed

with 4 MEADS transducers (S/N 002, 028, 033, and 035) at 1.33 grms vibration conditions during

a simulated pressure profile. Three vibration tests were performed for each axis of the transducer,

where the y-axis test is directed along the pressure path. The measured transducer outputs from

these tests are shown in Figures 4.2–4.4.

The noise due to vibration was then estimated from this test data. First, an “in-flight” zero was

applied to the data to remove bias, and then residuals were computed between the true pressure

and the measured pressure. These residuals were filtered using 1 Hz optimal Fourier filter. The

27
Figure 4.2: X-Axis Vibration Test Data

Table 4.1: Vibration Errors, 1σ % Full Scale

Transducer Axis Stationary Noise Unfiltered Error Filtered Error

P1 X 0.0135 2.5576 1.245

P2 X 0.0097 2.7153 1.2752

P3 X 0.0124 3.8236 1.7622

P4 X 0.0104 3.3704 1.6166

P1 Y 0.0102 3.8372 1.8969

P2 Y 0.0072 10.029 4.4757

P3 Y 0.0089 3.3062 1.559

P4 Y 0.0076 5.2139 2.5568

P1 Z 0.0167 0.4979 0.3481

P2 Z 0.0346 0.6368 0.3618

P3 Z 0.0143 0.4401 0.3044

P4 Z 0.0174 0.4994 0.3291

errors due to vibration were then computed from these filtered residuals. Error statistics from these

residuals are shown in Table 4.1.

From these results, an uncertainty model of the form

σnoise =

q

qmax

q

σ

2

vibe − σ

2

0

(4.6)

is introduced, where σvibe is the total measured error, σ0 is the stationary noise uncertainty, and

28
Figure 4.3: Y-Axis Vibration Test Data

σnoise is the noise uncertainty due solely to vibration. The vibrational noise term is then scaled by

the ratio of instantaneous dynamic pressure to the maximum dynamic pressure.

Next, a study of this noise model for different filtering frequencies was conducted. First, the

errors introduced by filtering perfect data was studied. A 1 Hz filter and a 0.1 Hz filter were

applied to the data. In this case, some true high frequency vehicle dynamics are removed by low

pass filtering. This behavior is illustrated for the Port 5 pressure in Figure 4.5. Figure 4.5 shows

the entire pressure profile, Figure 4.6 shows a detail view of the pressure at maximum dynamic

pressure. Here it can be seen that the 0.1 Hz filter effectively removed all rigid body dynamics of

the vehicle. Figure 4.7 shows the errors in pressure that arise due to filtering the truth data.

Figures 4.8 and 4.9 show a similar set of results for the case with 0.5% (of full scale) measurement noise at peak dynamic pressure. Figure4.10 shows the errors between unfiltered and filtered

pressures at 1 and 0.1 Hz. Here, the 0.1 Hz filter has large errors because it has filtered the rigid

body dynamics. The 1 Hz filter produces lower errors because it filters some of the noise while

retaining the rigid body motion of the capsule oscillations.

A more stressful case is shown in Figure 4.11–4.13, in which the vibrational noise is set to 5% of

the full scale pressure at peak dynamic pressure. In this case, the noise is large enough in amplitude

that it dominates over the capsule’s rigid body motions. As a result, the 0.1 Hz filter produces

a better estimate of the true pressure. The results of these three experiments are summarized in

Table 4.2, which show the 1-σ pressure errors over the entire trajectory for each case. These results

indicate that the choice of filter cutoff frequency should be guided by the expected vibration noise

environment. This is further illustrated in Figures 4.14–??, which shows power spectral densities

for each of the three test cases, and for unfiltered, 1 Hz filter, and 0.1 Hz filter data. From these

plots, it can clearly be seen that the vibration noise dominates over the rigid body modes as the

29
Figure 4.4: Z-Axis Vibration Test Data

noise level increases. Given these results and the expected noise environment based on vibration

tests, the 1 Hz filter is recommended for use on MEADS data reduction.

Table 4.2: Pressure Errors over Trajectory, 1σ % Full Scale

No Noise 0.5% FS Noise 5.0% FS Noise

Unfiltered 0.0 0.1596 1.5817

1 Hz filter 0.0471 0.0932 0.7289

0.1 Hz filter 0.1172 0.1193 0.2026

30
Figure 4.5: Port 5 Pressure: No Noise

Figure 4.6: Port 5 Pressure: No Noise (Detail)

31
Figure 4.7: Pressure Error Due to Filtering

Figure 4.8: Port 5 Pressure: 0.5% Full Scale Noise at Maximum Dynamic Pressure

32
Figure 4.9: Port 5 Pressure: 0.5% Full Scale Noise at Maximum Dynamic Pressure

(Detail)

Figure 4.10: Pressure Error Due to Filtering

33
Figure 4.11: Port 5 Pressure: 5% Full Scale Noise at Maximum Dynamic Pressure

Figure 4.12: Port 5 Pressure: 5% Full Scale Noise at Maximum Dynamic Pressure

(Detail)

34
Figure 4.13: Pressure Error Due to Filtering

Figure 4.14: Port 5 Power Spectral Density: No Noise

35
Figure 4.15: Port 5 Power Spectral Density: 0.5% Noise

Figure 4.16: Port 5 Power Spectral Density: 5% Noise

36
4.1.6 Pneumatic Lag

The MEADS system response model, or lag model, captures the dynamics of the pressure measurement from the surface port location to the pressure transducer (the sensor). In general, these

characteristics are a function of the line properties (tube diameter and length), fluid properties

(density, dynamic viscosity, etc.), as well as flight conditions (pressure and temperature at the

port and temperature at the transducer). The system response models are used to accomplish

two objectives: firstly, to accurately model the response so that pre-flight simulation can be used

to assess hardware, algorithms, and telemetry rates, and secondly, to characterize the system response so that measured pressures can be corrected to actual surface pressures for use in generating

atmospheric data estimates.

High–fidelity response models based on the Navier–Stokes equations are available in the literature, in particular the infinite–order frequency–domain Bergh–Tijdeman response model [30] and

variations on this model for branched systems developed by Whitmore [31]. In these models, the

pneumatic system is broken up into a series of segments, each with constant line and fluid properties. The end to end frequency response from port to transducer becomes the product of the

individual response functions for each segment. Entrapped volume in any of the segments can also

be captured. In this manner changes in tubing diameter as well as temperature gradients can be

explicitly modeled. The response is evaluated across a range of input frequencies and the result is

a complex frequency response that can be represented as magnitude and phase.

The frequency domain results for each flight condition are not readily suited either for time

domain simulation or for direct analysis of time histories of measured pressure. For these purposes,

a low–order response model must be utilized. For simple 2nd order systems, this response can be

characterized by a natural frequency and damping, with transfer functions of the form

PL

P0

=

ω

2

n

s

2 + 2ζωn + ω2

n

(4.7)

where P0 is the applied pressure, PL is the lagged pressure, and ζ and ωn are the damping ratio

and natural frequency, respectively, and s is the Laplace variable.

A variety of 2nd order models based on simplified fluid mechanics relations are available in the

literature with varying assumptions and classifications [32]. A new 2nd order response model based

on first principles is presented in [32]. This model is derived directly from the Bergh–Tijdeman

equations using order reduction techniques and was found to be more accurate than other 2nd order

models. The natural frequency and damping coefficients of this model are

ω

2

n =

Aca

2

s/Lv

(LAc/2v)

h

1 + (1/12) (γLRd)

2

/ (asρ0)

2

i

+ 1 + (1/6) (γLRd)

2

/ (asρ0)

2

(4.8)

ζ =

ωn

2



γRd

ρ0

 "

vL

Aca

2

s

+

1

2



L

as

2

#

(4.9)

where L is the tube length, Ac is the cross-sectional area, v is the transducer entrapped volume,

ρ0 is the fluid density in the tube, c is the speed of sound, and γ is the ratio of specific heats. The

parameter Rd is known as the acoustic impedance and can be calculated as a function of Reynolds

number to capture laminar, transitional, or turbulent flow conditions, as described in [32].

Another approach to time domain analysis is look for a low-order system that matches the model

response. This assumed form of this equivalent system is chosen to capture the modeled dynamics

and to facilitate efficient simulation. Numerical optimization techniques have been utilized to fit

transfer function models to the high-fidelity frequency response model, including up to 4th order

37
systems with pure time delay. These results were not found to significantly improve the 2nd order

model and thus were not used to model lags for MEADS error analysis.

Due to computational complexities of simulating the tube and transducer response, these models

were employed in a stand–alone manner in order to assess impacts to system performance. These

studies include both the high–fidelity frequency domain models suitable for analyzing specific flight

conditions as well as 2nd–order approximate models suitable for analyzing time histories.

The first study is an assessment of the port diameter of 0.1 in. Three flight conditions were

explored using the high–fidelity frequency response model, including a high Mach/low pressure

case, the maximum pressure case, and a low Mach/low pressure case. The frequency response for

these three conditions are shown in Fig. 4.17 and 4.18. The frequency response of the 2nd order

model is also shown for comparison. Table 4.3 shows several important metrics of the frequency

response for these three flight conditions. Here, the time constant and the time delay (computed

from phase loss at 1 Hz frequency) are shown corresponding to the high–fidelity (HF) model as well

as the 2nd order model. While differences are apparent between the HF and 2nd order models, the

trends and orders of magnitude are similar. These results agree to within a factor of 2 or better with

an independent implementation using a reduced–order Bergh–Tijdeman model described in [33].

