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Dispersion analysis and linear error analysis capabilities of the space vehicle dynamics simulation program

Previous error analyses conducted by the Guidance and Dynamics Branch of NASA have used the Guidance Analysis Program (GAP) as the trajectory simulation tool. Plans are made to conduct all future error analyses using the Space Vehicle Dynamics Simulation (SVDS) program. A study was conducted to compare the inertial measurement unit (IMU) error simulations of the two programs. Results of the GAP/SVDS comparison are presented and problem areas encountered while attempting to simulate IMU errors, vehicle performance uncertainties and environmental uncertainties using SVDS are defined. An evaluation of the SVDS linear error analysis capability is also included.

Snow, L. S.↗

Coupled Solid Rocket Motor Ballistics and Trajectory Modeling for Higher Fidelity Launch Vehicle Design

Multi-stage launch vehicles with solid rocket motors (SRMs) face design optimization challenges, especially when the mission scope changes frequently. Significant performance benefits can be realized if the solid rocket motors are optimized to the changing requirements. While SRMs represent a fixed performance at launch, rapid design iterations enable flexibility at design time, yielding significant performance gains. The streamlining and integration of SRM design and analysis can be achieved with improved analysis tools. While powerful and versatile, the Solid Performance Program (SPP) is not conducive to rapid design iteration. Performing a design iteration with SPP and a trajectory solver is a labor intensive process. To enable a better workflow, SPP, the Program to Optimize Simulated Trajectories (POST), and the interfaces between them have been improved and automated, and a graphical user interface (GUI) has been developed. The GUI enables real-time visual feedback of grain and nozzle design inputs, enforces parameter dependencies, removes redundancies, and simplifies manipulation of SPP and POST's numerous options. Automating the analysis also simplifies batch analyses and trade studies. Finally, the GUI provides post-processing, visualization, and comparison of results. Wrapping legacy high-fidelity analysis codes with modern software provides the improved interface necessary to enable rapid coupled SRM ballistics and vehicle trajectory analysis. Low cost trade studies demonstrate the sensitivities of flight performance metrics to propulsion characteristics. Incorporating high fidelity analysis from SPP into vehicle design reduces performance margins and improves reliability. By flying an SRM designed with the same assumptions as the rest of the vehicle, accurate comparisons can be made between competing architectures. In summary, this flexible workflow is a critical component to designing a versatile launch vehicle model that can accommodate a volatile mission scope.

Ables, Brett↗

POST Explorer: A Design Space Exploration Tool for POST2

Recent improvements for the Program to Optimize Simulated Trajectories II (POST2) have included the development of an application programming interface (API). This API allows POST2 simulation inputs to be directly manipulated from other applications (such as MATLAB or Python), and the outputs from POST2 are streamed directly to the external application that enables visualization, data manipulation, etc. Through this framework, a new tool called POST Explorer is being developed that provides a user the capability to modify the simulation inputs and interrogate the outputs within the same application, with raw data inspection and visualization embedded. This tool can be leveraged for multiple types of analyses, such as parametric sweeps and sensitivity studies, and will be available with a future release of the POST2 software.

Robert Anthony Williams↗

POST Explorer: A Design Space Exploration Tool for POST2

Recent improvements for the Program to Optimize Simulated Trajectories II (POST2) have included the development of an application programming interface (API). This API allows POST2 simulation inputs to be directly manipulated from other applications (such as MATLAB or Python), and the outputs from POST2 are streamed directly to the external application that enables visualization, data manipulation, etc. Through this framework, a new tool called POST Explorer is being developed that provides a user the capability to modify the simulation inputs and interrogate the outputs within the same application, with raw data inspection and visualization embedded. This tool can be leveraged for multiple types of analyses, such as parametric sweeps and sensitivity studies, and will be available with a future release of the POST2 software.

Anthony Williams↗

Trajectory Reconstruction of the Low-Earth Orbit Flight Test of an Inflatable Decelerator

