Abstract. THOMAS, CASEY. Aerodynamic Validation using MER and Phoenix Entry Flight Data. (Under the supervision of Dr. Robert Tolson.

Transcription

1 Abstract THOMAS, CASEY. Aerodynamic Validation using MER and Phoenix Entry Flight Data. (Under the supervision of Dr. Robert Tolson.) Every NASA Mars landing mission has used a 70-degree half-cone forebody, however with different aft shapes for each mission. To keep with future NASA goals, it is important to evaluate the aerodynamic database for this forebody design. The purpose of this thesis is to first assemble the heritage aerodynamic data for this forebody, and then compare this ground based data with flight data taken from three most reason Mars entries (MER A, MER B, and Phoenix). The current Mars entry vehicle aerodynamic database (MEVAD) was updated from the initial Viking wind tunnel data with results from computational fluid dynamics (CFD) codes. The traditional MEVAD aerodynamic coefficients of C N, C Y, C m and C n were used in comparison with the flight derived coefficients. The metrics for validation were based upon the coefficient differences and the uncertainty associated with MEVAD. The validation of MEVAD indicated that coefficients from MEVAD produced slightly higher force coefficients than the flightderived coefficients during the second hypersonic instability, which resulted in less than 1 degrees difference in α and β. The difference from the coefficients comparison was equal to or less than the uncertainty from MEVAD and in the case of the force coefficients was half the uncertainty from MEVAD. An inconsistency in MEVAD was suggested by a difference of 2.5 degrees in the resulting α and β determined from the comparison of the interpolation of the flight derived moment and force coefficients into MEVAD from 20 second from parachute deployment to parachute deployment for all three entries examined. A rolling moment, C l was discovered for MER A and Phoenix

2 and in the case of Phoenix the C l corresponded to the change of the total angle of attack during the hypersonic instabilities regions.

3 Aerodynamic Validation using MER and Phoenix Entry Flight Data by Casey Thomas A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science Aerospace Engineering Raleigh, North Carolina 2011 APPROVED BY: Dr. Fred Dejarnette Dr. Larry Silverberg Dr. Robert Tolson Chair of Advisory Committee

4 Biography Casey Thomas was born in Northern Hospital of Surry County on August 22, 1983, to Mr. Donald and Gaynell Thomas. He is the older brother of Donna Thomas. He attended White Plains Elementary School, Gentry Middle School, and North Surry High School. In high school, he worked at his father s automobile repair center. It is here where he became interested in modifying mechanical components for better performance. After high school, he attended Surry Community College and where he developed an interest in engineering. He graduated with an Associates in Science from Surry Community College in He transferred to the University of North Carolina at Charlotte where he graduated with a Bachelors of Science Degree in Mechanical Engineering in He is currently working at the National Institute of Aerospace and at NASA Langley Research Center under the supervision of Dr. Robert Tolson. While at the National Institute of Aerospace he has been attending North Carolina State University. He plans on graduating with his Masters of Science in Aerospace Engineering in ii

5 Acknowledgements I would like to thank everyone that made this report possible. A special thanks to Dr. Tolson who guided and inspired me. A special thanks to Professor Blanchard who pushed me further than I thought was possible. To my family and friends thank you for your patients and encouragement. iii

6 Table of Contents List of Figures... vi List of Tables... viii Nomenclature... xi 1. Introduction Mars Entry Vehicle Aerodynamic Database Entry trajectory reconstruction Step one Step two Step three Atmospheric models Flight extracted model Atmosphere models effect on MEVAD inputs Atmosphere effects on MEVAD coefficients Density effects on flight derived aerodynamic coefficients Aerodynamic coefficient comparisons Force coefficients Moment coefficients Rolling moment Angle of attack and sideslip angle comparisons Summary of results Works cited Appendix Appendix A: The aerodynamic database Viking Pathfinder Mars Exploration Rover Phoenix Mars Science Laboratory Transition and free molecular flow regimes data Summary of the MEVAD Appendix B: Viking aerodynamic coefficients Wind tunnel data Viking ballistic range data Viking flight data Appendix C: Pathfinder aerodynamic coefficients iv

7 13.1 Pathfinder CFD data Appendix D: MER aerodynamic coefficients Appendix E: Phoenix aerodynamic coefficients Appendix F: MSL aerodynamic coefficients Appendix G: Free molecular flow and Knudsen number data Appendix H: Plots of quaternions, aerodynamic coefficient definitions, coefficient comparisons, and angles v

8 List of Figures Figure 3.1: Body-axis (X B, Y B, Z B ) and cruise-axis (X C, Y C, Z C ) coordinate systems...7 Figure 3.2: Accelerations along the body x-axis for MER A, MER B, and Phoenix...10 Figure 3.3: MER A angular rates in body coordinate system Figure 3.4: MER B angular rates in body coordinate system Figure 3.5: Phoenix angular rate components in cruise coordinate system Figure 3.6: MER A angular accelerations in body coordinate system Figure 3.7: MER B angular accelerations in body coordinate system Figure 3.8: Phoenix angular accelerations in body coordinate system...20 Figure 3.9: MER A accelerations in body coordinate system Figure 3.10: MER B accelerations in body coordinate system Figure 3.11: Phoenix acceleration components in cruise coordinate system Figure 3.12: Areodetic altitude and atmospheric relative velocity of the MER A, MER B, and Phoenix entry vehicles...30 Figure 3.13: Total angle of attack from all entry vehicles Figure 4.1: MER A Mach and Knudsen numbers for flight exacted and preflight atmospheres...36 Figure 4.2: MER B Mach and Knudsen numbers for flight extracted and preflight atmospheres...37 Figure 4.3: Phoenix Mach and Knudsen numbers for flight exacted and preflight atmospheres...39 Figure 5.1: MER A database force coefficient differences using two atmospheric models...40 Figure 5.2: MER A database moment coefficient differences using two atmospheric models...41 Figure 5.3: MER B database force coefficient differences using two atmospheric models...42 Figure 5.4: MER B database moment coefficient differences using two atmospheric models Figure 5.5: Phoenix force database force coefficient differences using two atmospheric models Figure 5.6: Phoenix database moment coefficient differences using two atmospheric models...45 Figure 6.1: MER A atmospheric comparison for C N...48 Figure 6.2: MER B atmospheric comparison for C m...49 Figure 6.3: Phoenix atmospheric comparison for C n...50 Figure 7.1: Combination coefficient determination procedure Figure 7.2: MER A C N comparison with three methods for determining coefficients..55 Figure 7.3: MER B C Y with three methods for determining coefficients Figure 7.4: Phoenix C N with three methods for determining coefficients Figure 7.5: MER A C m with three methods for determining coefficients Figure 7.6: MER B C n with three methods for determining coefficients Figure 7.7: Phoenix C n with three methods for determining coefficients vi

9 Figure 7.8: MER A, MER B, and Phoenix rolling moment aerodynamic coefficient, C l Figure 8.1: MER A angle of attack and sideslip angle differences from the combined coefficient method...70 Figure 8.2: MER B angle of attack and sideslip angle differences from the combined coefficient method...71 Figure 8.3: Phoenix angle of attack and sideslip angle differences from the combined coefficient method Figure 18.1: MER A Earth J2000 to body frame quaternion Figure 18.2: MER B Earth J2000 to body frame quaternion Figure 18.3: Phoenix PICS to cruise frame quaternion Figure 18.4: Aerodynamic coefficient definitions Figure 18.5: MER A C Y comparison with three methods for determining coefficients Figure 18.6: MER A C n comparison with three methods for determining coefficients Figure 18.7: MER B C N comparison with three methods for determining coefficients Figure 18.8: MER B C m comparison with three methods for determining coefficients Figure 18.9: Phoenix C Y comparison with three methods for determining coefficients Figure 18.10: Phoenix C m comparison with three methods for determining coefficients Figure 18.11: MER A angle of attack comparison with three methods for determining the angle Figure 18.12: MER A sideslip angle comparison with three methods for determining the angle Figure 18.13: MER B angle of attack comparison with three methods for determining the angle Figure 18.14: MER B sideslip angle comparison with three methods for determining the angle Figure 18.15: Phoenix angle of attack comparison with three methods for determining the angle Figure 18.16: Phoenix sideslip angle comparison with three methods for determining the angle vii

10 List of Tables Table 3.1 Body coordinate system to IMU frame quaternion Table 3.2 MER A PICS to Earth J2000 DCM Table 3.3 MER B PICS to Earth J2000 DCM Table 3.4 Distance Components from the IMU to COM in the Body-Axis Frame Table 3.5 Biases by mission Table 3.6 Misalignments in the rover IMU accelerations Table 3.7 Initial conditions for Mars entry missions in PICS Table 6.1 Moments of inertia and mass Table 7.1 MER A Force coefficient average differences Table 7.2 MER B Force coefficient average differences Table 7.3 Phoenix Force coefficient average differences Table 7.4 MER A moment coefficient average difference Table 7.5 MER B moment coefficient average difference Table 7.6 Phoenix moment coefficient average difference Table 11.1 Force and moment coefficient accuracy for Viking wind tunnel supersonic data...82 Table 11.2 Force and moment coefficient accuracy for Viking wind tunnel transonic data Table 11.3 MER aerodynamic database program uncertainties Table 11.4 Uncertainties for the Phoenix entry capsule aerodynamic database viii

11 Table 11.5 Uncertainties in the static coefficients for transitional and free molecular flow for MER and Phoenix Table 12.1 Viking wind tunnel data Table 12.2 Viking ballistic range data from PBR at Mach 2 in air Table 12.3 Viking ballistic range data from HFFAF at Mach 2 in air Table 12.4 Viking ballistic range data from HFFAF at Mach 11 in CO Table 12.5 Viking ballistic range data from HFFAF in air with Reynolds number held constant Table 12.6 Viking ballistic range data from HFFAF in CO 2 with Reynolds number held constant Table 12.7 Viking ballistic range data from HFFAF with total angle of attack held constant Table 12.8 Viking flight data from Viking Table 13.1 Pathfinder perfect gas aerodynamic coefficients determined from Halis CFD Table 13.2 Pathfinder real gas aerodynamic coefficients determined from LAURA CFD code Table 13.3 Pathfinder aerodynamic database aerodynamic coefficients Table 14.1 MER ballistic range testing Table 14.2 MER aerodynamic database program aerodynamic coefficients Table 15.1 Phoenix aerodynamic database program aerodynamic coefficients Table 16.1 MSL aerodynamic database program aerodynamic coefficients ix

12 Table 17.1 Pathfinder DAC aerodynamic coefficients Table 17.2 Pathfinder DACFree aerodynamic coefficients Table 17.3 Pathfinder aerodynamic database program aerodynamic coefficients Table 17.4 Pathfinder aerodynamic database program aerodynamic coefficients Table 17.5 MER aerodynamic database program DAC aerodynamic coefficients Table 17.6 MER aerodynamic database DACFree aerodynamic coefficients x

13 Nomenclature A com A imu A C A C l C m C N C n C Y D d bar g g x, g y, g z h J 2 Kn M n Na q q 1 acceleration at the center of mass acceleration at the IMU location reference area axial force coefficient rolling moment coefficient pitching moment coefficient normal force coefficient yawing moment coefficient side force coefficients spacecraft diameter CO 2 hard sphere gas diameter, 4.64e-10 m local gravity gravitation components in PICS geodetic altitude second zonal harmonic Knudsen number Mach number number density Avogadro's Number, 6.023e26 1/mole quaternion X sin(θ/2) xi

14 q 2 q 3 q 4 Y sin(θ/2) Z sin(θ/2) cos(θ/2) time rate of change of the quaternion P pressure specific gas constant for CO 2, R arm R cti R Mars R postion R e V V int V s distance from nose to moment reference location position vector from center of mass to the IMU Mars equatorial radius, m position of the spacecraft in PICS Reynolds number atmosphere relative velocity velocity in PICS speed of sound Acronyms AHFFAF APBR CFHT CFD DCM HALIS Ames Hypervelocity Free-Flight Aerodynamic Facility Ames Pressurized Ballistic Range Continuous Flow Hypersonic Tunnel Computational Fluid Dynamics Directional Cosine Matrix High Alpha Inviscid Solution xii

15 IMU LAURA LEFTP MER MEVAD PICS MRP MSL MST UPWT Inertial Measurement Unit Langley Aerothermodynamic Upwind Relaxation Algorithm Langley Eight Foot Transonic Pressure Tunnel Mars Exploration Rover Mars entry vehicle aerodynamic Database Planet Inertial Coordinated System Moment Reference Point Mars Science Laboratory Mach Six Tunnel Unitary Plan Wind Tunnel Greek α α T β λ d angle of attack total angle of attack sideslip angle mean free path of a gas molecule γ ratio of specific heats, 1.3 ρ density µ gravitation parameter ω ω Mars angular rotation rate of the spacecraft rotation rate of Mars angular accelerations xiii