These results indicate that the response time is acceptable even for the worst–case lag time at the

low Mach, low pressure condition.

100101102103

−40

−30

−20

−10

0

10

20

Frequency [Hz]

Magnitude [db]

Case 1 (High−Fidelity)

Case 1 (2nd Order)

Case 2 (High−Fidelity)

Case 2 (2nd Order)

Case 3 (High−Fidelity)

Case 3 (2nd Order)

Figure 4.17: Tube Response: Magnitude

A time history of the pressure difference computed using the 2nd order model is shown in

Fig. 4.19. If the input signal is of sufficiently low frequency content, then these lag effects are

completely deterministic in nature and can effectively be corrected for by inverting the transfer

function to solve for the pressure signal at the port. Assuming no model uncertainties, then the

lag effects can be corrected without error. However, errors can arise due to the presence of tube

38
100

101102103

−800

−700

−600

−500

−400

−300

−200

−100

0

Frequency [Hz]

Phase [deg]

Case 1 (High−Fidelity)

Case 1 (2nd Order)

Case 2 (High−Fidelity)

Case 2 (2nd Order)

Case 3 (High−Fidelity)

Case 3 (2nd Order)

Figure 4.18: Tube Response: Phase

Table 4.3: Response Model Conditions and Results

Condition M∞ q∞, Pa P, Pa τ , sec (HF) τ , sec (2nd) ∆t, sec (HF) ∆t, sec (2nd)

1 (High Mach) 29.0 850.0 1630.0 0.34·10−3 0.72·10−3 0.70·10−3 0.75·10−3

2 (Max q∞) 16.8 14015.3 26788.5 0.45·10−3 0.33·10−3 0.55·10−3 0.14·10−3

3 (Low Mach) 3.1 850.0 1595.7 1.31·10−3 0.78·10−3 2.01·10−3 1.09·10−3

geometry uncertainties. Therefore it is of interest to understand the sensitivities to diameter and

length uncertainties.

Table 4.4: Response Model Port Diameter Results

Port Diameter, in τ , sec (HF) τ , sec (2nd) ∆t, sec (HF) ∆t, sec (2nd)

0.07 6.13·10−3 0.86·10−3 6.61·10−3 1.21·10−3

0.04 5.69·10−2 0.96·10−3 5.49·10−2 1.36·10−3

0.02 2.62 1.04·10−3 0.22 1.47·10−3

Table 4.4 shows the results of a study varying the port diameter for the worst–case flight

condition (low pressure, low Mach) discussed above. Here, the port diameter is varied to as low

as 0.02 in. These results indicate that the 0.07 in case may be acceptable but the 0.04 in case

and below quickly become unacceptable. Figures 4.20 and 4.21 show the frequency response of the

high-fidelity and 2nd-order models for these port diameters. Discrepancies between the HF and 2nd

39
25 20 15 10 5

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Mach [q

∞

 > 850 Pa]

∆ Pressure [% Reading]

Port 1

Port 2

Port 3

Port 4

Port 5

Port 6

Port 7

Figure 4.19: Nominal Pressure Lab

100101102103

−80

−70

−60

−50

−40

−30

−20

−10

0

10

Frequency [Hz]

Magnitude [db]

D=0.07in (High−Fidelity)

D=0.07in (2nd Order)

D=0.04in (High−Fidelity)

D=0.04in (2nd Order)

D=0.02in (High−Fidelity)

D=0.02in (2nd Order)

Figure 4.20: Diameter Sensitivity: Magnitude

40
100

101102103

−800

−700

−600

−500

−400

−300

−200

−100

0

Frequency [Hz]

Phase [deg]

D=0.07in (High−Fidelity)

D=0.07in (2nd Order)

D=0.04in (High−Fidelity)

D=0.04in (2nd Order)

D=0.02in (High−Fidelity)

D=0.02in (2nd Order)

Figure 4.21: Diameter Sensitivity: Phase

order models tend to increase with decreasing port diameter. Arc jet tests conducted for various

port diameters indicate that the 0.10 in case is acceptable, therefore the diameter has been kept as

originally designed. However, these results serve to indicate the sensitivity to the port diameter,

therefore the diameter uncertainties should be kept as small as possible. The port 5 (worst–case

port) pressure lag error due to diameter uncertainty is shown in Fig. 4.22 for a range of diameter

uncertainty up to 0.03 in. In all cases the lag error is small (note that the errors are shown in % of

reading).

Table 4.5: Response Model Tube Length Results

Tube Length, in τ , sec (HF) τ , sec (2nd) ∆t, sec (HF) ∆t, sec (2nd)

+0.1 1.22·10−3 0.80·10−3 2.03·10−3 1.11·10−3

+0.25 1.26·10−3 0.82·10−3 2.08·10−3 1.14·10−3

+0.5 1.31·10−3 0.84·10−3 2.15·10−3 1.18·10−3

Next, a study was conducted to assess the sensitivity to tube length. Three cases were investigated using at the low pressure, low Mach flight condition. Table 4.5 summarizes the effects

perturbing the total tube length by increments of 0.1 in, 0.25 in, and 0.5 in. In each case the

time constant and time delay metrics do not change considerably. Figures 4.23 and 4.24 show the

frequency response results for these perturbations. These results indicate that the pressure system

is not highly sensitive to the tube length. Figure 4.25 shows the time history of the lag error for

port 5 induced by length uncertainties of up to 0.5 in. As in the previous case, these errors are

acceptably small.

41
25 20 15 10 5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

x 10−4

Mach [qbar > 850 Pa]

Pressure Error [% Reading]

10δ

5δ

1δ

Figure 4.22: Port 5 Lag Sensitivity

Based on the system requirements of 1.41 mm length uncertainty and 0.254 mm diameter

uncertainty, a worst-case lag error over the entire trajectory was determined from these sensitivity

results to be 6.94e-04% of reading at each port, in a 3σ sense.

42
100

101102103

−40

−35

−30

−25

−20

−15

−10

−5

0

5

Frequency [Hz]

Magnitude [db]

L+0.5in (High−Fidelity)

L+0.5in (2nd Order)

L+0.25in (High−Fidelity)

L+0.25in (2nd Order)

L+0.1in (High−Fidelity)

L+0.1in (2nd Order)

Figure 4.23: Length Sensitivity: Magnitude

100101102103

−800

−700

−600

−500

−400

−300

−200

−100

0

Frequency [Hz]

Phase [deg]

L+0.5in (High−Fidelity)

L+0.5in (2nd Order)

L+0.25in (High−Fidelity)

L+0.25in (2nd Order)

L+0.1in (High−Fidelity)

L+0.1in (2nd Order)

Figure 4.24: Length Sensitivity: Phase

43
25 20 15 10 5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

x 10−3

Mach [qbar > 850 Pa]

Pressure Error [% Reading]

0.5in

0.25in

0.1in

Figure 4.25: Port 5 Lag Sensitivity

4.1.7 Thermal Transpiration

Under rarefied flow conditions, transpiration induced effects within a tubing system can cause the

pressure measured by the transducers to be significantly different from the surface pressure. The

effects can be divided into those caused by temperature gradients between the transducer and the

surface, and those caused by heat transfer and/or shear stress.

A study of the available literature yielded three models to account for transpiration effects; two

models for simulating the difference between measured and orifice pressure due to thermomolecular

flow effects and one model for simulating the difference between the surface and orifice pressure due

to shear stress and/or heat transfer. The first transpiration model is provided in [34], which is an

application of thermomolecular flow theory developed by Knudsen in [35, 36]. Knudsen’s general

formula for the thermomolecular pressure effect is

dp

dT =

1

(1 + b

0r/λ)

2

P

2T

, where b

0 = b0

1 + b1r/λ

1 + b2r/λ (4.10)

where r is a physical length scale, λ is the mean free path, P is the pressure, T is the temperature,

and b0, b1, and b2 are empirical constants. The empirical constants have been obtained by Knudsen,

using least–squares fit to data acquired with hydrogen in glass tubes [35]. The results are b0 = 2.46,

b1 = 3.15, and b2 = 24.6.

Assuming that the temperature in the tubing between the surface and the transducer is known

as a function of length x, Eq. (4.10) can be written as

∂p (x)

∂x =

p (x)

2T (x)



∂T (x)

∂x 

"

κ (p, T, D)

2 + b0κ (p, T, D)

κ (p, T, R)

2 + (b0 + b1) κ (p, T, D) + b1b2

#2

(4.11)

44
Table 4.6: Gas Constants for Carbon Dioxide

Constant Value

Rg, J/kg-K 191.8

μ0, Pa-s 14.8·10−6

T0, K 293.15

C, K 240.0

where the parameter κ is the Knudsen number, given by

κ =

μ

Dps

πRgT

2

(4.12)

where Rg is the specific gas constant. The viscosity μ can be calculated as a function of temperature

using Sutherland’s relation [37]

μ = μ0



T0 + C

T + C

  T

T0

3/2

(4.13)

The constants associated with carbon dioxide are summarized in Table 4.6.