The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) project conducted a flight test of a 6m inflatable aeroshell. The LOFTID test article was a secondary payload on an Atlas V launcher that carried the Joint Polar Satellite System-2 (JPSS-2) as its primary payload. The vehicle launched on November 10th, 2022. After reaching orbit, the LOFTID test article inflated the aeroshell, separated from the upper stage on an entry trajectory, and entered the atmosphere to splash down in the Pacific Ocean under parachutes. The test concept of operations is shown in Figure 1. The test article was instrumented with a variety of sensors to be used for post-flight evaluation of vehicle performance. Data from one of the key sensors for trajectory reconstruction, the Inertial Measurement Unit (IMU), was not captured in the data recorder due to a malfunction. Data from the nose cone mounted Flush Air Data Sensing (FADS) system were successfully acquired. The layout of the FADS sensors and the measured pressures during atmospheric entry are shown in Figure 2. The FADS data were combined with a Newtonian flow pressure model [1, 2] to produce estimates of the atmospheric relative trajectory. A Mach number anchoring technique given in [2] was used to stabilize estimates in high speed flight conditions. Since no IMU data were available, a trajectory simulation was used to provide the Mach number time history. The resulting estimates of the atmospheric-relative trajectory are shown in Figures 3. Given the loss of the IMU data, alternate methods for trajectory reconstruction are being explored. One approach under investigation is the use of the on-board video recorder data to be analyzed to reconstruct attitude motion. This approach is currently under investigation and will be reported on in the final paper. The Newtonian flow pressure model for the FADS analysis will also be updated with a CFD-based pressure model.

Christopher D Karlgaard↗

Trajectory Reconstruction of the Low-Earth Orbit Flight Test of an Inflatable Decelerator

The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) project conducted a flight test of a 6m inflatable aeroshell. The LOFTID test article was a secondary payload on an Atlas V launcher that carried the Joint Polar Satellite System-2 (JPSS-2) as its primary payload. The vehicle launched on November 10th, 2022. After reaching orbit, the LOFTID test article inflated the aeroshell, separated from the upper stage on an entry trajectory, and entered the atmosphere to splash down in the Pacific Ocean under parachutes. The test concept of operations is shown in Figure 1. The test article was instrumented with a variety of sensors to be used for post-flight evaluation of vehicle performance. Data from one of the key sensors for trajectory reconstruction, the Inertial Measurement Unit (IMU), was not captured in the data recorder due to a malfunction. Data from the nose cone mounted Flush Air Data Sensing (FADS) system were successfully acquired. The layout of the FADS sensors and the measured pressures during atmospheric entry are shown in Figure 2. The FADS data were combined with a Newtonian flow pressure model [1, 2] to produce estimates of the atmospheric relative trajectory. A Mach number anchoring technique given in [2] was used to stabilize estimates in high speed flight conditions. Since no IMU data were available, a trajectory simulation was used to provide the Mach number time history. The resulting estimates of the atmospheric-relative trajectory are shown in Figures 3. Given the loss of the IMU data, alternate methods for trajectory reconstruction are being explored. One approach under investigation is the use of the on-board video recorder data to be analyzed to reconstruct attitude motion. This approach is currently under investigation and will be reported on in the final paper. The Newtonian flow pressure model for the FADS analysis will also be updated with a CFD-based pressure model.

Christopher D. Karlgaard↗

Overview of Additively Manufactured TPS Proposed Flight Test and Earth Re-Entry Capsule Design

A flight mechanics overview is presented of an Earth flight test designed to investigate a novel, 3D printed thermal protection system (TPS) that is currently in development at NASA as part of the Additive Manufacturing of Thermal Protection Systems project. The project is pioneering a method to print a thermal protection system onto an entry vehicle forebody one layer at a time. This method reduces labor and complexity as compared to traditional manufacturing methods while increasing mission-dependent customization of through-depth materials properties. The flight test has three objectives. First, subject the forebody stagnation point of a capsule equipped with additively manufactured TPS (AMTPS) material to peak heat fluxes in excess of 100 $W/cm^2$. Second, capture in-flight data to enable flight reconstruction and AMTPS material thermal response model improvement. Third, recover the capsule with data storage and forebody AMTPS intact to enable post-flight inspection and analysis of AMTPS performance. The flight test trajectory is designed to achieve a peak stagnation point, cold-wall, entry heat flux of 135~$W/cm^2$. Flight mechanics simulations are performed using the Program to Optimize Simulated Trajectories II (POST2) and Monte-Carlo analysis yields statistical percentiles on vehicle performance at key points along the trajectory. Based on the flight mechanics analysis presented in this paper, a prototype capsule was designed, partially fabricated, and underwent preliminary component stress testing in preparation for fabrication of the flight unit capsule. The capsule outer mold line is a modified version of the heritage Mars Microprobe geometry. The capsule has a 0.356~m diameter, a 30~kg mass, and a hypersonic ballistic coefficient of 300~$kg/m^2$. Sensor selection is guided by flight dynamics simulations with the goal of resolving the re-entry heating pulse. On-board instrumentation include forebody and aftbody pressure sensors and thermocouples, a 9-axis IMU, a GPS receiver, and an Iridium satellite modem, all of which collect and store data throughout flight via on-board avionics systems. A two-stage parachute system is designed to decelerate the capsule to touchdown velocities that will not result in significant fracture or deformation of the charred AMTPS material at ground impact.