16 1. Introduction. Planetary exploration has been one of humanity's goals since the time of Galileo. In keeping with this tradition, NASA developed a planetary exploration program. The NASA planetary exploration program has sent satellites to all planets in our solar system and has deployed entry vehicles to some. Entry vehicle designs are significantly more challenging from an engineering point of view because not only do they travel through space and enter orbit like the satellites, but also they must traverse the atmosphere of the host planet. The aerodynamics of the entry vehicle becomes critical to mission success in several ways. For example, by altering the landing location and by dissipating kinetic energy from planet approach velocity such that parachute deployment is possible. NASA has landed six entry vehicles on Mars to date. The entry vehicles sent to Mars have used a 70-degree half-cone angle forebody shape. This forebody shape is to be used for the entry phase on the upcoming Mars Science Laboratory landing mission. NASA selected this forebody shape due to its high drag characteristics at hypersonic velocities. High drag vehicles, such as those with the 70-degree half-cone angle forebody, facilitate the transfer of planet approach kinetic energy into the atmosphere of the planet, thus reducing vehicle velocity without additional propulsive maneuvers. Also, the last two Mars missions landed down track of the predicted landing site, which raised concerns about the current aerodynamic database 1,2. Because of these two reasons and NASA s future interest in Mars exploration, it is important to verify the current Mars entry vehicle aerodynamic database (MEVAD). 1

17 The goal of this thesis is to validate the existing MEVAD using flight data. The validation is based upon the comparison of flight data from the last few Mars missions, i.e. MER A, MER B, and Phoenix, and their respective aerodynamic databases. The two respective aerodynamic databases were used because the bounded static hypersonic instabilities are functions of velocity and altitude, which are mission dependent 3. The validation was based upon the difference in traditional aerodynamic coefficients, i.e., C N, C Y, C m, C n, and C l. C A is not in the list because it was used for calculating the density and as a result was not used in the comparison. The metrics of the validation were the nominal difference in the coefficients as well as the uncertainties associated with the coefficients from the corresponding aerodynamic database from each mission. The flight derived aerodynamic coefficients determinations from each mission require four data quantities, namely, atmospheric relative velocity, accelerations, angular rates, and density. The atmospheric relative velocity was determined from a trajectory reconstruction. All three entry vehicles had onboard accelerometers and gyros, which produced acceleration and angular rate data throughout entry. The atmospheric density was not measured directly on any of the examined missions. To circumvent the lack of density measurements, two methods for determining atmospheric properties were utilized. The first method for determining density utilized a preflight model that was used for mission planning and the second method derived density from flight data using the database axial coefficient, C A along with axial acceleration. The MEVAD contains all of the force and moment coefficients for each Mars mission. Each MEVAD coefficient is a function of total angle of attack, and Mach 2

18 number (or Knudsen number in the rarefied flow regime). Angle of attack, sideslip angle, and atmospheric relative velocity are determined from a trajectory reconstruction process. The Mach number and Knudsen number require a density. As mentioned, two different methods for determining density are used in this analysis. These methods for determining density will be discussed later in the report. Section 2 provides a brief summary of the MEVAD and Appendixes A-G provides a full report on the MEVAD along with tables for the aerodynamic coefficients. 2. Mars Entry Vehicle Aerodynamic Database. The MEVAD was created for Viking and was modified for every subsequent NASA Mars entry mission. The Viking aerodynamic database consisted of ballistic range and wind tunnel data 4,5. Since the Viking era, MEVAD has been updated with computational fluid dynamics (CFD). In its current state, the MEVAD is a combination of Viking wind tunnel data for subsonic through supersonic regimes and CFD results were used for the hypersonic through rarefied flow regimes 3. Each mission built around the core of MEVAD and developed a unique aerodynamic database for mission planning. Since the Viking era, subsequent additions to the coefficient database included regions where the entry vehicle is unstable. There are three vehicles instabilities; two bounded static hypersonic instabilities and one dynamic instability that all Mars entry vehicles have the possibility of going through during entry. The first in-flight or high speed bounded static hypersonic instability occurs as a result of the sonic line moving from the shoulder on the leeside (opposite the windward side) of the vehicle to the nose region. The sonic line moving results from the gas chemistry changing from 3

19 nonequilibrium to equilibrium. This change typically occurs during the transition from rarefied flow to continuum flow 6. The second in-flight or low speed bounded static hypersonic instability only occurs at low total angles of attack (approximately less than 4 degrees) and results from the sonic line moving back from the nose region to shoulder on the leeside. The sonic line moves due to the flow enthalpy decreasing in a near equilibrium gas chemistry regime 6. Viking flew at a high total angle of attack (approximately 11 degrees) so it never experienced the second instability. Each mission developed its respective mission aerodynamic database because the bounded static hypersonic instabilities are functions of flow energy and gas chemistry, which are mission dependent 6. The aerodynamic coefficients outside the bounded static hypersonic instabilities regions are not significantly different between the different aerodynamic databases and form the core of MEVAD. The third instability, the dynamic instability, occurs at low Mach numbers (less than Mach 3.5) and was observed in ballistic range tests for Viking and MER 4,7. The dynamic instability has been well documented from flight data for Pathfinder, MER, and Phoenix and is a function of center of mass and the basic geometry of these bodies 6,8,2. As mentioned earlier, the MEVAD was designed such that the dependent variables are Mach number (or Knudsen number for the free molecular flow and transitional regimes), and a total angle of attack. Total angle of attack is used instead of angle of attack and sideslip angle because an axisymmetric vehicle was used to obtain the aerodynamic database. Using total angle of attack, is sufficient to describe the out of the plane aerodynamics with two coefficients, which are the total normal force coefficient 4

20 C NT and total moment coefficient C mt. However, for flight coefficient comparisons with the database, the database total coefficients are broken up geometrically by projecting the total coefficients into angle of attack and sideslip planes, which result in the traditional aerodynamic coefficients of C N, C Y, C m, and C 3 n. In summary, the validation of MEVAD, uses the traditional coefficients and are discussed in section 7. The Mach and Knudsen numbers are determined from the entry reconstruction trajectory parameters combined with atmospheric properties discussed in section 5. A detailed discussion of the MEVAD with uncertainties is given in Appendix A and the total aerodynamic coefficients tables are given appendices B through G. For the purposes of this validation, the mission planning aerodynamic databases for MER and Phoenix missions are utilized. That is, the force and moment coefficients from MER and Phoenix aerodynamic databases, which are part of MEVAD, were compared to flight data from their respective missions. 3. Entry trajectory reconstruction. The MEVAD validation is based upon the comparison of the aerodynamic coefficients from MEVAD with flight derived aerodynamic coefficients, both of which need quantities from the entry reconstruction. The entry reconstruction method used initial conditions, measured accelerations, measured angular rates, as inputs into the equations of motion. These motion equations were integrated to solve for the velocity, attitude, and position of the entry vehicle during entry. With the velocity, angle of attack, sideslip angle, and position of the entry vehicle known, atmospheric properties (density, and pressure) were determined in a separate process. 5

21 The method of entry reconstruction used in this study is the double integration of the equations of motion in an inertial frame using the vehicle telemetry data obtained from the onboard inertial measurement unit (IMU). This reconstruction process is similar to the one used by the onboard navigation computer and require no aerodynamic, nor atmospheric models. Although, a gravity is needed, this will be presented later. The telemetry data, which consists of delta velocity and delta angles, is converted into accelerations and angular rates respectively. The accelerations and angular rates are processed before integration and discussed in section 3.2. The entry reconstructions for all three vehicles followed the same three steps. The first step transforms the telemetry data obtained from the IMU to a body coordinate system. Embedded in this step are the selections of a reference time and the definition of an inertial coordinate system. Step two processed the telemetry data by applying filters, and the third and final step was the double integration of the equations of motion in an inertial frame, which provided the needed trajectory results of position, velocity, and attitude as a function of time. 3.1 Step one. The first part of step one was to transform all telemetry data into a body coordinate system, which were the body axis frame (MER missions) and the cruise frame (Phoenix mission). The telemetry data was processed for Phoenix in the cruise frame (see Fig. 3.1), which is a 90-degree rotation about the axisymmetric axis from the body axis frame and for data processing purposes is equivalent to the body frame. 6

22 It is necessary that the telemetry data be transformed into a body coordinate system (see Fig. 3.1), since the aerodynamic forces and moments are referenced to a body coordinate system. The origin of both the body axis frame and cruise frame is at the center of mass, the X B axis is through the axis of symmetry, the Y B axis is perpendicular to the x axis and the Z B axis makes a right hand orthogonal system 9,3. The V vector in Fig. 3.1 is the atmosphere relative velocity vector and the angle between the atmosphere relative velocity vector and the x-axis is the total angle of attack. Figure 3.1 Body-axis (XB, YB, ZB) and cruise-axis (XC, YC, ZC) coordinate systems. The location of the IMU frame was measured in relationship to the entry vehicle before launch. The transformation of the telemetry data from the IMU frame to the body 7

23 coordinate system is not time dependent, thus, the transformation is accomplished once for the entire data sets with the quaternion in Table 3.1. MER A and MER B had two IMUs (one on the Rover and the other on the disposable backshell) that collected data during entry and both are included in the table. Table 3.1 Body coordinate system to IMU frame quaternion. q 1 q 2 q 3 q 4 MER A Rover MER A Backshell MER B Rover MER B Backshell Phoenix It was desired that all three missions use a common time system such that comparisons between the flight data from each mission can be made. The time reference point for all three vehicles was based an entry interface altitude, which occurred at an altitude of 125 km. Mission operations and mission designers commonly use this reference. At this altitude, the atmospheric drag is typically lower than the accelerometer sensitivity threshold. The raw telemetry data was available for Phoenix for the length of the entry, but for MER A, and MER B the telemetry data was available only after 90 seconds after entry interface. The telemetry data available for MER A, and MER B before 90 seconds were processed by the onboard navigation computer and as such, is currently in the body axis frame. The angular rates for MER A, and MER B before 90 seconds were derived from the quaternion and more details are given in the proceeding section. All telemetry data sets were processed for the trajectory from entry interface to landing; but, the aerodynamic database does not include parachute aerodynamics, thus 8

24 this analysis stops at parachute deployment. Fig. 3.2 y-axis shows the positive body x- axis accelerations on a log scale as a function of linear time for MER A, MER B, and Phoenix; top, middle and bottom figures respectively. The parachute deployment occurred near 250 seconds from entry interface for both MER A, and MER B and near 228 seconds from entry interface for Phoenix as shown in Fig In Fig. 3.2, the parachute deployment appears as the largest peak in acceleration, and an abrupt jump in acceleration precedes the peak. At entry interface, the accelerations due to the atmosphere drag are near the sensitivity limits of the IMU and are denoted in Fig. 3.2 with very small acceleration levels accompanied with relatively large oscillation in acceleration. The analysis of the flight data started after a steady increase in acceleration was observed in Fig The steady increase in acceleration was the result of higher atmospheric drag and indicated that the atmospheric drag is above the accelerometer sensitivity threshold. The accelerometer sensitivity threshold is mission dependent, as seen in Fig 3.2. The time of the accelerometer sensitivity threshold occurred at about 10 seconds from entry interface for both MER A and MER B missions and about 35 seconds from entry interface for Phoenix. The times for accelerometer sensitivity threshold and parachute deployment set the time domain for the MEVAD validation. That is, only trajectory data after the accelerometer sensitivity threshold and before parachute deployment were used for the comparison and subsequent validation. The time domains used for the comparison and validation for MER A, and MER B are from 10 to 250 seconds from entry interface and for Phoenix, 35 to 228 seconds from entry interface. 9

25 Figure 3.2 Accelerations along the body x-axis for MER A, MER B, and Phoenix. The final part of step one was to define an inertial coordinate system where the equations of motion were integrated. The inertial coordinate system selected was the Planet Inertial Coordinated System (PICS), which placed the origin at the center of mass of the planet and the fundamental plane along the equator. The x-axis is along the Mars vernal equinox, and the z-axis is along the rotational axis of the planet with positive direction in the direction of the north pole 9. The processing of the accelerations and angular rates is discussed in section 3.2, and is performed in the body axes coordinate system before finally being transformed to the PICS prior to integration. 10

26 3.2 Step two. Step two goal was to process the telemetry data in order to make adjustments in the measured values and in order to prepare the telemetry data for integration of the equation of motion in the PICS. Measurement adjustments are needed for a variety of reasons, such as, the digitizing process, misalignments, sensor biases and sensor noise. Part of the data processing also included determining angular accelerations, correcting for center of mass offset of the accelerometers and transforming the telemetry data from the body axis coordinate system to PICS. At the end of data processing, all steps are completed such that the integration of the equation of motion in PICS can be accomplished. The telemetry data was processed first to reduce noise from the sensors, which involved filtering the telemetry data. There were two methods for filtering telemetry data utilized in the validation process, namely batch filtering and low-pass filtering. The lowpass filtering was needed because of the separation in sampling frequencies between MER and Phoenix missions. Phoenix had a sampling frequency of 200 Hz where MER A, and MER B had a sampling frequency of 8 Hz. The higher frequency signals in Phoenix telemetry data introduced unwanted noise from the over sampling. The removal of the unwanted high frequency signals in Phoenix telemetry data was completed in such a way as to maintain frequencies similar to the frequencies recorded by the MER sampling rate. The low pass filter, which removed the unwanted high frequency signals, uses a cut off frequency to remove higher frequencies 10. The cut off frequencies utilized for Phoenix range between 15 and 17 Hz, discussed later in this section. 11

27 The batch filtering method removed noise by fitting a second order polynomial to a batch of data. A batch of data, i.e. number of data points over a time period, ranged from 7 to 901 data points as required for a specific data set, discussed later in this section. The measured angular rates for each mission are used to correct the accelerations for center of mass offset. In order to accomplish these corrections, angular accelerations are needed. Angular accelerations were determined from numerically differentiating the measured angular rates. As result of the angular rates being used to correct the accelerations and to determine the angular accelerations, the angular rates are processed first. It is vital that the angular rates be processed correctly, as any error in the angular rates will propagate through to the calculations of aerodynamic coefficients discussed in section 7. The measured angular rates were recorded for Phoenix throughout entry and for MER A, and MER B starting at 90 seconds from entry interface to landing. The angular rates after 90 seconds from entry interface for MER A, and MER B are used in combination with the angular rates determined from the quaternion before 90 seconds from entry interface. The angular rates for MER A, and MER B before 90 seconds from entry interface were determined from the quaternion using the following, (3.1) where ω x, ω y, and ω z, are the components of the angular rates, q is the quaternion and is the derivative of the quaternion with respect to time 8. 12