The second transpiration model is based on an algorithm described by Potter. [38]. This model

is based on the theoretical formulation of [39] and empirical data obtained in [40]. The empirical

data were obtained in a sequence of experiments involving a wide range of tube lengths, diameters,

orifice shapes, and gases, including hydrogen, helium, nitrogen, and argon. The model is

∂p (x)

∂x =

p (x)

2T (x)



∂T (x)

∂x  1 +

c0

κ (p, T, D)

+

c1

κ (p, T, D) + c2/κ (p, T, D)

−2

(4.14)

where c0 = 0.275, c1 = 0.625, and c2 = 24.0.

Note that both the Knudsen and Potter transpiration models predict that (∂p/∂x) → 0 as

κ → 0.

The last model investigated for this paper is an augmentation of the Potter model [38] that

includes non–equilibrium effects due to heat transfer and shear stress. This model is described

in [41]. The solution relies on empirical fits to data obtained in a wide range of experiments. The

algorithm for calculating non–equilibrium effects is complicated and is not repeated here.

The thermal transpiration models were employed in stand–alone codes in order to assess impacts to system performance. Figure 4.26 shows the results of an analysis comparing the thermal

transpiration models along the nominal reference trajectory. Here, the pressure difference between

the nominal pressure and the pressure with the thermal transpiration effects is shown for Ports

1 and 5. Results are shown for the Knudsen model, the abbreviated Potter model (i.e. without

orifice effects) and the full Potter model including the orifice effects. While some difference are apparent between the Knudsen and Potter models, all show the same trend with similar magnitudes.

These results indicate that above 850 Pa dynamic pressure, the thermal transpiration effects are

negligible. The effects become more pronounced in the rarefied flow regime below 850 Pa dynamic

pressure. For MEADS uncertainty analysis, the worst-case error due to transpiration is assumed

to be 5e-4% of reading in a 3σ sense.

45
25 20 15 10 5

−5

−4

−3

−2

−1

0

x 10−4

Mach [q

∞

 > 850 Pa]

∆ Pressure [% Reading]

Knudsen Model

Potter Model (Abreviated)

Potter Model (Full)

(a) Port 1 Transpiration

25 20 15 10 5

−5

−4

−3

−2

−1

0

x 10−4

Mach [q

∞

 > 850 Pa]

∆ Pressure [% Reading]

Knudsen Model

Potter Model (Abreviated)

Potter Model (Full)

(b) Port 5 Transpiration

Figure 4.26: Thermal Transpiration Results

46
4.1.8 System Calibration and Temperature Uncertainties

The MEADS calibration error model is based on that described by Eq. 3.11. In summary, the

error model consists of calibration parameter uncertainties, transducer and SEE thermocouple

errors (noise and bias), and hysteresis and non-repeatability error estimates based on the final

calibration. The final calibration and associated uncertainty models are described in Chapter 3.

4.2 CFD Pressure Distribution Uncertainties

Errors in MEADS pressure measurements due to fluid dynamic phenomena not attributable to

MEADS hardware or software are estimated from computational and experimental results. Some

sources of error can be estimated directly from the CFD simulations at Mars entry conditions, and

include contributions from port location uncertainty, effects of grid refinement and topology, design cycle changes to the OML, ablation and deformation, tile gap filler protuberances, and orifice

induced errors. These error estimates are calculated by taking the difference between nominal and

off-nominal solutions, and scaling to freestream conditions where applicable, or by applying functional relationships found in the literature. Each of these factors are accounted for individually and

combined using the root sum square (RSS) method, where each MEADS port is treated seperately.

As MEADS pressures are expressed in dimensionless form Cp for scaling purposes, uncertainties in

the pressures are expressed in normalized form ∆Cp/Cp, where the numerator is the uncertainty

term, and the denominator is evaluated at current conditions. The RSS expression of uncertainty

terms can be written as:

∆Cp =

q

∆C2

plocation + ∆C2pOML + ∆C2pablation + ∆C2pdeformation + ∆C2pprotuberance + ∆C2porif ice

(4.15)

The ability of the LAURA code to yield “correct” answers was also to be estimated by comparing

CFD results against those obtained from wind-tunnel experimentation, and thus used to establish

confidence in the flight CFD solutions. Significant variability in wind tunnel measurements due to

nonuniform test section conditions were experienced. Analysis required to make the data useful for

CFD validation purposes is beyond the scope of this work.

4.2.1 Port Location Uncertainty

Laser scan metrology was performed on the MSL heatshield at the Lockheed Martin Space Systems Company in order to provide high-fidelity measurements [42] of the MEDLI/MEADS sensor

locations and to help quantify the accuracy of heatshield-to-IMU alignment. The measurements

indicated that the MEADS port locations are known to within approximately 1 mm, and so the

uncertainty in their locations is quite small in comparison to other heatshield geometric features,

e.g., discontinuities at PICA tile edges or protruding gap fillers. The effect of port location uncertainty on MEADS pressure measurement is estimated using the magnitude of pressure coefficient

gradient extracted from flight CFD solutions, and is expressed at each port as

∆Cplocation =

|∇p|∆s

q

(4.16)

The 3σ value for port location uncertainty ∆Cp is based on ∆s corresponding to the metrology

tolerance, or 1 millimeter, and is mapped over the entire nominal trajectory space. In order that

it might be scaled to other trajectories, it is expressed in the tables normalized to the current Cp,

i.e., ∆Cp/Cp.

47
4.2.2 Grid Refinement and Topology, OML Design Cycle Changes

The discretization of grids used for computation of the MSL nominal aerodatabase would be considered rather coarse by today’s standards. After design cycle changes to the OML brought about

as a consequence of changes to TPS requirements, a new grid of much-improved resolution was constructed for the flight geometry and used to compute point checks for comparison against nominal

aerodatabase results. The OML differences are shown in Fig. 4.27.

Figure 4.27: Outer Mold Lines Described by Original (Grid a) and Refined (Grid b)

CFD Grids

Because the two grids describe different OMLs and are of differering resolution and topology,

the effects of changing these three factors are coupled, and so are combined within one uncertainty

term. It is important to note the limitations imposed by grid resolution and numerical stability as

applicable to the LAURA code. On one hand, the coarse nominal aerodatabase grid is near the

lower limit for acceptably resolved solutions; on the other hand, the updated fine grid is near the

practical limit for computing solutions without numerical instabilities that occur with LAURA due

to point clustering in body-tangent directions. In other words, solution accuracy will not improve

monotonically as grid density tends to infinity. For these reasons, only the results from the original

aerodatabase grid and the final OML fine grid are used to approximate the errors due to both grid

effects and OML changes. The expression for the combined uncertainty term is written as

∆CpOML = |Cpf inegrid − Cpcoarsegrid | (4.17)

The left hand side of Eq. (4.17 is assumed to lie at the 2σ bounds, as the data were only available

for a few flow conditions. A grid sensitivity study deemed necessary to estimate to 3σ confidence

is beyond the scope of this work. The right hand side of Eq. (4.17) is only known over a small

portion of the trajectory space and so is implemented in a form amenable to scaling over the entire

trajectory, i.e., ∆Cp/Cp. The maximum value of ∆Cp/Cp is used from the available data at each

port and applied over the entirety of the trajectory space.

48
4.2.3 Ablation and Deformation

Shape changes to the heatshield that occur due to ablation and deformation were modeled for the

OML13F configuration. The ablation case was computed at the 07-25 trajectory peak heating

condition, for a bounding worst-case scenario where the TPS is recessed to a maximum of approximately 20 millimeters along the symmetry plane leeside [19]. The uncertainty term due to ablation

is an engineering estimate defined as the absolute difference between baseline and ablated cases,

scaled to the sum of dynamic pressure and heat load, normalized to their maximum and total

values, respectively

∆Cp = |Cpablated − Cpbaseline |

1

2



q

qmax

+

Q

Qmax 

(4.18)

where Q is the instantaneous heat load and Qmax is the total heat load.

For analysis of heatshield deformation and its effect on aerodynamics, a finite element model

subjected to 12.2 g decelerative load on the 06-05 nominal trajectory was used to modify the

baseline grid, where predicted heatshield apex deflection is approximately 13 millimeters. As the

current trajectory has a 3σ high deceleration of 13.4 g, a scale factor is applied to the right hand

side in order to reflect the current conditions via linear extrapolation. The expression for the 3σ

loading term is then based upon the difference between baseline and deflected solutions, and scaled

to the ratio of instantaneous to maximum dynamic pressure. This term is written as

∆Cploading = 1.1|Cpdeformed − Cpbaseline |

q

qmax

(4.19)

The ablation and deformation terms are only known at their corresponding peak conditions, so

are implemented over the trajectory space using the ∆Cp/Cp form as used for the OML term.

4.2.4 Gap Filler Protuberances

The effect of PICA tile gap filler protuberances at maximum heating conditions on the 0801-A

trajectory were investigated for three locations on the heatshield [43], where the nose cap case was

deemed most relevant to MEADS performance. Heatshield flowfields with gap filler heights of 0.1

inch, 0.2 inch, and 0.4 inch were computed at fully turbulent conditions, and curves of pressure

along a surface streamline traversing the protrusion were extracted from the solutions, as shown in

Fig. 4.28, where positive distance denotes downstream location.