Flight Mechanics↗

NASA Advanced Concepts Office, Earth-To-Orbit Team Design Process and Tools

The Earth-to-Orbit Team (ETO) of the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) is considered the pre-eminent go-to group for pre-phase A and phase A concept definition. Over the past several years the ETO team has evaluated thousands of launch vehicle concept variations for a significant number of studies including agency-wide efforts such as the Exploration Systems Architecture Study (ESAS), Constellation, Heavy Lift Launch Vehicle (HLLV), Augustine Report, Heavy Lift Propulsion Technology (HLPT), Human Exploration Framework Team (HEFT), and Space Launch System (SLS). The ACO ETO Team is called upon to address many needs in NASA s design community; some of these are defining extremely large trade-spaces, evaluating advanced technology concepts which have not been addressed by a large majority of the aerospace community, and the rapid turn-around of highly time critical actions. It is the time critical actions, those often limited by schedule or little advanced warning, that have forced the five member ETO team to develop a design process robust enough to handle their current output level in order to meet their customer s needs. Based on the number of vehicle concepts evaluated over the past year this output level averages to four completed vehicle concepts per day. Each of these completed vehicle concepts includes a full mass breakdown of the vehicle to a tertiary level of subsystem components and a vehicle trajectory analysis to determine optimized payload delivery to specified orbital parameters, flight environments, and delta v capability. A structural analysis of the vehicle to determine flight loads based on the trajectory output, material properties, and geometry of the concept is also performed. Due to working in this fast-paced and sometimes rapidly changing environment, the ETO Team has developed a finely tuned process to maximize their delivery capabilities. The objective of this paper is to describe the interfaces between the three disciplines used in the design process: weights and sizing, trajectory, and structural analysis. The tools used to perform such analysis are INtegrated Rocket Sizing (INTROS), Program to Optimize Simulated Trajectories (POST), and Launch Vehicle Analysis (LVA) respectively. The methods each discipline uses to streamline their particular part of the design process will also be discussed.

Waters, Eric D.↗

NASA Advanced Concepts Office, Earth-To-Orbit Team Design Process and Tools

The Earth-to-Orbit Team (ETO) of the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) is considered the pre-eminent "go-to" group for pre-phase A and phase A concept definition. Over the past several years the ETO team has evaluated thousands of launch vehicle concept variations for a significant number of studies including agency-wide efforts such as the Exploration Systems Architecture Study (ESAS), Constellation, Heavy Lift Launch Vehicle (HLLV), Augustine Report, Heavy Lift Propulsion Technology (HLPT), Human Exploration Framework Team (HEFT), and Space Launch System (SLS). The ACO ETO Team is called upon to address many needs in NASA's design community; some of these are defining extremely large trade-spaces, evaluating advanced technology concepts which have not been addressed by a large majority of the aerospace community, and the rapid turn-around of highly time critical actions. It is the time critical actions, those often limited by schedule or little advanced warning, that have forced the five member ETO team to develop a design process robust enough to handle their current output level in order to meet their customer's needs. Based on the number of vehicle concepts evaluated over the past year this output level averages to four completed vehicle concepts per day. Each of these completed vehicle concepts includes a full mass breakdown of the vehicle to a tertiary level of subsystem components and a vehicle trajectory analysis to determine optimized payload delivery to specified orbital parameters, flight environments, and delta v capability. A structural analysis of the vehicle to determine flight loads based on the trajectory output, material properties, and geometry of the concept is also performed. Due to working in this fast-paced and sometimes rapidly changing environment, the ETO Team has developed a finely tuned process to maximize their delivery capabilities. The objective of this paper is to describe the interfaces between the three disciplines used in the design process: weights and sizing, trajectory, and structural analysis. The tools used to perform such analysis are INtegrated Rocket Sizing (INTROS), Program to Optimize Simulated Trajectories (POST), and Launch Vehicle Analysis (LVA) respectively. The methods each discipline uses to streamline their particular part of the design process will also be discussed.