28 Determining the angular rate from the quaternion required that a derivative of the quaternion be determined which can potentially create additional noise in the rate data. These numerical differentiating errors could affect the angular rates significantly. Fortunately, from entry to 90 seconds from entry interface there was not a significant change in angular rates. The angular rates along the x, y, and z axes for MER A are shown in Fig. 3.3 top, middle, and bottom respectively with the blue line being the unfiltered angular rates and the red being the filtered angular rates. The angular rate about the x-axis shows an unexpected change around 120 seconds from entry interface, which will be discussed in the section 7. The change in angular rate in the x-axis is unexplained because the entry vehicle is supposed to be axisymmetric and therefore should not have a rolling moment, Cl, which would cause a change in angular rate. The largest difference between the filtered and unfiltered angular rates was a spike in the x-axis around 170 seconds from entry interface. The angular rates from 90 seconds after entry interface to parachute deployment were filtered by using a second order least square fit over 7 data points. Several batch sizes were tested to determine the optimal batch size. The criterion for selecting the optimal batch size was the sum of residual from the unfiltered and filtered data sets that were closest to zero. 13

29 Figure 3.3 MER A angular rates in body coordinate system. MER B angular rates are presented in Fig The results for the filtered angular rates are similar to MER A. The largest difference after the angular rates were filtered occurred in the x-axis around 170 seconds from entry interface. The angular rates from 90 seconds after entry interface to parachute deployment were filtered by using a second order least squares fit over seven data points, basically using the same process as MER A. Like MER A, the x-axis has an unexpected change in angular rate near 140 seconds from entry interface. 14

30 Figure 3.4 MER B angular rates in body coordinate system. Phoenix angular rates are presented in Fig The unfiltered angular rates for Phoenix (indicated by a blue curve) contained significantly higher noise levels compared to MER A, and MER B, as seen in Figs. 3.3 and 3.4. (Note: the blue curve in the Phoenix figure is more dominant than on either MER A or MER B figures). This noise is most likely due to a combination of digitization and over sampling. The y and z axes angular rate presents significantly smaller amplitude compared to the y and z axes MER A, and MER B. The amplitude difference in angular rates in the y and z axes is most likely the result of the torque from the thermal blanket for MER A, and MER B 12. Phoenix presented the same change in angular rate as MER A, and MER B about the x-axis near 15

31 130 seconds from entry interface. A low pass filter with a cutoff frequency of 17 Hz was used for filtering the angular rates from Phoenix. Figure 3.5 Phoenix angular rate components in cruise coordinate system. With the angular rates accomplished, the next process was to determine the bodyaxis to inertial quaternion and angular accelerations for each entry vehicle. The quaternion is needed to transform the telemetry data from the body axis coordinate system into the PICS. The angular accelerations were needed to correct for center of mass offset in the accelerations and for calculating the aerodynamic torque applied to the vehicle during entry. 16

32 The angular accelerations were determined by subtracting each adjacent filtered angular rate and dividing by the time difference. The angular accelerations were then filtered in a similarly manner as the angular rates. Again, it is necessary to take the derivative of digital data, which could add noise to the data. The noisy signals are most clearly visible in the angular accelerations before 90 seconds from entry interface for MER A, and MER B shown in Figs.3.6 and 3.7, where the angular accelerations are the results of two derivatives; one to obtain the angular rate from the quaternion, and the other to get the angular acceleration from the angular rates. MER A angular accelerations for the x, y, and z axes are presented in Fig. 3.6 top, middle, and bottom respectively. The blue lines are the unfiltered angular accelerations and the red are filtered angular accelerations, which were filtered with a second order polynomial over seven data points. The increase in angular acceleration and nonsymmetric values along the x-axis between 110 and 150 seconds from entry interface indicates that a torque was applied to the entry vehicle. The increase in noise level on the angular accelerations from entry to 90 seconds from entry interface was the result of two digital derivatives adding noise into data. 17

33 Figure 3.6 MER A angular accelerations in body coordinate system. MER B angular accelerations are shown in Fig The accelerations were filtered with a second order polynomial over seven data points. The angular acceleration about the x-axis is symmetric with the exception of a 7 second region near 130 seconds from entry interface. 18

34 Figure 3.7 MER B angular accelerations in body coordinate system. The angular accelerations for Phoenix are shown in Fig. 3.8 and were filtered with a low pass filter with a cutoff frequency of 15 Hz. The x-axis angular acceleration produced a slight decrease between 80 and 130 seconds from entry interface. The increase in angular acceleration amplitude after 200 seconds from entry interface is the result of the dynamic instability. 19

35 Figure 3.8 Phoenix angular accelerations in body coordinate system. As mentioned earlier, a quaternion was utilized to transform the acceleration data from the body coordinate system to PICS. The body coordinate system changes in relation to PICS throughout entry and thus is time dependent. The quaternion for MER A and MER B (shown in appendix H) transfers the telemetry data from body coordinate system to Earth J2000 coordinate system, which a direction cosine matrix (DCM) (shown in table 3.2 and 3.3) is used to transfer to the PICS. The Earth J2000 coordinate system is based on Earth mean equator and equinox of J2000 and is changing with respect to PICS, however for the purpose of MER A, and MER B entry reconstruction the Earth J

36 coordinate system to PICS transformation was assumed to be a fixed rotation 9. For the Phoenix data set, the cruise frame coordinate system to PICS is directly available. Table 3.2 MER A PICS to Earth J2000 DCM Table 3.3 MER B PICS to Earth J2000 DCM The JPL navigation team estimated the sun unit vector of MER A and MER B at entry interface. The sun unit vector is in the direction of the sun from the entry vehicle in Earth J2000 coordinate system at entry interface 9. It is necessary to rotate about the sun unit vector to achieve reasonable landing position and velocity. The proper rotational angle was determined for MER A, and MER B by using the landing conditions and parachute conditions to determine a feasible match. The resulting rotational angle about the sun vector was adjusted to -0.5 and degrees for MER A, and MER B respectively. Changing the rotational angle about the sun unit vector by more than 2 degrees caused trajectory parachute and landing conditions to be unrealistic. Small angle rotations about the sun vector have a large impact on parachute deployment conditions and a large impact on the trajectory angle of attack after the second hypersonic instability. The quaternion was calculated for Phoenix using an initial condition provided by the onboard navigation computer and the filtered angular rates using, 21

37 (3.2) where q is the quaternion, is the derivative of the quaternion and ω is the filtered angular rates. The last part of the data processing section focuses on the accelerations. The accelerations were first filtered then transformed into the PICS utilizing the body axis coordinate system to PICS quaternion. The basic filtering of the accelerations utilized the same processes as the angular rates; however, in addition biases were determined since accelerations data was recorded before entry interface. The accelerations unlike the angular rates had two special issues, the first was to correct for a center of mass offset and the second was correct for a misalignment. The accelerations like the angular rates were measured by the IMUs. However, the accelerations values from the IMUs are not based at the center of mass of the entry vehicle, required by the equation of motions. The measured accelerations include the accelerations at the center of mass and a rotational acceleration component, which it is necessary to remove. The removal of the rotational component in the acceleration was accomplished using, where A IMU is the acceleration value from the IMU, ( 3.3) is the angular acceleration, ω is the angular rate, Rcti is the distance from the IMU to the center of mass of the entry vehicle which is given in component form in Table 3.4, and Acom is the acceleration at the center of mass of the entry vehicle. 22

38 Table 3.4 Distance Components from the IMU to COM in the Body-Axis Frame. X (m) Y (m) Z (m) MER A Rover MER A Backshell MER B Rover MER B Backshell Phoenix After the accelerations were corrected for the center of mass offset, the biases were determined with acceleration data before entry interface. Before entry interface, the entry vehicle will have little detectable acceleration as atmospheric drag is well below the acceleration sensitivity threshold discussed earlier. This period before entry interface allows for an opportunity to determine the bias for the accelerometers. The integrated velocity values over several seconds before entry interface were fit with a first order polynomial for all three entry vehicles. The bias value for an accelerometer was the slope in the first order polynomial and bias values presented for each mission in Table 3.5. Table 3.5 Biases by mission. x (m/s 2 ) y (m/s 2 ) z (m/s 2 ) MER A 1.36E E E-07 MER B 5.32E E E-05 Phoenix -3.85E E E-04 With the acceleration corrected to the center of mass and biases removed, the accelerations from the rover and backshell IMUs are compared for MER A. Shown in Ref. 11, the accelerations from the rover and backshell disagree. MER B rover and backshell corrected acceleration showed similar results. The disagreement in accelerations indicates that one or both of the IMUs were misaligned. A misalignment in the IMU would result in a portion of the accelerations from the x-axis of the body 23

39 coordinate system to be measured in the y and z axes of body coordinate system. The portion of x-axis accelerations measured in y and z axes was determined by projecting the x-axis acceleration onto the accelerations of the y and z axes of the body coordinate system in a linear least squares fit. The slope of the linear least squares fit was interpreted as the misalignment in the IMU 11. The acceleration data used in the linear least squares projection was limited to two regions, the first one being entry to 10 second from entry interface and the second one from 140 to 250 seconds from entry interface. The resulting misalignments angles are used to correct MER A, and MER B rover IMU accelerations and are presented in Table 3.6. Shown in Ref. 11, after the IMU misalignment correction the acceleration data from both rover and backshell IMUs agree well for both MER A, and MER B. The misalignment angles determined for this validation are within degrees of the misalignment angles determined from Ref. 11. Table 3.6 Misalignments in the rover IMU accelerations. y (deg.) z (deg.) MER A MER B Like the MER A and MER B angular rates, the accelerations for are split before and after 90 second from entry interface. The onboard navigational computer processed the accelerations before 90 seconds from entry interface. The accelerations after 90 seconds from entry interface were filtered using a second order polynomial over a batch of data. The two acceleration data set time segments were combined into one data set for purpose of this validation. The unfiltered and filtered/corrected acceleration data sets from the MER A rover IMU are shown in Fig. 3.9, blue and red respectively. The filtered accelerations have 24

40 been corrected for the misalignment. The misalignment correction to the non-axial forces produces the largest change during the instability regions. The misalignment correction in the acceleration in the y-axis body coordinate system shown in the middle panel of Fig. 3.9 acts as a bias correction during the first and second instability resigns. The misalignment correction in acceleration along the z-axis shown in the bottom panel of Fig. 3.9 shifts the acceleration by less than 0.02 m/s2. The MER A acceleration data from 90 seconds from entry interface to parachute deployment was filtered using a second order least squares fit over seven data points. Figure 3.9 MER A accelerations in body coordinate system. 25

41 MER B x, y, and z axes accelerations in the body coordinate system are shown in Fig top, middle, and bottom respectively. The accelerations measured from the backshell IMU were used from entry to 90 seconds from entry interface and for the remainder of the acceleration data set, the rover IMU accelerations were used. The rover accelerations were fit with a second order least squares fit over seven data points. The misalignment correction shifted the acceleration less than m/s2 during the instability regions. Figure 3.10 MER B accelerations in body coordinate system. Phoenix x, y, and z axis accelerations in cruise frame are shown in Fig top, middle and bottom respectively. Phoenix accelerations posed special issues due to the 26

42 large amount of noise. Two filters are used to remove noise from the Phoenix accelerations. A low pass filter with a cut off frequency of 15 Hz was used first to remove the high frequency noise. The low frequency noise in the accelerations was decreased by fitting a second order polynomial over 901 data points. The second filter was utilized due to concerns that a lower cut off frequency for the low pass filter would remove parts of the acceleration signal. Figure 3.11 Phoenix acceleration components in cruise coordinate system. 3.3 Step three. The final step was to integrate the equations of motion in the PICS. The equations of motion were integrated to determine velocity and position. The integration of the 27

43 equation of motion required the initial conditions and the telemetry data, which was transformed into PICS. The initial conditions for all three missions came from the onboard navigation computer at entry interface and are given in Table 3.7. Table 3.7 Initial conditions for Mars entry missions in PICS. X (m) Y (m) Z (m) V x (m/s) V y (m/s) V z (m/s) MER A -2,833,658-1,800,899-1,064,442 3,522-4,166 1,383 MER B -3,128,460-1,608, ,209 3,535-4, Phoenix 1,060, ,718 3,296,296 1,465 5, The equations of motion for the entry vehicle in PICS are defined as, (3.4) The gravitation term is defined in PICS by differentiating the gravitational potential function. The gravitational model used in the integration process contains up to the second zonal harmonic, a portion of which is shown as, (3.5) where x, y, and z are the corresponding location in PICS, r was the magnitude of the position vector, J 2 is the second zonal harmonic of Mars, R Mars is the equatorial radius of Mars and µ is the gravitation parameter of Mars 14. Areodetic altitude was determined from position and was used for interpolation of the atmospheric models discussed in the next section. The areodetic altitudes for all three missions were determined utilizing the methods defined in Ref. 15. The solution for the areodetic altitude involved solving a fourth order polynomial and assumed Mars is an 28