The radius of influence of these protrusions was shown to be on the order of 0.3 meters. For

conditions where the MEADS port is in close proximity to a gap filler protrusion, the corresponding

magnitude of error ∆Cp is as large as 0.4 and dwarfs the sum of all other uncertainty terms

considered here. In addition, the protrusion radius of influence and magnitude of error would

increase if the flow were modeled as laminar. Uncertainty is inferred from the turbulent results and

scaled in the same way as the ablation term, where the expression is written as

∆Cpgapf iller = |Cpgapf iller − Cpbaseline |

1

2



q

qmax

+

Q

Qmax 

(4.20)

While a gap filler protuberance term would dominate the uncertainty model, the likelihood

of its occurrence was considered low, and so the term was omitted from the model. If gap filler

protuberances did occur, they would likely be identifiable in the pressure data as large excursions

from the nominal model.

49
Figure 4.28: Pressure Coefficient Disturbance vs. Relative Distance from a Step Discontinuity on Nose Cap. Flow is From Left to Right.

4.2.5 Orifice Induced Errors

The presence of a pressure orifice in a flowfield can cause errors in surface pressure measurements,

where the errors are a function of the orifice diameter, shear stress at the wall, and the working

fluid density and viscosity [45]. This relationship may be expressed as

e

τw

= f



d

+



(4.21)

where e is the pressure error and d

+ is the orifice Reynold’s number, uτ d/v.

The plot of this relationship, shown in Fig. 4.29(a), shows that the left hand side becomes

quite small (on order of 0.1) when d

+ is less than 100 [45]. Using the TPS stressing trajectories

for reference conditions, the orifice Reynolds number at MEADS port locations never exceeds

approximately 70, and so the corresponding pressure error never exceeds approximately 5 Pa. A

plot of orifice Reynolds number is shown for the peak dynamic pressure along the most stressful

trajectory in Fig. 4.29(b). In ∆Cp/Cp form, the peak magnitude of this error is of order 1.E-4, and

is vanishingly small for all but the lateral ports at conditions at or near peak dynamic pressure.

For this reason, and as the curves describing this error relationship are not well established at such

low values of orifice Reynolds number and wall shear stress, the term is omitted from the current

model.

50
(a) Orifice Induced Error Curve

(b) d

+ at Peak Conditions

Figure 4.29: Orifice Effects

51
4.2.6 Uncertainty Term Implementation

Table 4.7 gives 3σ values for the error terms that are implemented in ∆Cp/Cp form. To obtain the

scaled uncertainty ∆Cp for each, they are multiplied by the base Cp, which is interpolated from

the lookup tables for the current flight condition. The terms may then be summed as in equation

4.15.

Table 4.7: 3σ ∆Cp Values for Uncertainty Terms Scaled Over the Trajectory Space

Port 1 Port 2 Port 3 Port 4 Port 5 Port 6 Port 7

OML + grid 4.711e-03 5.418e-03 3.824e-03 4.080e-3 1.264e-02 4.969e-03 4.969e-03

Ablation 1.000e-03 1.221e-03 1.807e-03 3.469e-02 2.057e-03 7.671e-03 7.671e-03

Deformation 8.400e-04 3.698e-04 3.798e-03 1.223e-02 2.296e-02 1.098e-02 1.098e-02

4.3 Error Analysis Results and Sensitivity Studies

This section describes the total system performance results for both the flight and flight spare

transducer sets. Monte Carlo analysis is utilized with the basic pressure-only MEADS algorithm

to determine the angle of attack, sideslip, dynamic pressure, and Mach number estimation performance. Monte Carlo analysis described in this section is based on the 09-HOL-01 nominal

trajectory.

Figure 4.30: Pressure Measurement Errors Along Trajectory

The total uncertainties for the MEADS flight system evaluated along the nominal trajectory

are shown in Figure 4.30. The values of the error model parameters are listed in Table 4.8. Note

that the error parameters are assumed to be Gaussian except where otherwise noted.

52
Table 4.8: Error Parameters

Parameter Name Value

Mensor Accuracy (σc) (Ref. 47) 0.001 psi

Transducer Thermocouple Bias (σb1) 2.5 deg C (uniformly distributed)

SSE Thermocouple Bias (σb2) 1.5 deg C (uniformly distributed)

Thermocouple Noise (σn1 = σn2) 0.05 deg C

SSE Pressure Channel Noise (σV ) 10 counts

A/D bit size 14

Time Stamp Error 25 μs (uniformly distributed)

Port Location Uncertainties 0.04 in (uniformly distributed)

Maximum Leak Rate 0.047022% (uniformly distributed)

Pressure Path Length Uncertainty (Ref. 48) 1.41 mm

Pressure Path Diameter Uncertainty (Ref. 48) 0.254 mm

The results of the Monte Carlo analysis are shown in the following figures. Figure 4.31 shows

the total system error for the angle of attack estimate, Figure 4.32 shows the total system error

for the angle of sideslip estimate, and Figure 4.33 shows the total system error for the dynamic

pressure estimate. In these figures, the errors are shown only for the portion over which the MEADS

hardware requirements pertain. Specifically the total hardware and total CFD errors are shown

(cyan and red curves, respectively) along with the total combined error (blue).for dynamic pressures

greater than 1750 Pa for angle of attack errors, greater than 1250 for sideslip errors, and greater

than 850 Pa for dynamic pressure errors. These plots indicate that the MEADS hardware meets

requirements over the entire dynamic pressure range range.

Figure 4.31: Total Estimation Error: Angle of Attack

53
Figure 4.32: Total Estimation Error: Angle of Sideslip

Figure 4.33: Total Estimation Error: Dynamic Pressure

Plots of individual error sources are given in Appendix B. Here, the trajectory average errors

for the uncertainties are tabulated in Table 4.9. These uncertainties indicate that, on average,

the MEADS system achieves angle of attack and sideslip estimation errors less than 0.5 degrees

54
and dynamic pressure estimation errors less than 1%. The largest contributors of errors are the

transducer performance and the OML/grid CFD errors.

Table 4.9: Trajectory Average Errors (3σ)

Error Model Parameter Angle of Angle of Dynamic

Attack (deg) Sideslip (deg) Pressure (%)

Transducer Errors Calibration Error 0.1982 0.1364 0.2377

Temperature Uncertainty 0.0788 0.1060 0.1217

SSE Errors Quantization 0.1205e-11 0.0015e-11 0.7133e-11

Noise 0.0488 0.0730 0.0971

Temperature Uncertainty 0.0096 0.0082 0.0170

Geometry Error Port Location 0.0387 0.0301 0.0268

Pressure Leak 0.0960 0.1055 0.1228

Lag Uncertainty 9.4486e-4 1.0377e-3 1.2138e-3

Thermal Transpiration 6.8808e-4 0.7477e-3 0.8749e-3

Latencies Time Tag Error 0.1380e-3 0.1233e-3 0.1560e-3

Mechanical Vibration 0.0823 0.0966 0.0977

CFD OML/grid 0.1966 0.2088 0.2376

Ablation 0.0426 0.1293 0.0400

Deformation 0.1294 0.1879 0.0941

Total Hardware System Error 0.2558 0.2391 0.3262

Total CFD Error 0.2392 0.3092 0.2586

Total (Combined) Error 0.3503 0.3909 1.3785

55
Chapter 5

Conclusions

This document describes the as-built MEADS error budgets for the angle of attack, angle of sideslip,

and dynamic pressure reconstruction based on pressure measurements. The error models include

hardware, calibration, vibration, and CFD pressure distribution uncertainties. The MEADS nominal pressure model and its corresponding CFD-based uncertainty model are presented, where

uncertainty terms due to OML changes, grid induced error, and flight ablation and deformation

effects are approximated using nominal aerodatabase and off-nominal CFD results. It is currently

recommended that TPS tile gap filler protuberance effects be omitted from the uncertainty model,

as their likelihood and magnitude are not understood. Uncertainties due to orifice induced error

are shown to be inconsequential for MEADS at flight conditions. CFD validation and uncertainty

models based on wind tunnel data are absent from the present work, as the variability of wind

tunnel conditions make such models impractical to implement. Nevertheless, some improvements

to the current uncertainty models can be suggested. These would include recomputation of the

MSL nominal aerodatabase on the 12-GAL-01 trajectory, using the fine OML-13F grid and full

Navier-Stokes equations. Ablation and deformation effect approximations can also be improved in

this way. Additional uncertainty terms for code-to-code comparisons relevant to the MSL aerodatabase can also be made using different versions of LAURA, as at least two major versions have

been released since the MSL nominal aerodatabase was computed.

Applying Monte Carlo simulation techniques to the MEADS system model shows that the asbuilt hardware will meet Level 2 requirements over the MSL entry trajectory.The preflight modeling

efforts described herein were validated via post-flight data processing and trajectory reconstruction

efforts performed after MSL’s landing on Mars on August 6th, 2012. The MEDLI flight data and

associated reconstruction activities are described in [49–52].