Waters, Eric D.↗

Development of a system for transition characterization

The present system for real-time boundary layer transition detection and characterization encompasses aerodynamic simulations, sensor characteristics, and a hybrid analog/digital system for signal analysis, verification, and compression. By using artificial, intermittently laminar/turbulent signals, in conjunction with trajectory simulation, it becomes possible to conduct algorithm development which is independent of, and in advance of, sensor buildup. Attention is given to the illustrative case of the Pegasus launch vehicle's trajectory.

Bertelrud, Arild↗

Selective capture and recovery of uranium oxide colloids from aqueous soil suspensions using high gradient magnetic filtration

High Gradient Magnetic Filtration (HGMF) is a promising method for the selective capture and recovery of uranium oxide from surface soils. To date, however, magnetic filtration of uranium oxide has only been demonstrated at a proof-of-principle scale using relatively small filters (<5 cm 3 ) at low flowrates (<60 mL/min). Here, to explore the efficacy of magnetic filtration of uranium oxide at a larger scale, a newly designed HGMF apparatus that is more than an order of magnitude larger than our earlier filters (106 cm 3 ) was designed, fabricated, and tested at relatively high flowrates. Filtration experiments were performed using aqueous uranium oxide particle suspensions with Arizona Road Dust (ARD) as a soil simulant. At a flowrate of 125 mL/min, the apparatus’ uranium capture rate was exceptionally high (96 %), but selectivity was poor due to the high rate of capture for diamagnetic soil constituents (e.g., 77 % for silicon). All particles were captured at a lower rate when the flowrate was increased to 250 mL/min, but uranium selectivity was significantly increased due to the more substantial reduction in diamagnetic particle capture (i.e., capture rate of 77 % and 15 % for uranium and silicon, respectively). When backwashing the apparatus at the same flowrates used during filtration experiments, the rate of uranium recovery tended to be fairly low. Nevertheless, higher flowrates (1 L/min) and sonication were both shown to be highly effective methods of increasing uranium recovery. Magnetic field simulations were also performed to investigate potential optimizations to the design of the apparatus. These simulations showed that the intensity of the applied magnetic field could be increased by increasing the thickness of the steel magnetic housing. Additionally, stochastic trajectory simulations were performed to investigate the potential mechanisms of particle capture.

HGMF↗

Polar wind ion dynamics in the magnetotail

The circulation of polar wind ions from the high-latitude ionosphere to the plasma sheet is investigated. Single-particle trajectory simulations for the geomagnetic tail show, in addition to the breaking of adiabaticity, the possible creation of new high-altitude mirror points. This trajectory feature results from an intense parallel deceleration imparted by the magnetic field rotation during fast ExB transport. This centrifugal deceleration yields a critical parallel velocity which depends on the magnitude of the convection electric field and below which ions remain trapped inside the neutral sheet.

Delcourt, D. C.↗

Mars 2020 Navigation Performance

On February 18, 2021, the Perseverance rover and Ingenuity helicopter demonstration landed at Jezero Crater. The Entry, Descent, and Landing (EDL) architecture, largely the same used to land Curiosity at Gale Crater on August 6, 2012, required high-fidelity flight dynamics simulation with two independent tools to verify performance. The process for creating the EDL simulation using the Dynamics Simulator for Entry, Descent and Surface landing (DSENDS) tool will be discussed, along with its use for for independent verification of the EDL statistical analysis results and reference trajectory simulation. Analysis and usage details both in development and cruise, along with post-landing assessment of the prediction performance of the simulation, will also be discussed.

Wagner, Sean↗

Simulation and analysis of a geopotential research mission

Computer simulations were performed for a Geopotential Research Mission (GRM) to enable the study of the gravitational sensitivity of the range rate measurements between the two satellites and to provide a set of simulated measurements to assist in the evaluation of techniques developed for the determination of the gravity field. The simulations were conducted with two satellites in near circular, frozen orbits at 160 km altitudes separated by 300 km. High precision numerical integration of the polar orbits were used with a gravitational field complete to degree and order 360. The set of simulated data for a mission duration of about 32 days was generated on a Cray X-MP computer. The results presented cover the most recent simulation, S8703, and includes a summary of the numerical integration of the simulated trajectories, a summary of the requirements to compute nominal reference trajectories to meet the initial orbit determination requirements for the recovery of the geopotential, an analysis of the nature of the one way integrated Doppler measurements associated with the simulation, and a discussion of the data set to be made available.