44 oblate spheroid 15. The resulting areodetic altitudes by time from entry interface are present in top of Fig with MER A in blue, MER B in red, and Phoenix in black. The velocity determined from the integration of the equations of motion was the inertial velocity in the PICS frame and as such does not include the rotation of the Martian atmosphere. In addition, the MEVAD requires angle of attack, sideslip angle, and Mach number for interpolation, which require the atmospheric relative velocity. The atmospheric relative velocity was determined by assuming a rigid rotating atmosphere using, (3.6) where V x, V y, and V z are the atmospheric relative velocity components in PICS, V intx, V inty, and V intz are the velocities in PICS from the integration of the equation of motions, and ω Mars is the angular rotation rate of Mars. The magnitude of velocity of the entry vehicle, corrected for the rigid rotating atmosphere, is present in bottom of Fig MER A and MER B entered the atmosphere of Mars with a velocity around 5.3 km/s, where Phoenix had a slightly higher velocity of around 5.5 km/s. All three entry vehicles had a velocity between 0.3 and 0.45 km/s at parachute deployment with Phoenix parachute deployment occurred earliest near 228 seconds from entry interface. 29

45 Figure 3.12 Areodetic altitude and atmospheric relative velocity of the MER A, MER B, and Phoenix entry vehicles. The atmospheric relative velocity was transferred from PICS into to the body coordinate system using the quaternion from section 3.2. The atmospheric relative velocity (assuming no winds) was utilized to determine the total angle of attack, angle of attack, and sideslip angle from, (3.7) 30

46 (3.8) (3.9) The total angle of attack for MER A, MER B, and Phoenix is presented in Fig top, middle, and bottom respectively. The instability regions are clearly visible in MER A, and Phoenix. The first and second instabilities occurred for MER A and Phoenix near 75 and 125 seconds from entry interface. The first instability is not clearly visible for MER B; however, there was some question before launch if MER A, and MER B would go through the first instability 16. The second instability for MER B occurred near 125 seconds from entry interface. Figure 3.13 Total angle of attack from all entry vehicles. 31

47 4. Atmospheric models. The comparison between MEVAD and flight aerodynamic coefficients require the trajectory results from integration of the equations of motion and atmospheric state properties. The atmospheric state properties, namely pressure and density, are used to determine Mach numbers, and Knudsen numbers in the interpolation of MEVAD. Further, density is also needed in the calculation of all the flight derived aerodynamic coefficients. Lacking atmospheric measurement information during the entries introduce special challenges in obtaining flight aerodynamic coefficients. To help mitigate the lack of atmosphere measurements, and to limit the dependence of the analysis of unknown atmosphere properties, two independent approaches for determining density have been developed. The first method for determining the atmospheric properties was simply using the preflight models for MER A, MER B, and Phoenix. The preflight atmosphere models main focus was to predict winds near the surface 17,19. The second method employed a well-documented procedure utilized by earlier researchers, of using the axial coefficient, C A along with the axial measurement acceleration to obtain a flight extracted density. From density and the gravity model, the pressure is calculated from the hydrostatic equation, discussed later. The purpose for using two independent atmosphere models is to consider flight coefficient data during instances when both models produce coefficients with small differences. The densities from the two methods in determining coefficients from MEVAD are displayed and discussed in section 5. The two atmosphere models are also used in calculating the flight aerodynamic coefficients, which are compared in section 6. 32

48 4.1 Flight extracted model. The flight extracted model calculated density using, (4.1) In the density equation, CA is a function of total angle of attack, t and Mach number, M and is a transcendental equation because density appears on both sides of the equation and cannot be separated algebraically. To solve the C A equation requires an iterative process. This is accomplished by assuming an initial estimate of C A and subsequently iterating with the database. That is, with the new C A, the cycle repeats until the change in density decreased to percent of the previous density value. The trajectory reconstructed total angle of attack, t and the corresponding aerodynamic database for that particular mission were used when acquiring the C A. The Mach number calculation is shown subsequently. In conjunction with the density being calculated from equation 4.1, the pressure was calculated by integrating the hydrostatic equation as such, (4.2) The flight extracted atmosphere approach started at entry interface where the atmospheric pressure was near zero. For the initial pressure, zero was assumed. With these properties determined, Knudsen numbers and Mach numbers were simultaneously calculated. The resulting Mach number and Knudsen numbers are shown in section 5. 33

49 The atmosphere properties of importance to the database application are Mach number and Knudsen number. The Mach number calculations follows, (4.3) where the V is the atmospheric relative velocity and s is the speed of sound. The speed of sound was calculated using, (4.4) The Knudsen number is defined as, where λ d is the mean free path and L reff is the reference lengths for MER and Phoenix entry vehicles, which were 2.65 meters 16,3. The mean free path is, (4.5) (4.6) 4.2 Atmosphere models effect on MEVAD inputs. The two atmosphere dependent inputs to the MEVAD are Mach number and Knudsen number. It is necessary to show the difference that the atmosphere models have on the inputs to the database. This is discussed next. The atmospheric proprieties determined from both models introduced in this section generate two values of Knudsen numbers and two values of Mach numbers. The two resulting Mach and Knudsen numbers for MER A are shown in Fig. 4.1 top and bottom respectively. The solid blue line is the Mach numbers and Knudsen numbers determined utilizing the flight extracted atmospheric model and the red dotted line are the Mach numbers and Knudsen numbers determined with the preflight model atmospheric 34

50 model. The vertical dotted blue line is the transition line from transitional flow to continuum flow. The Mach numbers from the two atmospheric models agree with the exception of the first 30 seconds from entry interface. This difference occurs when the flow regime is transitional flow so Mach numbers were not used for interpolation for this period. The greatest difference in Mach number, where Mach number was used for interpolation into the aerodynamic database, was less than 1.7 and it occurred near 95 seconds after entry interface. The largest difference in Knudsen number, which was less than 50 percent, occurred at entry interface then decreased until 40 seconds from entry interface. This large difference in Knudsen number will require a comparison in the resulting interpolated coefficients from MEVAD for both methods of determining atmospheric properties and is shown later in this section. 35

51 Figure 4.1 MER A Mach and Knudsen numbers for flight exacted and preflight atmospheres. MER B resulting Mach and Knudsen numbers are shown in Fig. 4.2 top and bottom respectively. From entry interface to 25 seconds from entry interface the flight extracted model suffered from small accelerations, which caused large fluctuation in density and resulted in the signal issues in Mach and Knudsen numbers. The greatest difference between the flight extracted and preflight models for Mach number occurred before 40 seconds from entry interface, however, this was in the transitional flow regimes. The largest difference in Mach numbers where the Mach numbers were used for interpolation occurred near 90 seconds from entry interface and it was less than 1.5. From 36

52 125 seconds from entry interface to parachute deployment there was not a significant difference between atmospheric models for Mach numbers. MER B Knudsen numbers models agree very well with the exception of from entry interface to around 40 seconds from entry interface, which produced a difference less than 50 percent. Again this difference in Knudsen will require a comparison of the resulting coefficients from MEVAD shown later in this section. Figure 4.2 MER B Mach and Knudsen numbers for flight extracted and preflight atmospheres. 37

53 Mach and Knudsen number results for Phoenix are shown in Fig The Mach numbers from both atmospheric models agrees well throughout entry. The maximum difference in Mach numbers between the atmospheric models after 80 seconds from entry interface was less than 1.7 and it occurred near 110 seconds from entry interface. The Knudsen number comparisons shows a constant, but relatively small, difference between the preflight and flight extracted atmospheric models with the preflight model producing higher Knudsen number throughout the entry. The difference in the resulting coefficients from the interpolation of MEVAD utilizing both methods of determining atmospheric properties is shown later in this section. 38

54 Figure 4.3 Phoenix Mach and Knudsen numbers for flight exacted and preflight atmospheres. 5. Atmosphere effects on MEVAD coefficients. It is important to understand the effects that the two atmosphere models have in term of the aerodynamic coefficients. To accomplish this goal, the Mach number and Knudsen number (the MEVAD input quantities) time histories using the preceding equations for each of the three entry mission have been performed. The results from the preceding equation (using C A, measured acceleration, and trajectory reconstruction results) are referred to as flight Mach number and Knudsen number. In addition, the same calculations are made substituting the three preflight model atmosphere properties and are labeled preflight Mach number and Knudsen number. The difference results from both calculations are presented and discussed next. The differences in the interpolated coefficients from MEVAD for MER A force and moment coefficients utilizing both atmosphere models of determining atmospheric properties are presented in Figs. in 5.1, and 5.2. The difference in the coefficients near 125 seconds from entry interface occurred during the second hypersonic instability, which the coefficients from MEVAD in this region are very sensitive to density. The difference in density from the two methods appeared as an oscillation from 200 seconds from entry interface to parachute deployment. The uncertainties for in the MEVAD for MER (given in the Appendix D) is 0.01 for the force coefficients. Thus, the largest coefficient difference due to the atmosphere models is about 4 percent of the database uncertainty. The MEVAD uncertainties for the moment coefficients are and

55 for the hypersonic and supersonic flight regimes respectively 9. Thus, the differences in the moment coefficients are less than of 3 percent of the MEVAD uncertainty. Figure 5.1 MER A database force coefficient differences using two atmospheric models. 40

56 Figure 5.2 MER A database moment coefficient differences using two atmospheric models. The differences in the interpolated force and moment coefficients from MEVAD for MER B utilizing both methods for determining atmospheric properties are shown in Figs. 5.3 and 5.4. The difference near 10 seconds from entry comes from the fluctuations in acceleration used to determine the flight extracted atmospheric model. The oscillation near 175 seconds from entry interface to parachute deployment was the result of a difference in density. The differences from MEVAD are larger for MER B than for MER A and are less than 10 percent of uncertainty. 41

57 Figure 5.3 MER B database force coefficient differences using two atmospheric models. 42

58 Figure 5.4 MER B database moment coefficient differences using two atmospheric models. The differences in the interpolated force and moment coefficients from MEVAD for Phoenix utilizing both methods for determining atmospheric properties are shown in Figs. 5.5 and 5.6. The differences near 35 second from entry interface was the result of acceleration fluctuations from the flight extracted atmospheric model, and the differences around 120 seconds from entry interface were the result of MEVAD sensitive to density during the second hypersonic instability. The uncertainties from MEVAD for Phoenix for C N and C Y are 0.01 and 0.08 respectively. The moment coefficient uncertainties for C m and C n are and in the hypersonic regime and and in the 43

59 supersonic regime 3. The differences in the coefficients are less than 8 percent of the uncertainty of MEVAD for Phoenix. Figure 5.5 Phoenix force database force coefficient differences using two atmospheric models. 44

60 Figure 5.6 Phoenix database moment coefficient differences using two atmospheric models. The differences in the interpolated coefficients from MEVAD for the two methods of determining atmospheric properties are less than 10 percent uncertainty of the MEVAD force and moment coefficient uncertainty for all three entries. The 10 percent of uncertainty of MEVAD results indicate that the atmosphere models produce the same force and moment coefficients within 10 percent uncertainty of the database. This is good agreement showing that either atmosphere model can be used in the validation process. 45

61 6. Density effects on flight derived aerodynamic coefficients. It has been established that using either atmosphere models ( flight or preflight ) produce equivalent aerodynamic coefficient (within an acceptable tolerance, 10 percent) from the database. In this section, the flight coefficient using both atmosphere models are generated. The results from this analysis use the same nomenclature as the preceding section. That is, flight is used when flight derived atmosphere properties are used and preflight is used when the atmosphere models are used. The flight and preflight derived aerodynamic coefficients are the C N, C Y, C m, C n, and C l. The flight derived aerodynamic coefficients were calculated using, (6.1) (6.2) (6.3) (6.4) (6.5) where A y, and A z are accelerations in the y and z axes of the body coordinate system. M x, M y, and M z are the moments about the x, y, and z axes of the body coordinate system respectively and are determined using Euler's equations for rigid body rotation, 46

62 (6.6) (6.7) (6.8) The moments of inertia and mass for each entry vehicle used to calculate the flight derived aerodynamic coefficients are presented in Table 6.1. Ixx (Kgm 2 ) Table 6.1 Moments of inertia and mass. Iyy (Kgm 2 ) Izz (Kgm 2 ) Ixy (Kgm 2 ) Ixz (Kgm 2 ) Iyz (Kgm 2 ) Mass (Kg) MER A MER B Phoenix An aerodynamic coefficient sample from each of the three entry missions flight derived coefficients using the two atmosphere models is presented. The remaining flight derived coefficients determined with the two atmosphere models are not shown here, but yield similar conclusions. MER A flight derived C N from the flight extracted and preflight atmospheric models are shown in the top panel of Fig. 6.1 blue and red respectively. The percent difference between the C N from the two atmospheric models, based upon the uncertainty from MEVAD, is presented in the bottom panel of Fig The two atmospheric models come into agreement near 50 seconds from entry interface. Prior to 50 seconds, the differences are due to density differences. From 50 seconds from entry interface to parachute deployment the difference in C N from the two methods of determining atmospheric properties is small, less than of , which resulted in a percent difference of at most 25 percent of the uncertainty of MEVAD. This is acceptable for 47

63 validation purposes. Figure 6.1 MER A atmospheric comparison for CN. The coefficient selected as a sample for MER B is C m. MER B C m from the flight and preflight atmospheric models are presented in top of Fig. 6.2 blue and red lines respectively. The percent difference in C m from the two methods based upon uncertainty form MEVAD is shown in the bottom of Fig 6.2. Like MER A, the largest percent difference in the two methods occurred in the transitional flow regime prior to 50 seconds from entry interface, and decreased to good agreement thereafter. From 50 seconds from entry interface to parachute deployment the largest percent difference in C m was less than 48