56
Appendix A

Data Reduction Look-Up Tables

This appendix contains the two-dimensional lookup tables that can be used to convert transducer Voltage outputs into pressures (in units of psi), given the transducer and SSE temperatures.

First, the coefficients a0, a1, and a2 are evaluated as a function of temperatures T1 (Transducer) and

T2 (SSE), and pressure is calculated from the equation p = a0 +a1V +a2V

2 where V is the Voltage

in units on mV. Similarly, the uncertainties in each polynomial coefficient can be interpolated to

compute a pressure uncertainty due to calibration uncertainties.

57
Table A1: Transducer 020 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-129.092308 -21.438462 0.482379 0.519986 -0.000210229 0.13954 0.0565904 0.00081251-129.092308 -13.030769 0.482213 0.519962 -0.000217417 0.139573 0.0565741 0.000811887-129.092308 31.553846 0.478299 0.520059 -0.000201228 0.140301 0.056817 0.000813278-129.092308 62.115385 0.477094 0.519105 -0.000162541 0.140517 0.0566831 0.000809004-104.496154 -21.438462 0.434568 0.516379 -0.000157892 0.146667 0.0581563 0.000791759-104.496154 -13.030769 0.434144 0.516348 -0.000165196 0.146747 0.058151 0.000791086-104.496154 31.553846 0.431658 0.51647 -0.000150791 0.147216 0.0583246 0.000792521-104.496154 62.115385 0.430129 0.515532 -0.000112304 0.147492 0.058211 0.000788346

-56.107692 -21.438462 0.331968 0.510057 -0.000127047 0.165652 0.0618372 0.000754709-56.107692 -13.030769 0.331422 0.510023 -0.000134406 0.165753 0.061837 0.000754014-56.107692 31.553846 0.329602 0.510156 -0.000120832 0.166102 0.0619783 0.000755468-56.107692 62.115385 0.327923 0.509225 -8.24387e-05 0.166405 0.0618743 0.000751339

-129.092308 4.307692 0.493424 0.520216 -0.00022702 0.137547 0.0560506 0.000812812-104.496154 5.496154 0.446123 0.51662 -0.000175457 0.144583 0.0575916 0.000792075

-56.107692 6.050000 0.34376 0.510303 -0.000144974 0.163525 0.0612609 0.000755033-86.207692 -21.438462 0.386489 0.513746 -0.000142894 0.154947 0.059958 0.000776263-85.707692 -13.030769 0.386094 0.513717 -0.000150185 0.155021 0.0599515 0.000775596-85.161538 5.361539 0.397987 0.513986 -0.000160372 0.152872 0.0593961 0.000776578-82.984615 31.553846 0.383447 0.513835 -0.000135577 0.15552 0.0601329 0.000777026-81.623077 62.115385 0.381954 0.512895 -9.70682e-05 0.155788 0.0600171 0.000772839

58
Table A2: Transducer 021 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-126.130769 -19.853846 0.113921 0.521182 -0.000203197 0.225624 0.0764047 0.000818045-126.130769 -10.969231 0.112461 0.521505 -0.000226062 0.22608 0.0765081 0.000818553-126.130769 37.046154 0.0979738 0.521647 -0.00021961 0.230136 0.0773113 0.000819297-126.130769 65.669231 0.100222 0.521234 -0.000211379 0.229523 0.0770936 0.000817223-103.996154 -19.853846 0.170309 0.518764 -0.000273909 0.207999 0.0724353 0.000799721-103.996154 -10.969231 0.16888 0.519087 -0.000296756 0.208446 0.0725369 0.000800227-103.996154 37.046154 0.154238 0.519227 -0.000290126 0.212545 0.0733485 0.000800972-103.996154 65.669231 0.156524 0.518814 -0.000281921 0.211921 0.0731287 0.000798895

-57.015384 -19.853846 0.288085 0.512354 -0.000315442 0.177054 0.0644687 0.000759752-57.015384 -10.969231 0.286734 0.512676 -0.000338246 0.17748 0.0645659 0.000760256-57.015384 37.046154 0.271713 0.512813 -0.000331182 0.181683 0.0653979 0.000761003-57.015384 65.669231 0.274089 0.5124 -0.000323038 0.181034 0.0651729 0.000758919

-126.130769 5.884615 0.135011 0.521766 -0.000255454 0.219917 0.0753016 0.000818621-103.996154 5.823077 0.191348 0.519347 -0.000326041 0.202305 0.0713349 0.000800295

-57.015384 5.673077 0.309001 0.512933 -0.000367269 0.171394 0.0633746 0.000760323-84.484615 -19.853846 0.195609 0.515771 -0.000267428 0.200899 0.0702739 0.000781927-84.538462 -10.969231 0.192023 0.516124 -0.000291466 0.201944 0.0704949 0.00078251-83.915385 9.982051 0.220056 0.516448 -0.000328003 0.194283 0.0689952 0.000782594-82.900000 37.046154 0.187889 0.516344 -0.000296872 0.203159 0.0707406 0.000783181-82.700000 65.669231 0.187651 0.515953 -0.000286949 0.203231 0.0706643 0.000781292

59
Table A3: Transducer 022 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-125.476923 -19.853846 0.0692557 0.523176 -0.000465551 0.241117 0.0787944 0.000813783-125.476923 -10.969231 0.0686771 0.523462 -0.000487055 0.241449 0.0789281 0.000815098-125.476923 37.046154 0.0499839 0.5237 -0.000488725 0.247353 0.0799901 0.000815908-125.476923 65.669231 0.0527037 0.523482 -0.00048292 0.246527 0.0797839 0.000814827-102.880769 -19.853846 0.11024 0.520648 -0.000489134 0.227454 0.0756764 0.000796917-102.880769 -10.969231 0.109703 0.520933 -0.000510584 0.227773 0.0758076 0.000798228-102.880769 37.046154 0.0907927 0.521173 -0.000512268 0.233745 0.0768815 0.00079904-102.880769 65.669231 0.0935633 0.520953 -0.000506453 0.232903 0.0766724 0.000797956

-55.661538 -19.853846 0.22432 0.515224 -0.00052861 0.194243 0.0679796 0.000762979-55.661538 -10.969231 0.223885 0.515506 -0.000549929 0.19453 0.0681046 0.000764283-55.661538 37.046154 0.204444 0.515748 -0.000551646 0.200664 0.0692077 0.000765097-55.661538 65.669231 0.207339 0.515528 -0.000545809 0.199785 0.0689917 0.000764009

-125.476923 5.884615 0.100757 0.523384 -0.000485264 0.231596 0.0771719 0.000815238-102.880769 5.823077 0.141666 0.520855 -0.0005088 0.217956 0.0740578 0.000798368

-55.661538 5.673077 0.255562 0.515429 -0.000548161 0.1848 0.0663705 0.000764422-83.507692 -19.853846 0.12063 0.51819 -0.000480845 0.224571 0.0744244 0.00078216-83.315385 -10.969231 0.117267 0.518528 -0.000505922 0.225783 0.0747268 0.000783672-82.869230 9.982051 0.157146 0.518431 -0.000503696 0.213534 0.0725437 0.000783847-81.638462 37.046154 0.113049 0.518706 -0.000506702 0.22722 0.0749912 0.000784429-81.423077 65.669231 0.112386 0.518522 -0.000501513 0.227443 0.0749766 0.000783464

60
Table A4: Transducer 023 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-126.953846 -19.853846 0.607003 0.523657 -0.000356694 0.126025 0.0512664 0.000828577-126.953846 -10.969231 0.610104 0.523642 -0.000353075 0.125518 0.0511286 0.000828876-126.953846 37.046154 0.604506 0.523958 -0.000359426 0.126356 0.0514264 0.000829916-126.953846 65.669231 0.611119 0.523646 -0.000376449 0.12529 0.0510913 0.000828468-104.273077 -19.853846 0.513203 0.520504 -0.000363031 0.135643 0.0549891 0.000807538-104.273077 -10.969231 0.516317 0.520489 -0.000359439 0.135134 0.0548506 0.000807837-104.273077 37.046154 0.510613 0.520805 -0.000365721 0.135989 0.0551536 0.000808877-104.273077 65.669231 0.517254 0.520493 -0.000382769 0.134919 0.0548171 0.000807427

-56.630769 -19.853846 0.344951 0.513611 -0.000331945 0.162433 0.0616605 0.000765221-56.630769 -10.969231 0.3481 0.513596 -0.000328419 0.161919 0.0615203 0.000765519-56.630769 37.046154 0.342135 0.513911 -0.000334535 0.162814 0.061836 0.000766559-56.630769 65.669231 0.348844 0.513598 -0.000351644 0.161733 0.061496 0.000765104

-126.953846 5.884615 0.62715 0.523817 -0.000367432 0.122873 0.0503102 0.00082922-104.273077 5.823077 0.533301 0.520664 -0.000373743 0.132499 0.0540352 0.00080818

