Results for “probability generating function” — Page 10

NASA NTRS2009

Relation of Cloud Occurrence Frequency, Overlap, and Effective Thickness Derived from CALIPSO and CloudSat Merged Cloud Vertical Profiles

A cloud frequency of occurrence matrix is generated using merged cloud vertical profile derived from Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and Cloud Profiling Radar (CPR). The matrix contains vertical profiles of cloud occurrence frequency as a function of the uppermost cloud top. It is shown that the cloud fraction and uppermost cloud top vertical pro les can be related by a set of equations when the correlation distance of cloud occurrence, which is interpreted as an effective cloud thickness, is introduced. The underlying assumption in establishing the above relation is that cloud overlap approaches the random overlap with increasing distance separating cloud layers and that the probability of deviating from the random overlap decreases exponentially with distance. One month of CALIPSO and CloudSat data support these assumptions. However, the correlation distance sometimes becomes large, which might be an indication of precipitation. The cloud correlation distance is equivalent to the de-correlation distance introduced by Hogan and Illingworth [2000] when cloud fractions of both layers in a two-cloud layer system are the same.

Kato, Seiji↗

NASA NTRS1986

Three component plasma electron distribution in the intermediate ionized coma of Comet Giacobini-Zinner

The observation of three distinct components of the electron distribution function measured in the intermediate ionized coma (IIC) and plasma tail of Comet Giacobini-Zinner is reported. It is believed that the cold component represents electrons produced close to the comet nucleus by ionization of cometary matter and subsequent cooling by Coulomb collisions. The second component also appears to be composed of electrons produced by photoionization of cometary neutrals, but sufficiently far from the nucleus that the distributions are largely unaffected by Coulomb interactions. The hot component is probably a population of electrons originating in the solar wind. Throughout the IIC, the electrostatic potential of the spacecraft was very low (less than 0.8 eV), implying that ICE generated very little impact-produced plasma during its passage.

Zwickl, R. D.↗

NASA NTRS1985

An APL program for the distribution of energy deposition by charged particles passing through thin absorbers

An APL program which numerically evaluates the probability density function (PDF) for the energy deposited in a thin absorber by a charged particle is proposed, with application to the construction, pointing, and control of spacecraft. With this program, the PDF of the restricted energy loss distribution of Watts (1973) is derived, and Vavilov's (1957) distribution is obtained by proper parameter selection. The method is demonstrated with the example of the effect of charged particle induced radiation on the Hubble Space Telescope (HST) pointing accuracy. A Monte Carlo study simulates the photon noise caused by charged particles passing through the photomultiplier tube window, and the stochastic variation of energy loss is introduced into the simulation by generating random energy losses from a power law distribution. The program eliminates annoying loop procedures, and model parameter sensitivity can be studied using the graphical output.

Howell, L. W.↗

NASA NTRSDate not supplied

CLINICAL DECISION SUPPORT: PATH TO FUNCTIONAL REQUIREMENTS

Long-duration, deep-space exploration missions present significant challenges to crew health and performance. These challenges include the individual and combined effects of microgravity, radiation exposure, isolation, limited resources (mass, volume, power, data and crew time), limited options for evacuation and those associated with delayed or constrained communications, all of which demand greater crew autonomy. Specifically, as the communication delays intensify the further we explore space, the unqualified need for Earth-independent medical operations focused on autonomous diagnosis, treatment and prevention will be key to mission continuation and success. To augment the requisite knowledge, skills and abilities (KSAs) of a time-constrained crew operating under stressful conditions, combatting fatigue, and facing a potential medical crisis, a robust clinical decision support system (CDSS) is a probable solution that would facilitate, guide and inform Earth-independent medical operations, while assisting crewmembers through various clinical presentations. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) is expanding the boundaries of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit. ExMC is actively identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses gap Medical-701 within the Inflight Medical Conditions risk: “Enhance medical capabilities within an exploration medical system.” Though mass, volume, and power will face increasing constraints, the projected computational capabilities of spacecraft systems will increase exponentially as information technology continues to advance this decade and beyond. Hence, data, software and computational resources will play an essential and synergistic role in maintaining crew health, wellness and performance in deep space missions. The focus of the CDS project is to develop recommended requirements for an in-vehicle CDSS that acts as a ‘virtual assistant’ for delivering optimal health, performance and medical care during exploration missions. The CDSS is envisioned as an integrated, software-based tool deployed on a laptop computer or handheld device. The CDSS will assist the crew and ground support when interacting with knowledge/databases (e.g. records, pharmacy, schedule), instrumentation (e.g. imaging, physiological monitoring devices), and habitat (e.g. wellness system, task performance system) and vehicle systems (e.g. environmental system, communication system). In addition, the human interface will employ a context-based approach that accounts for the crew’s situation. Thus, extraneous and clinically/operationally non-relevant information are reduced to avoid an increase in cognitive load. The framework of an ideal spaceflight CDSS is to include core and advanced analytical features that incorporate work from collaborators yet maintain a flexible platform for integrating new technology in the future. In fiscal year 2021 (FY21), the CDS project identified requirements through two primary mechanisms: (i) the development of software implementation prototypes and (ii) the application of systems engineering processes. The CDS project developed and tested a series of increasingly complex system prototypes that were based on use cases derived from the CDSS concept of operations (ConOps). These software implementations yielded insights on CDSS functionality as well as lessons learned that provided the initial requirements for CDSS capability. By applying a systems engineering (SE) approach, medical scenarios provided in the ConOps and the use cases for software implementation underwent functional decomposition to identify CDSS functionality. Also, systems-based modeling language (SysML) tools such as activity diagrams were developed from the same ConOps and use cases to identify CDSS functionality. The lessons learned from software implementation defined both specific requirements and broad areas of requirements. Within these defined broad requirement areas, further analysis of the SE products identified specific capability that resulted in the final functional requirements. In summary, the software prototypes, functional decomposition of the ConOps and use cases, and SysML diagrams provided the basis for the CDSS requirements developed in FY21. In the upcoming year, these requirements will be refined for their final ExMC baseline review in latter FY22.