64 18 percent of the uncertainty of MEVAD. Again, an acceptable uncertainty for validation purposes. Figure 6.2 MER B atmospheric comparison for Cm. C n has been selected as a sample for the Phoenix mission analysis. Phoenix C n from the two methods of determining atmospheric properties is shown in the top of Fig. 6.3 with the flight and preflight atmospheric models in red and blue respectively. The percent difference for C n based on uncertainty is shown in the bottom of Fig Like MER B C m, the largest difference in C n occurred near accelerometer sensitivity threshold and decreased rapidly. The difference between the C n from both methods of determining atmospheric properties was greater than the uncertainty of MEVAD from entry to 40 49

65 seconds from entry interface. Near 50 seconds from entry interface, the percent difference decreased to near 35 percent of the uncertainty of MEVAD. At 80 seconds from entry interface, both methods agree well, but around 210 seconds from entry interface the percent difference increased to near 30 percent of the uncertainty of MEVAD. Constraining the time domain to greater than 50 seconds from entry interface is satisfactory for proceeding with the validation Figure 6.3 Phoenix atmospheric comparison for Cn. The uncertainty level of MEVAD is utilized as a metric for accepting the time domains of the flight data for the validation process. The validation time domain for all three entries was limited to times larger than 50 seconds from entry interface to parachute 50

66 deployment based upon the preceding analysis of the flight coefficients. This analysis resulted in further limiting the time domain that was previously discussed using the accelerometer sensitivity threshold. For time greater that 50 seconds from entry interface, the two methods for determining atmospheric properties produce similar results for all flight derived coefficients, which produced a difference less than 35 percent of the uncertainty of MEVAD. 7. Aerodynamic coefficient comparisons. The validation of MEVAD was based upon the comparison of coefficients from MEVAD with flight derived aerodynamic coefficients, and a combination coefficient, which effectively is a combination of both the database and flight coefficient. The combination coefficient is unique to this analysis. In general, this coefficient was obtained by using a database inverse lookup procedure. That is, given the flight-derived coefficient (as previously discussed), a new angle of attack (and sideslip) is found utilizing the database using an inverse procedure. Note, that the force coefficients are used to get the combination moment coefficients while the flight moment coefficients are used to get the combination force coefficients. This is necessary, otherwise, if the same force coefficient is used to produce the same force combination coefficient there would be no difference in the coefficients. An example of the process for determining the combination coefficient is shown in Fig Here, the process shown in Fig. 7.1 is simplified for clarity. Other variables (ex. Mach number, Knudsen Number) are need when accessing the database. The corresponding input coefficient in Fig. 7.1 is C N (see section 6) and the corresponding 51

67 output combination coefficient is C m. This combination coefficient was determined for all force and moment flight derived coefficients. The resulting angles of attack (and sideslip) angles utilized for the interpolation into MEVAD for the combination coefficient are shown in appendix H. Figure 7.1 Combination coefficient determination procedure. All flight aerodynamic coefficients presented next depend upon the relative velocity obtained from the trajectory reconstruction discussed earlier. There are three different flight aerodynamic coefficients determined in this analysis. The first coefficient (labeled MEVAD ) is obtained using the trajectory reconstruction body angles and the ancillary database atmosphere parameters (Mach and Knudsen numbers) from the atmosphere reconstruction. The second set of coefficients (labeled accels for force coefficients and gyro for moment coefficients) were obtained using the classical approach for force and moment coefficient determination from flight. That is, acceleration measurements combined with density obtained using C A, and the aerodynamic force equation (see section 6) the force coefficients are calculated. The moment coefficients use an analogous procedure with the measure angular accelerations. The third coefficient shown is the combination coefficient and these are labeled combine/xx, where xx is the coefficient used to obtain the combined coefficient shown. 52

68 The aerodynamic coefficients graphs shown in Figs. 7.2 thru 8.3 contain three additional doted vertical lines, which indicate the time from entry interface that the entry vehicle reached Mach 25 (blue line), Mach 15(green line), and Mach 5(red Line). The time from entry interface, which the entry vehicles reached the indicated Mach numbers were mission dependent and the Mach numbers were used as references. The MER A, and MER B thermal blanket did not burn up as expected during entry 11,12. The parts of the thermal blanket that remained attached to MER A, and MER B has been shown to produce aerodynamic torques during entry. The torques from the thermal blanket for MER A, and MER B are discussed in Refs. 11 and 12. The extraneous aerodynamic moments generated from the thermal blanket were visible in all MER A, and MER B aerodynamic coefficients and appear between the second hypersonic instability and parachute deployment. 7.1 Force coefficients. Selected graphs for the force coefficients (Fig. 7.2: C N for MER A, Fig. 7.3: C Y for MER B, and Fig. 7.4: C N for Phoenix) from each mission is presented and discussed next. The graphs provides details of the major findings from this investigation, however, the entire set of force coefficients graphs from each mission not presented here are given in Appendix H. In addition, a summary table, which shows the coefficient differences for each force coefficient from each mission, is also presented. This table provides an overview as to how well the three methods for determining the coefficient agree with each other, as well as any significant differences between the flight coefficients and the database. 53

69 Three C N coefficients are shown on each of figs. 7.2, 7.3, 7.4, and the labels for each coefficient are as defined earlier. Examining Fig. 7.2 (C N ), it is seen that both the combined C N (using C m ) and the MEVAD showed good agreement from 50 to 60 seconds from entry interface. The C N derived from the acceleration (labeled accels ) near 50 seconds from entry interface is believed to be near or below the accelerometers sensitivity threshold, which produced unreliable signals. The first hypersonic instability, which occurred around 75 seconds from entry interface by using the database, show an unexpected lag (5 to 10 seconds) from both the other two C N coefficients. The lag was unexpected and is currently unexplained. The combined C N coefficient results do not show the second hypersonic instability as expected since aerodynamic moments are a function of trim angle, which changes. This effect produced a near zero moment as the entry vehicles remained trim at the different angles of attack, and/or sideslip angle. From Mach 25 to Mach 15 the database yielded slightly higher values of C N compared to the C N determined from the accelerations ( accel ). The large spikes shown in the combine determined C N originate from the digital derivative calculation used to obtain the angular acceleration, and should be ignored. The three methods that determined the coefficients produced similar results from Mach 5 to parachute deployment. However, the aerodynamics of the entry vehicle did change dramatically as it approached the third instability. The remnants of the thermal blanket for this mission exaggerated the moments compared to predicted values, and, as will be seen later in the Phoenix results. The 54

70 Combine C N yields consistently larger values ( about 0.002) for C N than the other two methods from Mach 5 to parachute deployment. Figure 7.2 MER A CN comparison with three methods for determining coefficients. Tables are provided in an attempt to summarize all the force coefficient results from the three methods for a given mission. Four time periods have been selected throughout the flight domain. The four time periods for each table were selected at intervals of aerodynamic interest, namely from 50 seconds from entry interface to before the first hypersonic instability region, in-between the two hypersonic instabilities regions, Mach 15 to Mach 5, and Mach 5 to parachute deployment. 55

71 All force coefficient average differences for the MER A are presented in Table 7.1. As seen in the table, all three methods produced smaller differences in C Y than C N from 50 to 75 seconds from entry interface. The smaller differences in C Y during the 50 to 75 seconds time interval from entry interface region relative to the C N values are most likely the result of the sideslip angle being somewhat less than angle attack,. C N and C Y average differences have about the same differences for the rest of the time intervals. With the exception of the results from the accels method near 50 seconds from entry interface, this is believed to be a low signal-to-noise acceleration. In summary, all three methods are well within the uncertainty of the force coefficient given in the MEVAD, which was Table 7.1 MER A Force coefficient average differences. Time from entry (s) IMU-accels (C N ) IMU-C m (C N ) accels-c m (C N ) IMU-accels (C Y ) IMU-C n (C Y ) accels-c n (C Y ) MER B C Y is presented in Fig In general, all three methods for determining C Y showed good agreement throughout entry with the database overshooting the results from the accels method from 50 seconds from entry interface to Mach 15. The large spikes in the combined coefficient of C Y (using C n ) during the second hypersonic instability, which occurred near 125 seconds from entry interface, were the results of the digital derivatives used to obtain the moment. The aerodynamics of the entry vehicle changed dramatically around Mach 15 due to the remnants of the thermal blanket for this 56

72 mission, as mentioned earlier. From Mach 15 to parachute deployment the combined coefficient of C Y yields higher values than the results from the accels method of about Figure 7.3 MER B CY with three methods for determining coefficients. MER B force coefficients, C Y, average differences are presented in Table 7.2. All three methods utilized to produce C N and C Y have about the same differences throughout entry. As with MER A, the differences in C N and C Y for all three methods are within the uncertainty of the normal force coefficient for MEVAD of Table 7.2 MER B Force coefficient average differences. Time from entry (s)

73 IMU-accels (C N ) IMU-C m (C N ) accels-c m (C N ) IMU-accels (C Y ) IMU-C n (C Y ) accels-c n (C Y ) The results from Phoenix aerodynamic force coefficient, C N is shown in Fig The results from the accels method for Phoenix C N produced lower values of C N than the database from 50 seconds to around 150 seconds from entry interface. The combined coefficient of C N (using C m ) suffered from issues resulting from digital derivative used to calculate the moments, which were interpolated into MEVAD and resulted in the large spikes between 50 seconds from entry interface and Mach 25 and again near 125 second from entry interface. The results from the accels method pattern matched that of the database, however, the difference in the values of C N from the accels method and the database vary from C N near 125 seconds from entry interface to zero near 200 second from entry interface. All three methods agree around 180 seconds from entry interface. Near 205 seconds from entry interface, all three methods utilized for determining C N oscillate about zero. This oscillation is the result of the dynamic instability. Like MER A, and MER B, the combined coefficient of C N yielded higher values of around compared to the results from the accels method for C N from Mach 5 to parachute deployment. 58

74 Figure 7.4 Phoenix CN with three methods for determining coefficients. Table 7.3 is the average difference in the coefficients from all three methods for Phoenix C N. The largest difference in the coefficients occurred during the 50 to 70 seconds from entry interface region, which was dominated by the errors in combined coefficients of C N and C Y (using C m and C n respectively). The average difference in the force coefficients for Phoenix showed that the average difference decreases from 127 seconds from entry interface to parachute deployment. Again all average differences are within the uncertainty of the normal coefficients for MEVAD of

75 Table 7.3 Phoenix Force coefficient average differences. Time from entry (s) IMU-accels (C N ) IMU-C m (C N ) accels-c m (C N ) IMU-accels (C Y ) IMU-C n (C Y ) accels-c n (C Y ) In summary, flight extracted force coefficients for the three missions examined are well within the published database uncertainty. Difference between the database and between the two flight extraction methods are an order of magnitude smaller than the uncertainty in the database indicating a large degree of conservatism currently exists that eventually can be removed without compromising the mission. 7.2 Moment coefficients. Similar to the force coefficients, a sample of the moment coefficients results is presented and discussed below for C m during MER A entry (Fig. 7.5), C n during MER B entry (Fig. 7-6), and C n during Phoenix entry (Fig. 7.7). The moment coefficients that are not presented here are shown in appendix H and yield similar results. MER A C m is presented in Fig. 7.5 and showed good agreement between all three methods throughout entry. The torque from the remnants of the thermal blanket is clearly shown from Mach 5 to parachute deployment. From Mach 5 to parachute deployment the results from the gyros method yield higher values for C m than the database and the combination coefficient of C m (using C N ). 60

76 Figure 7.5 MER A Cm with three methods for determining coefficients. The average difference in the moment coefficients are presented in Table 7.4 for MER A. The lowest average difference for all three methods for determining coefficients occurred between 135 and 195 seconds from entry interface. The results from the gyros method produced the largest average difference for the moments, which was from 195 to 250 seconds form entry interface. The uncertainty for MEVAD for the MER mission in moment coefficients is flight regime dependent and was and for the hypersonic and supersonic regimes respectively 8. From Table 7.4 all of the methods are within the uncertainty limits of MEVAD. 61

77 Table 7.4 MER A moment coefficient average difference. Time from entry (s) IMU-gyros (C n ) IMU-C Y (C n ) gyros-c Y (C n ) IMU-gyros (C m ) IMU-C N (C m ) gyros-c N (C m ) MER B C n is shown in Fig. 7.6 and produced similar results as MER A. From 50 seconds from entry interface to Mach 15, the database over predicted Cn by compared to the other two methods. The results from the gyros method and the combination coefficient of C n (using C Y ) show good agreement from 50 seconds from entry interface to Mach 15. The results from the gyros method produced greater values for C n than the database and combination coefficient of C n from Mach 15 to parachute deployment. 62

78 Figure 7.6 MER B Cn with three methods for determining coefficients. MER B moment coefficient average differences are shown in Table 7.5. The differences in all three methods are within the uncertainty of MEVAD the MER mission. The results from the gyros method produced larger values of for the average differences in C n compared to the database and combination coefficients of C n (using C Y ) from 195 to 250 seconds from entry interface. Table 7.5 MER B moment coefficient average difference. Time from entry (s) IMU-gyros (C n ) IMU-C Y (C n ) gyros-c Y (C n ) IMU-gyros (C m )