-56.630769 5.673077 0.364932 0.513769 -0.000342595 0.159307 0.0607122 0.000765859-84.215385 -19.853846 0.423299 0.517586 -0.000351806 0.148377 0.0586947 0.000789212-84.330769 -10.969231 0.425463 0.517553 -0.000346407 0.148011 0.0586036 0.00078953-84.012821 9.982051 0.446653 0.517771 -0.000364253 0.144723 0.0575863 0.000789957-83.046154 37.046154 0.426987 0.517893 -0.0003573 0.147748 0.0585557 0.000790562-83.246154 65.669231 0.431721 0.517612 -0.000372652 0.146975 0.0583138 0.000789257

61
Table A5: Transducer 024 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-127.246154 -19.853846 0.514338 0.521517 -0.00026537 0.134911 0.055195 0.000818127-127.246154 -10.969231 0.515201 0.521534 -0.000253953 0.134789 0.0551726 0.000818795-127.246154 37.046154 0.509794 0.522027 -0.000290646 0.135544 0.0554667 0.000819608-127.246154 65.669231 0.51193 0.522215 -0.000312999 0.135247 0.0553945 0.000819957-104.261539 -19.853846 0.496193 0.51837 -0.000266292 0.13727 0.0554471 0.000799055-104.261539 -10.969231 0.497069 0.518387 -0.000254923 0.137146 0.0554241 0.000799723-104.261539 37.046154 0.491585 0.518879 -0.000291595 0.137912 0.0557217 0.000800531-104.261539 65.669231 0.493739 0.519067 -0.000313952 0.137612 0.0556487 0.000800881

-56.369231 -19.853846 0.459713 0.511207 -0.000226102 0.14236 0.0556947 0.000757105-56.369231 -10.969231 0.46062 0.511225 -0.00021485 0.142232 0.0556702 0.000757772-56.369231 37.046154 0.454948 0.511716 -0.000251473 0.143024 0.0559762 0.00075857-56.369231 65.669231 0.457147 0.511904 -0.00027384 0.142718 0.0559011 0.000758922

-127.246154 5.884615 0.527014 0.521782 -0.000270422 0.133163 0.0546614 0.00081986-104.261539 5.823077 0.508839 0.518634 -0.000271332 0.135526 0.0549148 0.000800784

-56.369231 5.673077 0.472285 0.51147 -0.000231113 0.140626 0.0551654 0.000758824-83.884615 -19.853846 0.47091 0.515273 -0.000242822 0.14077 0.0560162 0.000780851-84.023077 -10.969231 0.470919 0.515272 -0.000228205 0.140765 0.0560331 0.000781536-83.905128 9.982051 0.485604 0.51558 -0.000248678 0.138744 0.0553977 0.000782859-82.976923 37.046154 0.470648 0.515793 -0.000266242 0.140812 0.0560971 0.000782641-83.430769 65.669231 0.471553 0.515984 -0.000288337 0.140685 0.0560805 0.00078295

62
Table A6: Transducer 025 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-125.569231 -19.853846 0.196481 0.522173 -0.000239317 0.200111 0.0719516 0.000822736-125.569231 -10.969231 0.19651 0.522311 -0.00023888 0.200129 0.071984 0.000823536-125.569231 37.046154 0.185751 0.522262 -0.000227128 0.203017 0.0725454 0.000823492-125.569231 65.669231 0.186885 0.521841 -0.000220681 0.202743 0.0723955 0.000821407-103.253846 -19.853846 0.210493 0.519048 -0.000270645 0.196361 0.0703057 0.000801803-103.253846 -10.969231 0.210547 0.519186 -0.000270205 0.196372 0.0703366 0.000802601-103.253846 37.046154 0.199655 0.519137 -0.000258444 0.199295 0.0709052 0.000802556-103.253846 65.669231 0.200819 0.518716 -0.000251999 0.199013 0.0707536 0.000800469

-56.165385 -19.853846 0.262998 0.511388 -0.000251789 0.182848 0.0655577 0.000756265-56.165385 -10.969231 0.263113 0.511525 -0.000251344 0.182843 0.0655852 0.00075706-56.165385 37.046154 0.251895 0.511476 -0.00023956 0.185853 0.066171 0.000757011-56.165385 65.669231 0.253133 0.511054 -0.000233121 0.185551 0.0660153 0.000754919

-125.569231 5.884615 0.216442 0.522331 -0.000236396 0.194829 0.07092 0.000823775-103.253846 5.823077 0.230407 0.519205 -0.00026773 0.191091 0.0692765 0.000802839

-56.165385 5.673077 0.282795 0.511545 -0.000248891 0.177609 0.0645346 0.000757295-83.961538 -19.853846 0.212294 0.515549 -0.000242442 0.196031 0.0693272 0.000781614-83.900000 -10.969231 0.210654 0.515708 -0.000242144 0.196496 0.069454 0.000782522-83.243590 9.982051 0.235432 0.515732 -0.000239055 0.189908 0.0681314 0.000782818-82.053846 37.046154 0.208777 0.515673 -0.000231006 0.197019 0.0695431 0.000782573-81.830769 65.669231 0.207901 0.515277 -0.000224418 0.197279 0.0695058 0.000780613

63
Table A7: Transducer 026 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-128.376923 -21.438462 0.151218 0.521272 -6.08623e-05 0.213835 0.0746218 0.000826517-128.376923 -13.030769 0.151085 0.521399 -7.63139e-05 0.213859 0.0746078 0.000826158-128.376923 31.553846 0.149472 0.52119 -5.01051e-05 0.214292 0.0747002 0.000826397-128.376923 62.115385 0.155085 0.520848 -6.88512e-05 0.212737 0.0742371 0.00082291-103.911539 -21.438462 0.203361 0.51764 -7.66562e-05 0.198303 0.0706997 0.000803394-103.911539 -13.030769 0.202906 0.517761 -9.16995e-05 0.198412 0.0707013 0.000803008-103.911539 31.553846 0.202945 0.517622 -7.22545e-05 0.198409 0.0707085 0.000803292-103.911539 62.115385 0.20808 0.51727 -8.88552e-05 0.196981 0.0702738 0.000799871

-55.634615 -21.438462 0.288877 0.510307 -7.06614e-05 0.176319 0.0642509 0.000759086-55.634615 -13.030769 0.288271 0.510425 -8.55143e-05 0.176467 0.0642597 0.000758686-55.634615 31.553846 0.28908 0.510318 -6.92214e-05 0.176261 0.0642273 0.000758992-55.634615 62.115385 0.293993 0.509961 -8.48223e-05 0.174893 0.0638057 0.000755601-85.815385 -21.438462 0.200314 0.513568 3.62752e-05 0.19892 0.0700291 0.000784902-85.815385 -13.030769 0.192803 0.513554 3.01867e-05 0.200879 0.0703713 0.000783904-85.815385 31.553846 0.229062 0.514936 -9.86688e-05 0.191315 0.0685121 0.000785204-85.815385 62.115385 0.223722 0.514361 -6.82312e-05 0.192688 0.0686983 0.000783219-80.738462 -21.438462 0.188924 0.512429 9.72559e-05 0.201864 0.070466 0.000781299-80.738462 -13.030769 0.173138 0.512256 0.00010167 0.205992 0.0712079 0.000779585-80.738462 31.553846 0.251876 0.515421 -0.000201119 0.185215 0.0671594 0.000782074-80.738462 62.115385 0.234251 0.514585 -0.000115512 0.189873 0.0680741 0.000781775

-128.376923 4.307692 0.165185 0.521936 -0.000126424 0.21014 0.0738847 0.000826664-103.911539 5.496154 0.217973 0.518335 -0.000145245 0.194438 0.0699287 0.000803547

-55.634615 6.050000 0.303789 0.511016 -0.00014066 0.172374 0.063464 0.000759242-85.815385 -21.438462 0.229628 0.514961 -0.00010379 0.191169 0.0684953 0.000785308-85.284615 -13.030769 0.22921 0.515083 -0.00011888 0.191269 0.0684952 0.000784924-84.648718 5.361539 0.244167 0.515653 -0.000172036 0.187323 0.0677282 0.00078546-82.423077 31.553846 0.229062 0.514936 -9.86688e-05 0.191315 0.0685121 0.000785204-80.738462 62.115385 0.234251 0.514585 -0.000115512 0.189873 0.0680741 0.000781775

64
Table A8: Transducer 027 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-130.015385 -21.438462 -0.252748 0.523436 -0.000128498 0.404867 0.100443 0.000836022-130.015385 -13.030769 -0.251863 0.523106 -9.73333e-05 0.404433 0.100355 0.000835671-130.015385 31.553846 -0.251293 0.522446 -4.28205e-05 0.404224 0.100253 0.000834722-130.015385 62.115385 -0.250742 0.523286 -0.000151732 0.403735 0.100187 0.000833709-105.569231 -21.438462 -0.183349 0.519808 -0.000151848 0.363032 0.0944214 0.000811668-105.569231 -13.030769 -0.182576 0.519455 -0.000118668 0.362662 0.0943396 0.000811297-105.569231 31.553846 -0.181262 0.518865 -6.94264e-05 0.362039 0.0941918 0.000810408-105.569231 62.115385 -0.180867 0.519663 -0.000174246 0.361642 0.0941353 0.00080939