Schutz, B. E.↗

An Expert System-Driven Method for Parametric Trajectory Optimization During Conceptual Design

During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle cost. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult in both cost and schedule to enact. The current capability-based paradigm, which has emerged because of the constrained economic environment, calls for the infusion of knowledge usually acquired during later design phases into earlier design phases, i.e. bringing knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture yet little of the information required to successfully optimize a trajectory is known early in the design phase. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. When these obstacles are coupled with the Program to Optimize Simulated Trajectories (POST), an industry standard program to optimize ascent trajectories that is difficult to use, expert trajectory analysts are required to effectively optimize a vehicle's ascent trajectory. Over the course of this paper, the authors discuss a methodology developed at NASA Marshall's Advanced Concepts Office to address these issues. The methodology is two-fold: first, capture the heuristics developed by human analysts over their many years of experience; and secondly, leverage the power of modern computing to evaluate multiple trajectories simultaneously and therefore enable the exploration of the trajectory's design space early during the pre- conceptual and conceptual phases of design. This methodology is coupled with design of experiments in order to train surrogate models, which enables trajectory design space visualization and parametric optimal ascent trajectory information to be available when early design decisions are being made.

Dees, Patrick D.↗

Enabling Parametric Optimal Ascent Trajectory Modeling During Early Phases of Design

During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult -- in both cost and schedule -- to enact. Indeed, the current capability-based paradigm that has emerged because of the constrained economic environment calls for the infusion of knowledge acquired during later design phases into earlier design phases, i.e. bring knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture as the need for more economically viable access to space solutions are needed in today's constrained economic environment. The problem of ascent trajectory optimization is not a new one. There are several programs that are widely used in industry that allows trajectory analysts to, based on detailed vehicle and insertion orbit parameters, determine the optimal ascent trajectory. Yet, little information is known about the launch vehicle early in the design phase - information that is required of many different disciplines in order to successfully optimize the ascent trajectory. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. Additionally, when these obstacles are coupled with The Program to Optimize Simulated Trajectories [1] (POST), an industry standard program to optimize ascent trajectories that is difficult to use, it requires expert trajectory analysts to effectively optimize a vehicle's ascent trajectory. As it has been pointed out, the paradigm of trajectory optimization is still a very manual one because using modern computational resources on POST is still a challenging problem. The nuances and difficulties involved in correctly utilizing, and therefore automating, the program presents a large problem. In order to address these issues, the authors will discuss a methodology that has been developed. The methodology is two-fold: first, a set of heuristics will be introduced and discussed that were captured while working with expert analysts to replicate the current state-of-the-art; secondly, leveraging the power of modern computing to evaluate multiple trajectories simultaneously, and therefore, enable the exploration of the trajectory's design space early during the pre-conceptual and conceptual phases of design. When this methodology is coupled with design of experiments in order to train surrogate models, the authors were able to visualize the trajectory design space, enabling parametric optimal ascent trajectory information to be introduced with other pre-conceptual and conceptual design tools. The potential impact of this methodology's success would be a fully automated POST evaluation suite for the purpose of conceptual and preliminary design trade studies. This will enable engineers to characterize the ascent trajectory's sensitivity to design changes in an arbitrary number of dimensions and for finding settings for trajectory specific variables, which result in optimal performance for a "dialed-in" launch vehicle design. The effort described in this paper was developed for the Advanced Concepts Office [2] at NASA Marshall Space Flight Center

Holt, James B.↗

CFD Simulations of the Supersonic Inflatable Aerodynamic Decelerator (SIAD) Ballistic Range Tests

A series of ballistic range tests were performed on a scaled model of the Supersonic Flight Demonstration Test (SFDT) intended to test the Supersonic Inflatable Aerodynamic Decelerator (SIAD) geometry. The purpose of these experiments were to provide aerodynamic coefficients of the vehicle to aid in mission and vehicle design. The experimental data spans the moderate Mach number range, $3.8-2.0$, with a total angle of attack ($alpha_T$) range, $10o-20o$. These conditions are intended to span the Mach-$alpha$ space for the majority of the SFDT experiment. In an effort to validate the predictive capabilities of Computational Fluid Dynamics (CFD) for free-flight aerodynamic behavior, numerical simulations of the ballistic range experiment are performed using the unstructured finite volume Navier-Stokes solver, US3D. Comparisons to raw vehicle attitude, and post-processed aerodynamic coefficients are made between simulated results and experimental data. The resulting comparisons for both raw model attitude and derived aerodynamic coefficients show good agreement with experimental results. Additionally, near body pressure field values for each trajectory simulated are investigated. Extracted surface and wake pressure data gives further insights into dynamic flow coupling leading to a potential mechanism for dynamic instability.

CFD modeling↗