79 Table 7.5 Continued IMU-C N (C m ) gyros-c N (C m ) Phoenix C n is presented in Fig There is good agreement between all three methods from 50 to 75 seconds from entry interface. The MEVAD over predicted the C n from 75 to 200 seconds from entry interface compared to the combination coefficients of C n (using C Y ). From Mach 15 to 200 seconds form entry interface the results from the gyros and combination coefficient of C Y, matched. At 200 seconds from entry interface the gyros values of C n became the largest with an oscillation about zero due to the dynamic instability. The C Y and MEVAD values for C n oscillate and drift negatively from 200 seconds from entry interface to parachute deployment. The reason for the negative drift is unknown. 64

80 Figure 7.7 Phoenix Cn with three methods for determining coefficients. Table 7.6 provides a summary of the average differences between the methods for determining Phoenix moment coefficients. Like MER A, and MER B the gyros and corresponding coefficients of C Y and C N produced unexplained locally large average differences from 191 to 230 seconds from entry interface. The database uncertainty levels for Phoenix C m are and for hypersonic and supersonic flow regimes respectively. The database uncertainty levels for C n are and for the hypersonic and supersonic regimes respectively 3. The average differences for the moment coefficients between 92 and 118 seconds from entry interface, which is in hypersonic 65

81 regime, are at the level of the uncertainty for all methods. The average differences in all three methods with the expectation of this region are within the uncertainty of MEVAD. Table 7.6 Phoenix moment coefficient average difference. Time from entry (s) IMU-gyros (C n ) IMU-C Y (C n ) gyros-c Y (C n ) IMU-gyros (C m ) IMU-C N (C m ) gyros-c N (C m ) In summary, the three methods for determining the flight moment coefficients, C m and C n, for the three missions, produce differences of the same order of magnitude as the uncertainty in the database. Unlike the force coefficients, there is no conservatism in the published database uncertainties. 7.3 Rolling moment. All three entry vehicles are assumed to be axisymmetric and therefore should not produce a significant rolling moment (C l ) throughout entry. Phoenix aerodynamic database estimated the C l uncertainty of approximately 1.24 e-6 3.The angular rates about the axisymmetric axis from the IMU telemetry data showed an increase during entry, shown in section 3, Figs. 3.3, 3.4, and 3.5. The increase in angular rate is the result of an aerodynamic torque or a torque generated by the moment of inertia coupling terms. The moment of inertia coupling terms (I xz and I xy, see table 6.1) for MER A and Phoenix produced a torque that was one to two orders of magnitude less than the torque calculated about the x-axis. MER B had a higher I xy, which produced a torque of the same order of magnitude as the calculated torque about the x-axis and was the dominating term after 66

82 150 seconds from entry interface. The torque was converted into a C l using equation 6.5 from section 6. The resulting C l for MER A, MER B, and Phoenix are presented in the top, middle and bottom of Fig. 7.8 respectively. MER A C l shown in the top panel of Fig. 7.8 increased starting near 50 second (in the rarefied-flow flight regime) from entry interface to near zero at Mach 25. In the transitional flight regime, it s possible that unequal pressure on the vehicle could cause a rolling moment, C l, which dissipates when the MER A flight regime transitioned to continuum. In the continuum flow regime, specifically between Mach 25 and Mach 5, MER A had a higher than expected C l of approximately 5e-6 then transited to -5e-6 near 160 seconds from entry interface. As seen and discussed earlier, the MER missions had a thermal blanket remnant that possibly affected the aerodynamic moments and a significant change was easily observed after Mach = 5 (see Fig. 7.5) Clearly, any remnant could affect the C l as the entry vehicle is no longer axisymmetric. MER B C l shown in Fig. 7.8 middle panel shows similar results as MER A for the transitional flight regime with the C l decreased to near zero. From Mach 25 to Mach 15 MER B behaved as expected with a C l around 1e-6. Around 150 seconds from entry interface to parachute deployment, the torque from the moment of inertia coupling term I xy becomes the largest term in the torque about the x-axis and completely explains the deviation shown in Fig. 7.8 for MER B. Phoenix C l is shown in the bottom panel of Fig Again, the C l in the transitional flow regime is potentially due to unequal pressures on the entry vehicle. Near 75 seconds from entry interface to Mach 15, which was during the two hypersonic 67

83 instabilities, the C l mirrors the total angle of attack during the two instability regions, shown in Fig. 3.17, which suggests a connection with the these regions. At Mach 15, the C l decreased to near zero and remained near zero until 205 seconds from entry interface where the C l suddenly increases. The sudden increase in C l near parachute deployment is possibly due to the Phoenix becoming less dynamically stable as it approaches the third instability. Figure 7.8 MER A, MER B, and Phoenix rolling moment aerodynamic coefficient, Cl. 68

84 8. Angle of attack and sideslip angle comparisons. The comparisons of the aerodynamic moment and force coefficients from the previous section could be interpreted as a differences in angles of attack and sideslip angles. The graphs in appendix H show the comparison of the angles of attack and sideslip angles from the trajectory reconstruction, the angles used in the inverse database lookup to generate the combined force coefficients, and the angles used in the inverse database lookup to generate the combined moment coefficients from each mission. In summary, the differences in the angles are small. For example, the graphs shown in the Appendix H indicate that the difference in angles of attack and sideslip angles determined from the trajectory reconstruction and the combined coefficient angles are less than 2.5 degrees for MER A and MER B and less than 3 degrees for Phoenix. However, when comparing the difference in angles for the combined coefficients, the angles are larger and this is discussed next. For the combined coefficient method discussed earlier, angle of attack is obtained for both a force and a moment coefficient. Similarly, sideslip angle is also determined from a force and moment coefficient. It is anticipated that these angles would be the same between a force and moment coefficient. The differences between the angles utilized in generating the combined force and moment coefficient are shown in Fig. 8.1, Fig. 8.2, and 8.3, representing the three missions examined. The top panels show the angle of attack differences, while the bottom panels show the sideslip angles for each figure. All three entries presented a common pattern from around 20 seconds before parachute deployment to parachute deployment. The difference in angle of attack and 69

85 sideslip angle for all three entries for this region was around 2.5 degrees. The density is the same for both the force and moment coefficients so the difference in angle of attack and sideslip angle is not the result of an atmospheric difference. This difference for MER A, and MER B could be the result of torque from the remnants of the thermal blanket. However, Phoenix did not have a known issue near parachute deployment, which could account for this difference. This angle of attack and sideslip difference angles between the angle of attack and sideslip angles was equal for all three entries and could be interpreted as a representation of the uncertainty of the database in terms of angle of attack and sideslip, or simply an inconsistency in the MEVAD. Figure 8.1 MER A angle of attack and sideslip angle differences from the combined coefficient method. 70

86 Figure 8.2 MER B angle of attack and sideslip angle differences from the combined coefficient method. 71

87 Figure 8.3 Phoenix angle of attack and sideslip angle differences from the combined coefficient method. 9. Summary of results. The validation of MEVAD includes the assembly of the heritage aerodynamic database data for a 70-degree half-cone angle blunt body used in all NASA Mars missions. The aerodynamic database data for Viking, Pathfinder, MER, Phoenix, and MSL were assembled for the purpose of understanding the evolution of MEVAD for application to this research, as well as for future research projects. Each entry mission developed a unique aerodynamic database due to the vehicles hypersonic instabilities being mission dependent. 72

88 The validation was based upon the comparison of flight derived coefficients from MER A, MER B, and Phoenix entries missions with coefficients from their respective database. Coefficients from MEVAD and the flight derived aerodynamic coefficients required trajectory reconstruction results. The trajectory reconstruction was completed in three steps, which lead to the preparation of the flight data for integration by the equations of motion. The first two steps include a host of preparation functions, such as, filtering, bias removals, center-of-mass corrections, and instrument misalignment adjustments. Initial conditions from the navigational computer were used to start the integration process. In addition to results from the trajectory reconstruction, both the coefficients from MEVAD and flight derived coefficients require an atmospheric component, namely density. The lack of density measurements was overcome by using two different methods. This provided a useful domain constraining mechanism by comparing the database dependent (Mach and Knudsen numbers) and coefficient variables. The first method of determining density relied on using preflight atmospheric models, one for each mission. The second method consists of a density reconstruction by using the axial coefficient and axial accelerations, and reconstructed velocity. In general, the resulting atmospheric models were used to generate coefficients from MEVAD and the flight data. The coefficients from interpolation into MEVAD from the two methods for determining density were within 10 percent of the uncertainty of MEVAD throughout entry. The differences in the flight derived coefficients from the two methods for generating density were within 35 percent of the uncertainty from MEVAD after 50 73

89 seconds from entry interface. However, this difference decreased to about 5 percent of the uncertainty of the database over most of the time domain with an increase up to 30 percent as the vehicle approached parachute deployment. Because of larger differences in the coefficients before 50 seconds from entry interface for the flight derived coefficients, the validation was limited to data from 50 seconds from entry interface to parachute deployment. The comparison between the coefficients from MEVAD and flight derived coefficients utilized the traditional aerodynamic coefficients of C N, C Y, C m, and C n. The traditional aerodynamic coefficients were determined in three different methods. The first method was the interpolation of the coefficients from MEVAD, the second was the direct calculation of the flight derived coefficients, and the last method was a combination utilizing the flight derived coefficient in a database inverse lookup procedure to generate a combination coefficient. The comparisons of the flight derived coefficients and MEVAD resulted in the suggestion that MEVAD yields slightly higher values of C N, and C Y for MER A, and Phoenix during the second hypersonic instability, which amounts to less than 1 degree difference in angle of attack and sideslip angle in this region. The 1 degree difference could be the result of a higher trim angle than expected during the second hypersonic instability. MER B had excellent agreement between MEVAD and the flight derived coefficients throughout entry, which suggested MEVAD has an angle sensitivity because MER B had the lowest total angle of attack of all three entries. 74

90 All three entry missions from around 20 seconds before parachute deployment to parachute deployment showed an inconsistency between the flight derived force and moment coefficients. The flight derived moment and force coefficients were interpolated into MEVAD to yield angles of attack (and sideslip angles), which resulted in a 2.5 degree difference between the angles of attack (and sideslip angles). This pattern of a 2.5 degree difference was equal for both the comparisons of the angle of attack and sideslip angle for all three entries. Finally, the difference from the coefficients determined with the three different methods were compared with the uncertainties provided with MEVAD. The differences in coefficients were equal to or less than the uncertainties for all three entry missions, which indicated that MEVAD is valid. However, the given uncertainty in the database for force coefficients appears to have a larger uncertainty relative to the flight results. The flight moment uncertainties are of the same order of magnitude as the given database uncertainties. It is felt that the existing conservatism in the flight coefficient uncertainties can be significantly reduced without compromising mission success. Future work is needed to determine if the difference in the coefficients, which is less than the uncertainty of MEVAD, was large enough to account for MER and Phoenix missions landing down track of the predicted landing site. The unexpected relatively large rolling moment, C l for MER A, and Phoenix is of interest because the aerodynamic behavior driving it is unknown. The C l calculated for Phoenix suggests a correlation between the C l and the total angle of attack or hypersonic instabilities. 75

91 10. Works cited. 1. Desai, Prasun N. and Knocke, Philip C., "Mars Exploration Rovers Entry, Descent, and Landing Trajectory Analysis" AIAA AIAA/ASS Astrodynamics Specialist Conference and Exhibit, Providence, RI, August 16-19, Desai, Prasun N., Prince, Jill L., Queen, Eric M., Cruz, Juan R. and Myron R. Grover, "Entry, Descent, and Landing Performance of the Mars Phoenix Lander." AIAA AIAA, pp Edquist, Karl T., Desai, Prasun N. and Schoenenberger, Mark., "Aerodynamics for the Mars Phoenix Entry Capsule", AIAA/AAS Astrodynamic Specialist Conference, Honolulu, HI, pp Sammonds, Robert I. and Kruse, Robert L. "Viking Entry Vehicle Aerodynamics at M=2 in air and Some Preliminary Test Data for Flight in CO2 at M=11", NASA TN D-7974, Flaherty, T. Aerodynamics Data Book VER-1,. NASA TR , Gnoffo, Peter A., Braun, Robert D., Weilmuenster, K. J., Mitcheltree, Robert A., Engelund, Walter C., Richard W. Powel., "Prediction and Validation of Mars Pathfinder Hypersonic Aerodynamic Database" 7th Joint Thermophysics and Heat Transfer Conference : JOURNAL OF SPACECRAFT AND ROCKETS, Albuquerque, NM, Schoenenberger, Mark, Hathaway, Wayne. Yates, Leslie. Desai, Prasun. "Ballistic Range Testing of the Mars Exploration Rover Entry Capsule" AIAA , 43rd AIAA Aerospace Science Meeting and Exhibit, Reno, NV, Prasun N. Desai, Mark Schoenenberger, F.M. Cheatwood, "Mars Exploration Rover Six-Degree- Freedom Entry Trajectory Analysis" Vol. 43, 5, Journal of Spacecraft and Rockets, Sept-Oct, 2006, 9. Blanchard, Robert C., "Entry Descent and Landing Trajectory and Atmosphere Reconstruction for the Mars Exploration Rovers Missions A and B" NASA-JPL subcontract CCNS20568F, The George Washington University, April 15, The Mathworks Inc. FIR Filter Design. The Mathworks, Accelerating pace of engineering and science. [Online] [Cited: 4 2, 2010.] Tolson, Robert. "An analysis of MER entries" unpublished. 12. Tolson, Robert H., Willcockson, William H. Desai, Prasun N. Thomas, Paige., "Anomalistic Disturbance Torques During Entry Phase of the Mars Exploration Rover Missions A Telemetry and Mars- Surface Investigation", AAS , 29th Annual AAS Guidance and Control Conference, Breckenridge, CO, Thomson, William Tyrrell, Introduction to space dynamics, , Mineola : Dover Publications Inc., Vallado, David A. Fundamentals of Astrodynamics. New york : Microcosm Press,