-56.850000 -21.438462 -0.0494129 0.512534 -0.000184814 0.294136 0.083514 0.000765533-56.850000 -13.030769 -0.0486925 0.51217 -0.000150694 0.293796 0.0834349 0.000765152-56.850000 31.553846 -0.0470329 0.511613 -0.000103909 0.29298 0.0832658 0.000764291-56.850000 62.115385 -0.0467105 0.512392 -0.000206823 0.292627 0.0832137 0.000763271

-130.015385 4.307692 -0.245017 0.523474 -0.000123133 0.400663 0.0999095 0.000835837-105.569231 5.496154 -0.17526 0.519847 -0.000146235 0.358633 0.093863 0.000811474

-56.850000 6.050000 -0.0411581 0.512574 -0.000179086 0.289647 0.0829441 0.000765335-86.753846 -21.438462 -0.13527 0.517125 -0.000181281 0.336485 0.0902651 0.000792915-86.300000 -13.030769 -0.134484 0.516775 -0.000148329 0.336108 0.0901826 0.000792546-86.071795 5.361539 -0.127222 0.517164 -0.000175696 0.332108 0.0897095 0.000792722-83.953846 31.553846 -0.133255 0.516177 -9.84903e-05 0.335531 0.0900399 0.00079165-82.784615 62.115385 -0.132842 0.51698 -0.000203774 0.335124 0.0899824 0.000790633

65
Table A9: Transducer 029 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-126.092308 -19.853846 0.511832 0.520461 -0.000259862 0.135785 0.0551601 0.000812547-126.092308 -10.969231 0.513835 0.520581 -0.000266753 0.135475 0.0550838 0.000812991-126.092308 37.046154 0.502203 0.520971 -0.000271367 0.13729 0.0557424 0.000815275-126.092308 65.669231 0.505207 0.520562 -0.000260656 0.136813 0.0555162 0.000813293-103.696154 -19.853846 0.477103 0.517591 -0.000265736 0.140351 0.0561989 0.000793949-103.696154 -10.969231 0.479129 0.517711 -0.000272623 0.140036 0.0561214 0.000794393-103.696154 37.046154 0.467346 0.518101 -0.000277191 0.141875 0.0567872 0.000796675-103.696154 65.669231 0.470386 0.517691 -0.000266475 0.141392 0.0565591 0.00079469

-56.442308 -19.853846 0.389187 0.511028 -0.000224563 0.153994 0.0590317 0.000755337-56.442308 -10.969231 0.391272 0.511148 -0.00023144 0.153671 0.0589515 0.000755782-56.442308 37.046154 0.379119 0.511537 -0.000235897 0.155567 0.0596349 0.00075806-56.442308 65.669231 0.382246 0.511125 -0.000225166 0.15507 0.0594023 0.000756067

-126.092308 5.884615 0.536681 0.520776 -0.000276451 0.131995 0.054032 0.000814114-103.696154 5.823077 0.501892 0.517906 -0.000282286 0.13657 0.0550735 0.000795513

-56.442308 5.673077 0.413831 0.511341 -0.000241016 0.150235 0.0579129 0.000756892-84.261538 -19.853846 0.418068 0.514883 -0.000248292 0.149251 0.0584736 0.000777658-84.200000 -10.969231 0.418472 0.515005 -0.000255466 0.149183 0.0584734 0.000778078-83.569231 9.982051 0.446872 0.515248 -0.000267522 0.144857 0.0571659 0.000779474-82.484615 37.046154 0.416928 0.515417 -0.000263106 0.149456 0.0586514 0.000780482-82.300000 65.669231 0.417556 0.515048 -0.00025281 0.149345 0.0585483 0.000778709

66
Table A10: Transducer 030 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-129.623077 -21.438462 0.232667 0.525806 -0.000437709 0.190143 0.0705584 0.000835385-129.623077 -13.030769 0.232673 0.52577 -0.000441965 0.190139 0.0705265 0.000834759-129.623077 31.553846 0.228151 0.525656 -0.000407802 0.191321 0.0707535 0.000835176-129.623077 62.115385 0.231165 0.525134 -0.0004197 0.190505 0.0704406 0.000831498-105.253847 -21.438462 0.238468 0.522991 -0.000532104 0.188729 0.0693306 0.00081254-105.253847 -13.030769 0.238045 0.52295 -0.000536568 0.188835 0.0693193 0.000811861-105.253847 31.553846 0.235868 0.522858 -0.000503841 0.189411 0.0694257 0.000812379-105.253847 62.115385 0.238274 0.52234 -0.000514717 0.188753 0.0691472 0.000808762

-56.992307 -21.438462 0.250487 0.515561 -0.000507534 0.185747 0.0668137 0.000768097-56.992307 -13.030769 0.249865 0.515517 -0.000512094 0.185905 0.066812 0.000767394-56.992307 31.553846 0.24878 0.515436 -0.000480036 0.186199 0.0668623 0.000767958-56.992307 62.115385 0.250903 0.514921 -0.000490436 0.185615 0.0665998 0.00076437

-129.623077 4.307692 0.251818 0.525927 -0.000441487 0.185197 0.0695407 0.000835818-105.253847 5.496154 0.258503 0.523118 -0.000536056 0.183554 0.0682659 0.000812993

-56.992307 6.050000 0.270934 0.51569 -0.000511567 0.180467 0.0657271 0.000768559-86.746154 -21.438462 0.227983 0.51979 -0.000494254 0.191603 0.0691018 0.000794121-86.284615 -13.030769 0.227609 0.519749 -0.000498694 0.191697 0.0690882 0.000793448-85.948718 5.361539 0.247918 0.519916 -0.000498186 0.186454 0.0680424 0.000794571-83.753846 31.553846 0.225166 0.519655 -0.000465804 0.192341 0.0692083 0.000793953-82.223077 62.115385 0.227641 0.519137 -0.000476796 0.191665 0.0689259 0.00079033

67
Table A11: Transducer 031 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-129.084615 -21.438462 0.940105 0.520852 -0.000131118 0.113424 0.0368933 0.00082274-129.084615 -13.030769 0.939884 0.520976 -0.000132379 0.113435 0.0369076 0.00082312-129.084615 31.553846 0.936267 0.521088 -0.000157951 0.113592 0.0370367 0.000822171-129.084615 62.115385 0.933044 0.520214 -0.000102373 0.113752 0.0370706 0.000819458-104.815384 -21.438462 0.823966 0.517128 -9.90543e-05 0.113476 0.0408779 0.000800143-104.815384 -13.030769 0.823483 0.517258 -0.000100472 0.113498 0.0409036 0.000800543-104.815384 31.553846 0.82129 0.517363 -0.000124431 0.113598 0.0409732 0.000799625-104.815384 62.115385 0.81779 0.516509 -7.0688e-05 0.113769 0.0410205 0.000796948

-56.657692 -21.438462 0.61846 0.510247 -8.04153e-05 0.123125 0.0483669 0.000759071-56.657692 -13.030769 0.617854 0.510381 -8.19067e-05 0.123152 0.0483979 0.00075948-56.657692 31.553846 0.616326 0.510482 -0.000105113 0.123225 0.0484398 0.000758576-56.657692 62.115385 0.612696 0.509638 -5.22254e-05 0.123401 0.0484933 0.000755916

-129.084615 4.307692 0.95118 0.520953 -0.000127936 0.112986 0.036427 0.000823021-104.815384 5.496154 0.835552 0.517234 -9.57254e-05 0.113018 0.0403901 0.000800438

-56.657692 6.050000 0.630285 0.510356 -7.70179e-05 0.122657 0.0478691 0.000759371-86.538462 -21.438462 0.73315 0.514402 -9.73839e-05 0.116076 0.0441705 0.000783468-86.038462 -13.030769 0.732697 0.514532 -9.8784e-05 0.116097 0.0441949 0.000783866-85.612821 5.361539 0.744678 0.514508 -9.40716e-05 0.11562 0.0436851 0.000783761-83.323077 31.553846 0.730343 0.514638 -0.000122926 0.116203 0.0442713 0.000782944-81.592308 62.115385 0.726873 0.513782 -6.89746e-05 0.116373 0.044317 0.000780263

68
Table A12: Transducer 032 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-126.661538 -19.853846 0.00898127 0.524668 -0.000386791 0.266557 0.0830812 0.000827132-126.661538 -10.969231 0.00867607 0.524838 -0.00038845 0.266723 0.0831678 0.000828295-126.661538 37.046154 -0.000409183 0.524886 -0.000372714 0.270204 0.0837184 0.000829099-126.661538 65.669231 0.00139633 0.524639 -0.000371061 0.269587 0.0836046 0.00082836-104.215385 -19.853846 0.0303918 0.521515 -0.000441947 0.258071 0.0807178 0.000804552-104.215385 -10.969231 0.0301067 0.521685 -0.000443625 0.258229 0.0808031 0.000805712-104.215385 37.046154 0.020917 0.521732 -0.000427756 0.261749 0.0813598 0.000806518-104.215385 65.669231 0.0227475 0.521485 -0.000426133 0.261123 0.0812444 0.000805777

-56.884615 -19.853846 0.0905949 0.513947 -0.000447954 0.235726 0.0750528 0.000758956-56.884615 -10.969231 0.0903589 0.514116 -0.000449678 0.235865 0.0751348 0.000760108-56.884615 37.046154 0.0809145 0.514162 -0.000433486 0.239483 0.0757064 0.00076092-56.884615 65.669231 0.0828059 0.513914 -0.000431937 0.238833 0.0755875 0.000760176