92 15. Sofair, Isaac. A method for calculating exact geodetic latitude and altitude. Dahlgren : Naval Surface Warfare Center, NSWC TR AD-A Schoenenberger, Mark, Cheatwood, F. McNeil and Desai, Prasun N. "Static Aerodynamic of the Mars Exploration Rover Entry Capsule". AIAA rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Kass, D. M., Schofield, J. T., Michaels, T. I., Rafkin, S. C. R., Richardson, M. I., and Toigo, A. D., "Analysis of AtmosphericAtmospheric Mesoscale Models for Entry, Descent, and Landing", E12, Journal of Geophysical Research, Nov 25, 2003, Vol. 108, pp. ROV 31-1 to ROV D.M. Kass, J.T. Schofield, J. Crisp,E.S. Bailey, E.H. Konefat, W.J. Lee, E.C. Litty, R.M. Manning, A.M. San Martin, J.R. Willis, R.F. Beebe, J.R. Murphy and L.F. Huber,. MER1/MER2-M-IMU-4-EDL- V1.0. Planetary Data System-PDS Explorer. [Online] NASA, 8 24, [Cited: 3 28, 2010.] IMU-4-EDL-V1.0&volume=merimu_1001&dir=CATALOG. 19. Tamppari, L. K, Cantor, B. A. Friedson, A. J. Ghosh, A. Grover, M. R. Hale, A. S. Kass, D. Martin, T. Z. Mellon, M. Michaels, T. Murphy, J. Rafkin, S. Smith, M. D. Simth, P. H. Tsuyuki, G. Tyler, D. Wolff, M. "ATMOSPHERIC CHARACTERISTICS EXPECTED AT THE PHOENIX LANDING SEASON AND LOCATION", Seventh International Conference on Mars, Pasadena, CA, Cengel, Yonus A. and Cimbala, John M. Fluid Mechanics Fundamentals and applications. New York : McGraw-Hill, Engelund, Walt. Pathfinder Aerodynamic Database Program Blanchard, Robert. MSL Aerodynamic Database Program Blanchard, Robert C. and Walberg, Gerald D. Determination of the Hypersonic Continuum/Rarefied- Flow Drag Coefficient of the Viking Lander Capsule 1 and Aeroshell From Flight Data TP Gnoffo, Peter A., Weiilmuenster, K. James. Braun, Robert D. and Christopher I. Cruz. "Influence of Sonic-Line Location on Mars Pathfinder Probe Aerothermodynamics". Journal of Spacecraft and Rockets, Vol. 33, 2, March-April Blake, W. W. "Experimental Aerodynamic Characteristics of the Viking Entry Vehicle over the Mach Range of ". NASA TR , MARTIN MARIETTA CORPORATION, McGhee, Robert J., Siemers III, Paul M. and Pelc, Richard E. "Transonic Aerodynamic Characteristics of the Viking Entry and Lander Configurations", NASA TM X-2354, Spencer, David A., Blanchard, Robert C. Braun, Robert D. Kallemeyn, Pieter H. and Sam w. Thurman "Mars Pathfinder Entry, Descent, and Landing Reconstruction", Vol. 36, 3, JOURNAL OF SPACECRAFT AND ROCKETS, May-June Kirk, Donn B., Intrieri, Peter F. and Seiff, Alvin, "Aerodynamic Behavior of the Viking Entry Vehicle: Ground Test and Flight Results" J. Spacecraft, Vol. 15, 4, July-August, 1978, pp Malcolm, Gerald N. and Chapman, Gary T. "A Computer Program for Systematically analyzing Free- Flight Data to Determine the Aerodynamics of Axisymmetric Bodies." TN D-4766,

93 30. Seiff, Alvin and Wilkins, Max E., "Experimental Investigation of a Hypersonic Glider Configuration at Mach Numberof 6 and at Full-Scale Reynolds Numbers." NASA TN D-341, Moffett Field : Ames Research Center, January Edquist, Karl T., "Computations of Viking Lander Capsule Hypersonic Aerodynamics with Comparisons to Ground and Flight Data.", AIAA , Atmospheric Flight Mechanics Conference and Exhibit, Keystone, Colorado, Weilmuenster, K. James and II, H. Harris Hamilton, "Calculation of Inviscid flow over Shuttle-Like Vehicles at high Angles of Attack and Comparisons with Experimental data". NASA TP-2103, Cheatwood, F. McNeil and Gnoffo, Peter A., "User's Manual for Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA)" NASA TM 4674, Mitcheltree, Robert A., "Correction to Drag Coefficients Due to Base Pressure". 35. Moss, James, Blanchard, Robert C. Wilmoth Richard G. Bruan, Robert D., "Mars Pathfinder Rarefied Aerodynamics: Computations and Measurements" AIAA , 36th AIAA Aerospace Science Meeting and Exbit, Reno, NV 1998, January Prasun N. Desai, Robert C. Blanchard,Richard W. Powell, "ENTRY TRAJECTORY AND ATMOSPHERE RECONSTRUCTION METHODOLOGIES", NASA, Hampton,

94 Appendix 79

95 11. Appendix A: The aerodynamic database. The current Mars entry vehicle aerodynamic database (MEVAD) is a product of the heritage data. This database has changed from purely wind tunnel data during the Viking era, to initial CFD for Pathfinder, to matured CFD and CFD modified with a with a base pressure correction term, for the current database 5,20,21. These changes are important, because it explains the evolution of the aerodynamic database. These changes were implemented when data from flight, testing, or CFD showed a significantly difference from the current database. Viking being the first mission relied the most on wind tunnel data, however, this data was at lower Mach numbers and this data had the fewest number of data points compared to the other missions 5. Viking was the only entry vehicle to land on Mars that had pressure taps. The pressure taps were used to measure dynamic pressure and thusly density during entry. The dynamic pressure was utilized with measured accelerations to calculate the aerodynamic coefficients directly 23. Pathfinder extended the MEVAD by adding CFD code 21,24. MER, Phoenix, and MSL used wind tunnel data, and improved CFD code 16,3,22. The following describes the MEVAD data by mission in chronological order. Each source of data determined the moment reference point (mrp) at different locations. The mrp was relocated to the nose. The mrp relocation was done using, (11.1) where R arm is the distance to the nose from the original location of the mrp. R arm is positive if the original mrp is in front of the nose and negative if the original mrp is 80

96 behind the nose. Some of the data presented here was not used in the final mission planning aerodynamic database, so it was not used in the validation phase of this report and is presented here for completeness Viking. The Viking database was composed of wind tunnel data, ballistic range data, and the flight data from the Viking 1 entry capsule. The coefficients determined from these data sets can be found in appendix B. The Viking mission was the only mission to rely solely on wind tunnel data for static aerodynamic mission planning. The Viking wind tunnel data came from two primary sources. These two references where combined into a summary, Ref. 5. The first source of data covered the Mach (M) number range The data provided from the Mach number range Mach 1.5 to Mach 4.6 was collected in NASA Langley Research Center Unitary Plan Wind Tunnel (UPWT). The data from Mach 6 came from the 20 inch Mach Six Tunnel (MST) and the Mach 10 data came from the 31 inch Continuous Flow Hypersonic Tunnel (CFHT) 25. The second source of data provided the transonic data, which was over the Mach number range of 0.4 to Mach 1.2. The second source of data was collected at Langley Eight Foot Transonic Pressure Tunnel (LEFTP) 26. The data for Mach numbers between Mach 1.5 and Mach 10 from the first data source only listed data from a total angle of attack of 0 to 20 degrees and the summary source listed data from a total angle of attack of 0 to 23 degrees for this same Mach number range. The source for higher total angle of attack data is unknown. The Viking database had the least amount of data off all 81

97 the missions and had a large gap between Mach 6 and Mach The wind tunnel data forms the foundations for MEVAD and was used to validate the CFD data. The accuracies for the Viking wind tunnel data are presented in Tables 11.1 and Accuracies were based upon "data repeatability and instrument calibration" 25,26. Table 11.1 Force and moment coefficient accuracy for Viking wind tunnel supersonic data. Accuracy Facility M ±C N ±C A ±C m UPWT UPWT UPWT UPWT UPWT UPWT MST CFHT Table 11.2 Force and moment coefficient accuracy for Viking wind tunnel transonic data. LEFTP Mach C N ± C A ± C m ± C l ± C N ± C Y ± C P ± M ± α, ± deg The Viking ballistic range data came from two sources, both of which were collected at the Ames Research Center ballistic range facilities 4,28. These coefficients are located in appendix B. 82

98 The first source of Viking ballistic range data relied on the methods developed in Ref. 29 for determination of the aerodynamic coefficients 4,28. The Viking ballistic range data from the second source, which was Ref. 28 was digitized from plots, the reported data will have digitization errors and the reported uncertainties will not include the uncertainties from the digitization process. The ballistic range data was collected by divided the ballistic range into evenly spaced sections. At the end of these sections the location, time and total angle of attack were measured, so an effective drag coefficient (C Deff ) could be determined. During testing the total angle of attack changed from section to section making it impossible to determine the effect on the static aerodynamic coefficients due to a constant total angle of attack. The ballistic range tests were designed to determine the dynamic aerodynamic coefficients so a changing total angle of attack was necessary for testing. Because of the changing total angle of attack C D is modeled using, (11.2) when the total angle of attack is equal to root mean square of the angle of attack (α rms ) the effective drag is equal to C 30 D. The first source of ballistic range data consisted of three types of tests, two with air at Mach two and one with CO 2 at Mach The tests in air were conducted with scale models of Viking utilizing different base covers in different ballistic ranges. The center of mass (com) of model A was on the axis of symmetry and was located diameters from the nose. The com of model B was located off the axis of symmetry by 83

99 diameters from the centerline and diameters from the nose. Model B was designed such that it would have a trim angle of 11.5 degrees 4. The test for model A was conducted in air using the Ames Pressurized Ballistic Range (APBR). APBR was 62 meters long and had 24 observation locations. Model B had two tests, one was in air and the second was in CO 2 ; both were conducted using the Ames Hypervelocity Free-Flight Aerodynamic Facility (AHFFAF). AHFFAF was 23 meters long and had 16 observation locations. The Reynolds number for the air tests based on diameter of the models was 600,000 and for CO 2 test was 890,000. Model A was propelled using a 57 mm smooth bore powder gun and model B utilized a 38.1 mm diameter deformable piston light gas gun 4. Due to the nature of these tests the data was scattered around a point of interest. The point of interest of the air tests was Mach 2 and for the CO 2 tests it was Mach 11. The second source of ballistic range data for Viking came from Ref. 28. Two tests were conducted in the AHFFAF and both were used to determine the C D. The first test was to compare air and CO 2 while holding the Reynolds number constant at 800,000 and changed the total angle of attack. The total angle of attack for the air test varied from 5 to 15 degrees for the air test. The CO 2 test varied the total angle of attack from 1 to 13 degrees. The purpose of this test was to determine if there was a difference between the effects of air and CO 2 on the aerodynamics. CO 2 had a higher C D (less than 0.1) for all total angles of attack. The difference in C D decreased as total angle of attack increased 28. The second test from the second source of Viking ballistic range data changed Reynolds number while holding total angle of attack constant. The total angle of attack 84

100 was held constant at 11.2 degrees and Reynolds number varied from 500 to 1,000,000 and is shown in Fig The second test used two scale models of Viking with an offset of the com from the axis of symmetry by diameters, similar to model B used for the test conducted in Ref. 4. The diameters of the models were 1.02 and 2.03 cm, which were propelled from deformable piston light gas guns with bore diameters of 1.27 and 2.54 cm respectively. The test concluded that as Reynolds numbers drops to free molecular flow regime C D increases and C D is constant for Reynolds numbers larger than 100, The aerodynamic coefficients were recoverable from Viking Lander Capsule 1 flight data because the Viking capsule had five pressure ports so that the dynamic pressure and thusly the density could be measured. With the measured dynamic pressure the aerodynamic coefficient equations were solved directly 23. This data was digitized for use in Ref. 31 from the plots used in Ref. 23. This digitized data is presented in appendix B. The data was collected along the Viking 1 entry trajectory and as a result, the data is not as scattered as the ground test data. The Viking flight data yields the only independently measured density during entry. The independently measured density allowed the first chance to validate the MEVAD Pathfinder. The Pathfinder database was composed of a combination of CFD of the forebody and CFD of the forebody with a base correction term determined from Viking flight data. The first set of CFD data was calculated for the forebody of the spacecraft and compared at selected points to the full body solution

101 The first set of CFD data for Pathfinder data is presented in appendix C. The CFD code used to do this was the High Angle of Attack (α) Inviscid Solution (HALIS) for perfect gas data and for real gas data it was determined using Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) 32,33. The LAURA data only includes the forebody of the spacecraft and presents some comparisons between the forebody pressure and the approximated base pressure to determine the effect on the full body solution 24. At Mach 22.3 the base pressure is only 0.6 percent of the forebody pressure which implied that there is no significant effect from the base pressure. At Mach 1.9 the base pressure was 10 percent of the forebody and therefore it is significant 24. The second CFD data set came from the Pathfinder aerodynamic database and calculated the forebody coefficients then added a correction term to account for the base pressure or backshell pressure 21. This data is shown in appendix C. This data is believed to be a combination of LAURA and HAILS; however, no code was specifically indicated in the source. The base correction equation came from Viking 1 and 2 flight pressure data. The base correction equation was created by using the measured base pressure from flight data, which was assumed to be the average base pressure. The free stream pressure was subtracted from the measured base pressure and then the value was divided by the free stream pressure to generate a base pressure correction coefficient. The base pressure correction coefficient was fit with a third order polynomial equation producing the base correction equation. The methodology and procedures behind the base correction equation are defined in Ref. 34. The base correction equation is later used in MER, 86