-126.661538 5.884615 0.0240557 0.52496 -0.000406474 0.260869 0.0822746 0.000828137-104.215385 5.823077 0.0454301 0.521806 -0.000461583 0.252396 0.0799131 0.000805555

-56.884615 5.673077 0.105545 0.514236 -0.000467475 0.230084 0.0742528 0.000759953-84.407692 -19.853846 0.0386804 0.517924 -0.000421536 0.254965 0.0791894 0.00078353-84.507692 -10.969231 0.0370359 0.51811 -0.000421946 0.255649 0.0793648 0.000784891-84.015384 9.982051 0.0561545 0.518261 -0.000444352 0.248371 0.0782544 0.000784695-82.984615 37.046154 0.0349066 0.518198 -0.000415031 0.256479 0.0795084 0.00078553-83.030769 65.669231 0.0350482 0.517963 -0.000411366 0.256492 0.0794932 0.000784902

69
Table A13: Transducer 034 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-130.261538 -21.438462 0.333514 0.507344 0.00237657 0.167402 0.068691 0.000916354-130.261538 -13.030769 0.334217 0.507117 0.0023846 0.167207 0.0685706 0.000914815-130.261538 31.553846 0.329482 0.507277 0.00238002 0.16845 0.0689263 0.000916137-130.261538 62.115385 0.330642 0.506173 0.00246482 0.168159 0.068743 0.000913762-105.669231 -21.438462 0.306291 0.498876 0.00327037 0.174007 0.071297 0.000933726-105.669231 -13.030769 0.306395 0.498607 0.00328188 0.173963 0.0712147 0.000932202-105.669231 31.553846 0.305035 0.498916 0.00326196 0.174352 0.0713359 0.000933033-105.669231 62.115385 0.30541 0.497807 0.00334811 0.174259 0.0712096 0.000930826

-56.753846 -21.438462 0.265176 0.481756 0.00488219 0.184962 0.0746626 0.000944642-56.753846 -13.030769 0.265 0.481468 0.00489531 0.184989 0.074598 0.000943125-56.753846 31.553846 0.265213 0.481846 0.00486826 0.18498 0.0746099 0.000943728-56.753846 62.115385 0.265223 0.480734 0.00495503 0.18498 0.0745101 0.000941599

-130.261538 4.307692 0.362463 0.508502 0.00224616 0.160074 0.0666176 0.000910954-105.669231 5.496154 0.336577 0.500088 0.00313395 0.166341 0.0691279 0.000928076

-56.753846 6.050000 0.296085 0.482992 0.00474296 0.177139 0.0724488 0.000938876-86.584615 -21.438462 0.267733 0.490824 0.00403319 0.184129 0.0741988 0.00094152-86.176923 -13.030769 0.267905 0.490561 0.0040443 0.184068 0.0741122 0.000939995-85.994872 5.361539 0.297868 0.49203 0.00389744 0.176502 0.0720405 0.000935899-83.984615 31.553846 0.266162 0.490853 0.00402612 0.184554 0.0742599 0.000940881-82.969231 62.115385 0.266626 0.489744 0.00411212 0.184439 0.0741271 0.000938655

70
Table A14: Transducer 036 Data Reduction Table

Transducer SSE Coefficient Coefficient Coefficient Coefficient a0 Coefficient a1 Coefficient a2

Temperature Temperature a0 a1 a2 Variance Variance Variance

[deg C] [deg C] [psi] [psi/mV] [psi/mV2] [psi2/σc2] [psi2/σc2/mV2] [psi2/σc2/mV4]

-130.861538 -21.438462 0.376821 0.505876 0.00446423 0.156509 0.0678386 0.00100236-130.861538 -13.030769 0.377497 0.506079 0.00445119 0.156335 0.0676912 0.00100089-130.861538 31.553846 0.374126 0.505958 0.00441803 0.15702 0.0678874 0.000999647-130.861538 62.115385 0.377174 0.506197 0.0042472 0.15639 0.0674439 0.000991145-105.965384 -21.438462 0.369541 0.503298 0.00439765 0.158049 0.0674188 0.000978601-105.965384 -13.030769 0.369596 0.503497 0.0043855 0.157992 0.0673045 0.000977114-105.965384 31.553846 0.36964 0.503453 0.00434632 0.158019 0.0672919 0.000975652-105.965384 62.115385 0.371876 0.503669 0.00417977 0.157548 0.0669032 0.000967353

-56.723077 -21.438462 0.355497 0.49859 0.00417058 0.160707 0.0662358 0.000926496-56.723077 -13.030769 0.355262 0.498786 0.00415884 0.160705 0.066137 0.000925003-56.723077 31.553846 0.356898 0.498778 0.00411686 0.160425 0.0660271 0.000923438-56.723077 62.115385 0.358755 0.498985 0.00395231 0.160027 0.0656639 0.000915233

-130.861538 4.307692 0.406632 0.506727 0.00438466 0.150737 0.0659058 0.00099843-105.965384 5.496154 0.400728 0.504188 0.00431441 0.152011 0.0653968 0.000974489

-56.723077 6.050000 0.387325 0.499498 0.00408563 0.154544 0.0641723 0.000922299-86.469231 -21.438462 0.347242 0.500842 0.00436942 0.16259 0.0679172 0.000957979-86.169231 -13.030769 0.347367 0.501041 0.00435717 0.16252 0.0677992 0.000956494-86.082051 5.361539 0.378274 0.501727 0.0042866 0.156582 0.0659053 0.000953888-84.269231 31.553846 0.347025 0.500988 0.00431867 0.162622 0.0678102 0.000955057-83.253846 62.115385 0.349353 0.501208 0.00415164 0.162132 0.0674153 0.000946735

71
Appendix B

Error Analysis Sensitivities

Plots in this Appendix show the impact of the MEADS system errors in a single variable sense

in order to show sensitivities to each individual error parameter. The net effects of all errors

together are shown in Figures 4.31–4.33. Here, the MEADS hardware uncertainties are shown in

Figures B1–B11 and the errors due to CFD uncertainties are shown in Figures B12–B14.

Figure B1: Estimation Errors due to Calibration Uncertainty

72
Figure B2: Estimation Errors due to Transducer Temperature Uncertainty

Figure B3: Estimation Errors due to Quantization

73
Figure B4: Estimation Errors due to SSE Noise

Figure B5: Estimation Errors due to SSE Temperature Uncertainty)

74
Figure B6: Estimation Errors due to Port Location Uncertainty

Figure B7: Estimation Errors due to Pressure Leak Uncertainty

75
Figure B8: Estimation Errors due to Time Tag Uncertainty

Figure B9: Estimation Errors due to Pneumatic Lag Uncertainty

76
Figure B10: Estimation Errors due to Thermal Transpiration Uncertainty)

Figure B11: Estimation Errors due to Vibration

77
Figure B12: Estimation Errors due to Ablation

Figure B13: Estimation Errors due to Deformation

78
Figure B14: Estimation Errors due to OML Change

79
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83
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1. REPORT DATE (DD-MM-YYYY)

01-10-2014

2. REPORT TYPE

Technical Memorandum

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Mars Entry Atmospheric Data System Modeling, Calibration, and Error

Analysis

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

757285.01.07.20

6. AUTHOR(S)

Karlgaard, C. D., Van Norman, J., Siemers, P. M., Schoenenberger, M.,

and Munk, M. M.

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

NASA Langley Research Center

Hampton, Virginia 23681-2199

8. PERFORMING ORGANIZATION

REPORT NUMBER

L–20464

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National Aeronautics and Space Administration

Washington, DC 20546-0001

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NASA

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NASA/TM–2014–218535

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Unclassified-Unlimited

Subject Category 19 Spacecraft Instrumentation and Astronics

Availability: NASA CASI (443) 757-5802

13. SUPPLEMENTARY NOTES

An electronic version can be found at http://ntrs.nasa.gov.

14. ABSTRACT

The Mars Science Laboratory (MSL) Entry, Descent, and Landing Instrumentation (MEDLI)/Mars Entry Atmospheric Data

System (MEADS) project installed seven pressure ports through the MSL Phenolic Impregnated Carbon Ablator (PICA)

heatshield to measure heatshield surface pressures during entry. These measured surface pressures are used to generate

estimates of atmospheric quantities based on modeled surface pressure distributions. In particular, the quantities to be

estimated from the MEADS pressure measurements include the dynamic pressure, angle of attack, and angle of sideslip. This

report describes the calibration of the pressure transducers utilized to reconstruct the atmospheric data and associated

uncertainty models, pressure modeling and uncertainty analysis, and system performance results. The results indicate that

the MEADS pressure measurement system hardware meets the project requirements.

15. SUBJECT TERMS

16. SECURITY CLASSIFICATION OF:

a. REPORT

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b. ABSTRACT

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c. THIS PAGE

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17. LIMITATION OF

ABSTRACT

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18. NUMBER

OF

PAGES

97

19a. NAME OF RESPONSIBLE PERSON

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

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802