102 Phoenix, and MSL mission planning aerodynamic databases and as such, was used in the MEVAD validation 16,3,22. The effect of the base pressure is assumed to be insignificant on C NT and C MT. The base correction equation is the following, (11.3) where M is the Mach number, a is , b is , c is and d is From approximations made in Ref. 34 it is shown that C D and C A are equal such that the base correction equation is applied as such, (11.4) The Pathfinder aerodynamic database used this equation for Mach numbers equal to and less than Mach 10. Above Mach 10 there was a velocity version of this equation 21. However, it is believed that at Mach 10 and above the base pressure terms are not significant so the velocity version of the equation was not used for this summary database Mars Exploration Rover. The Mars Exploration Rover (MER) database is composed of two sources of data. The first is ballistic range data and the second is the MER aerodynamic database program version 9.1 which is composed of CFD and CFD with the base correction term derived from Viking flight data 7,16. The MER ballistic range data was collected at the Aeroballistics Research Facility at Eglin Air Force Base with two series of tests. The MER ballistic range data is presented in appendix D. The models that were tested had three different com locations and the dimensions of the models were 70 mm diameter and mm in length. The test 87

103 range was 207 meter long with fifty orthogonal spark shadowgraph stations. The stations were connected to a chronograph, which marks the time as each image is captured, then the aerodynamic parameters were determined from parameter identification techniques 7. The focus of the ballistic range test, like Viking ballistic range testing was on the dynamic coefficients so only the axial coefficient was determined. A multi-fit line was fit to data and was used to determine the C A 7. This data was digitized for Mach numbers of 1.5, 2, 3, and 3.5. The MER aerodynamic database program contained LAURA CFD forward body solutions for all data points. This data is presented in appendix D and was used for mission planning so was used for the validation of MEVAD. The supersonic solutions, which are for Mach numbers less than or equal to Mach 6.3, added the base correction equation, which is equation 11.3 and solved an equilibrium version of the CFD code. The Mach numbers greater than or equal to Mach 8.8 used only the solution of forebody to determine the aerodynamic coefficients as the backshell was thought not to significant contribution to the overall static aerodynamics. For Mach numbers greater than 8.8 the nonequilibrium effects are estimated using LAURA 16. Uncertainties for this data were used in Ref. 8 and presented in Table The MER database and uncertainties were used for the MEVAD validation. Table 11.3 MER aerodynamic database program uncertainties. Hypersonic Static 3 Sigma Uncertainty C A 5% C N,C Y C m,c n Supersonic Static C A 10% 88

104 Table 11.3 continued C N,C Y C m,c n Phoenix. The Phoenix database is made up entirely of the Phoenix aerodynamic database program version 2.3. This data is presented in appendix E and was used for mission planning so it was used for the MEVAD validation. The Phoenix aerodynamic database program used three sets of data. Mach numbers less then Mach 1.5 came from the Viking wind tunnel data, Mach numbers greater than Mach 2 and less than Mach 6.3 used LAURA forebody solutions with the base correction equation, which is equation 11.3, and for Mach numbers greater then Mach 8.8 LAURA forebody solutions were used. Again, it is believed that at higher Mach numbers the base pressure is not significant to the static aerodynamics. Like MER, the CFD solution for aerodynamic coefficients for Mach numbers greater than 8.8 estimated the nonequilibrium effects using LAURA 3. The Phoenix aerodynamic database uncertainties are explained as such. The uncertainties for the aerodynamic coefficients for Phoenix are based on engineering judgment and past experience and are very similar to MER 3. These uncertainties are presented in Table 11.4 and come from Ref. 3. Table 11.4 Uncertainties for the Phoenix entry capsule aerodynamic database. Hypersonic Static Kn<.001,M>10 3 Sigma Uncertainty C A 3% C N,C Y C m,c n C E-06 89

105 Table 11.4 continued Supersonic Static 1.5<M<5 C A 10% C N,C Y C m,c n C E Mars Science Laboratory. At the time of the construction of this database, the Mars Science Laboratory (MSL) had not been launched and as such the aerodynamic database is still evolving and will change after this database is constructed. Currently the only source for aerodynamic data for MSL is the MSL aerodynamic database program version This data is presented in appendix F. Like the Phoenix database, the MSL database used Viking wind tunnel data for Mach numbers less than 1.5. This data was extrapolated for total angle of attack of 24 degrees. Mach numbers between 1.5 and 6.03 used the LAURA forebody data with the base correction equation, which is equation The MSL database utilized the LAURA forebody solution for Mach numbers greater than Mach 8.8. The higher Mach numbers range in MSL estimated the nonequilibrium effects using LAURA Transition and free molecular flow regimes data. In transition and free molecular flow regimes the distance between the molecules of the gas are at relatively large distances compared to the diameter of the entry vehicle and thus the gas behaves differently when it is in a continuum flow. In free molecular flow regime the collisions between molecules are neglected changing behavior again 16,

106 Due to the changes in behavior of the gas the static coefficients must be modeled differently. The model of the free and transitional flow regimes is divide by using the Knudsen number, which is the ratio of the mean free path of the gas over the diameter of the entry vehicle instead of Mach number 16. All data in these regimes are divided up by Knudsen number or are described as free molecular flow. Two sources of the data came from Pathfinder. MER, Phoenix, and MSL used the same data and it was used in the MEVAD validation. All three sets of data are presented in appendix G. In the first Pathfinder source Ref. 35 and the MER data Ref. 16 the static coefficients were determined by using Direct Simulation Monte Carlo (DSMC) methods. The DSMC was used in DSMC Analysis Code (DAC) and DACFree codes, which modeled the molecular collisions by using a variable hard shell method 16,35. The second source of Pathfinder data Ref. 21 contained data sets similar to the other references; however, it is not known how this data was generated. All Knudsen number data was generated such that it increased logarithmically. The first Pathfinder data source assumed the atmosphere to contain 97% CO 2 and 3% N 2 by mass and solution were obtained with and without chemical reactions 35. It is unknown how the second data source for Pathfinder, which is the Pathfinder aerodynamic database, generated the Knudsen number data. However, it is believed that the DAC and DACFree codes were used as well. The MER aerodynamic database transitional flow data assumed the atmosphere to contain 100% CO 2 at higher Knudsen numbers, where the chemical reactions are not as important, and at lower Knudsen numbers 97.3% CO 2 and 2.7% N 2 by mass 16. The MER 91

107 transitional flow data was used in the MER aerodynamic database, Phoenix aerodynamic database, and currently in the MSL aerodynamic database and was utilized for MEVAD validation 8,3,22. The uncertainties for this data were reported in two different sources and are present in Table These uncertainties were utilized for the validation of MEVAD. Table 11.5 Uncertainties in the static coefficients for transitional and free molecular flow for MER and Phoenix. Transitional/Free Molecular Aerodynamics MER Phoenix C A 5% 5% C N,C Y C m,c n Summary of the MEVAD. The Viking era wind tunnel data is the foundation of MEVAD. Ballistic range testing done for Viking showed a difference in C D between air and CO 2. The difference in C D is possibly a source in difference between the MEVAD and flight data. MER and Phoenix aerodynamic databases used CFD forebody solution and added a base pressure correction term for low Mach numbers and forebody solutions only for higher Mach numbers. The base pressure correction equation is equation 11.3 and was determined from Viking flight data. Data and uncertainties from MER and Phoenix mission planning aerodynamic databases were utilized for MEVAD validation. 92

108 12. Appendix B: Viking aerodynamic coefficients Wind tunnel data. Table 12.1 Viking wind tunnel data. Mach number total angle of attack C A C NT C MT

109 Table 12.1 Continued

110 Table 12.1 Continued

111 Table 12.1 Continued

112 Table 12.1 Continued

113 Table 12.1 Continued

114 Table 12.1 Continued

115 Table 12.1 Continued

116 Table 12.1 Continued

117 12.2 Viking ballistic range data. Table 12.1 Continued Table 12.2 Viking ballistic range data from PBR at Mach 2 in air. Mach number RMS of total angle of attack C D

118 Table 12.3 Viking ballistic range data from HFFAF at Mach 2 in air. Mach number RMS of total angle of attack C D Table 12.4 Viking ballistic range data from HFFAF at Mach 11 in CO2. Mach number RMS of total angle of attack C D

119 Table 12.4 Continued Table 12.5 Viking ballistic range data from HFFAF in air with Reynolds Reynolds numbers number held constant. total angle of attack C D Velocity Km/sec Table 12.6 Viking ballistic range data from HFFAF in CO2 with Reynolds Reynolds numbers number held constant. total angle of attack C D Velocity Km/sec

120 Table 12.7 Viking ballistic range data from HFFAF with total angle of attack Reynolds numbers 12.3 Viking flight data. held constant. total angle of attack C D Velocity Km/sec Table 12.7 continued Table 12.8 Viking flight data from Viking 1. Mach number total angle of attack C A C NT

121 Table 12.8 Continued

122 Table 12.8 continued

123 Table 12.8 continued

124 Table 12.8 continued

125 Table 12.8 continued

126 Table 12.8 continued

127 Table 12.8 continued

128 Table 12.8 continued

129 Table 12.8 continued

130 Table 12.8 continued

131 Table 12.8 continued

132 Table 12.8 continued Appendix C: Pathfinder aerodynamic coefficients Pathfinder CFD data. Table 13.1 Pathfinder perfect gas aerodynamic coefficients determined from Mach number Halis CFD. total angle of attack C A C N C mt

133 Table 13.1 continued

134 Table 13.2 Pathfinder real gas aerodynamic coefficients determined from Mach number LAURA CFD code. total angle of attack C A C NT C mt

135 Table 13.3 Pathfinder aerodynamic database aerodynamic coefficients. Mach number total angle of attack C A C NT C mt

136 Table 13.3 Continued Appendix D: MER aerodynamic coefficients. Table 14.1 MER ballistic range testing. Mach number total angle of attack C A Table 14.1 continued

137 Table 14.1 continued

138 Table 14.1 continued

139 Table 14.1 continued

140 Table 14.1 continued

141 Table 14.1 continued

142 Table 14.1 continued Table 14.2 MER aerodynamic database program aerodynamic coefficients. Mach number total angle of attack C A C N C mt

143 Table 14.2 continued

144 Table 14.2 continued

145 15. Appendix E: Phoenix aerodynamic coefficients. Table 15.1 Phoenix aerodynamic database program aerodynamic coefficients Mach number total angle of attack C A C NT C MT

146 Table 15.1 continued

147 Table 15.1 continued

148 Table 15.1 continued

149 Table 15.1 continued

150 Table 15.1 continued Appendix F: MSL aerodynamic coefficients. Table 16.1 MSL aerodynamic database program aerodynamic coefficients. Mach number total angle of attack C A C NT C mt

151 Table 16.1 Continued

152 Table 16.1 Continued

153 Table 16.1 Continued

154 Table 16.1 Continued Appendix G: Free molecular flow and Knudsen number data. Table 17.1 Pathfinder DAC aerodynamic coefficients. Knudsen number total angle of attack C A C NT C mt

155 Table 17.1 continued

156 Table 17.1 continued Table 17.2 Pathfinder DACFree aerodynamic coefficients. total angle of attack C A C NT C mt

157 Table 17.2 continued Table 17.3 Pathfinder aerodynamic database program aerodynamic Knudsen number coefficients. total angle of attack C A C NT C mt

158 Table 17.3 continued Table 17.4 Pathfinder aerodynamic database program aerodynamic coefficients. total angle of attack C A C NT C mt

159 Table 17.5 MER aerodynamic database program DAC aerodynamic Knudsen number coefficients. total angle of attack C A C NT C mt

160 Table 17.5 continued Table 17.6 MER aerodynamic database DACFree aerodynamic coefficients. total angle of attack C A C NT C mt

161 Table 17.6 continued

162 Table 17.6 continued

163 18. Appendix H: Plots of quaternions, aerodynamic coefficient definitions, coefficient comparisons, and angles. Figure 18.1 MER A Earth J2000 to body frame quaternion. 148

164 Figure 18.2 MER B Earth J2000 to body frame quaternion. Figure 18.3 Phoenix PICS to cruise frame quaternion. 149

165 Figure 18.4 Aerodynamic coefficient definitions. 150

166 Figure 18.5 MER A CY comparison with three methods for determining coefficients. 151

167 Figure 18.6 MER A Cn comparison with three methods for determining coefficients. 152

168 Figure 18.7 MER B CN comparison with three methods for determining coefficients. 153

169 Figure 18.8 MER B Cm comparison with three methods for determining coefficients. 154

170 Figure 18.9 Phoenix CY comparison with three methods for determining coefficients. 155

171 Figure Phoenix Cm comparison with three methods for determining coefficients. 156

172 Figure MER A angle of attack comparison with three methods for determining the angle. 157

173 Figure MER A sideslip angle comparison with three methods for determining the angle. 158

174 Figure MER B angle of attack comparison with three methods for determining the angle. 159