clinical decision support↗

NASA NTRSDate not supplied

Clinical Decision Support: Path to Functional Requirements

Long-duration, deep-space exploration missions present significant challenges to crew health and performance. These challenges include the individual and combined effects of microgravity, radiation exposure, isolation, limited resources (mass, volume, power, data and crew time), limited options for evacuation and those associated with delayed or constrained communications, all of which demand greater crew autonomy. Specifically, as the communication delays intensify the further we explore space, the unqualified need for Earth-independent medical operations focused on autonomous diagnosis, treatment and prevention will be key to mission continuation and success. To augment the requisite knowledge, skills and abilities (KSAs) of a time-constrained crew operating under stressful conditions, combatting fatigue, and facing a potential medical crisis, a robust clinical decision support system (CDSS) is a probable solution that would facilitate, guide and inform Earth-independent medical operations, while assisting crewmembers through various clinical presentations. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) is expanding the boundaries of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit. ExMC is actively identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses gap Medical-701 within the Inflight Medical Conditions risk: “Enhance medical capabilities within an exploration medical system.” Though mass, volume, and power will face increasing constraints, the projected computational capabilities of spacecraft systems will increase exponentially as information technology continues to advance this decade and beyond. Hence, data, software and computational resources will play an essential and synergistic role in maintaining crew health, wellness and performance in deep space missions. The focus of the CDS project is to develop recommended requirements for an in-vehicle CDSS that acts as a ‘virtual assistant’ for delivering optimal health, performance and medical care during exploration missions. The CDSS is envisioned as an integrated, software-based tool deployed on a laptop computer or handheld device. The CDSS will assist the crew and ground support when interacting with knowledge/databases (e.g. records, pharmacy, schedule), instrumentation (e.g. imaging, physiological monitoring devices), and habitat (e.g. wellness system, task performance system) and vehicle systems (e.g. environmental system, communication system). In addition, the human interface will employ a context-based approach that accounts for the crew’s situation. Thus, extraneous and clinically/operationally non-relevant information are reduced to avoid an increase in cognitive load. The framework of an ideal spaceflight CDSS is to include core and advanced analytical features that incorporate work from collaborators yet maintain a flexible platform for integrating new technology in the future. In fiscal year 2021 (FY21), the CDS project identified requirements through two primary mechanisms: (i) the development of software implementation prototypes and (ii) the application of systems engineering processes. The CDS project developed and tested a series of increasingly complex system prototypes that were based on use cases derived from the CDSS concept of operations (ConOps). These software implementations yielded insights on CDSS functionality as well as lessons learned that provided the initial requirements for CDSS capability. By applying a systems engineering (SE) approach, medical scenarios provided in the ConOps and the use cases for software implementation underwent functional decomposition to identify CDSS functionality. Also, systems-based modeling language (SysML) tools such as activity diagrams were developed from the same ConOps and use cases to identify CDSS functionality. The lessons learned from software implementation defined both specific requirements and broad areas of requirements. Within these defined broad requirement areas, further analysis of the SE products identified specific capability that resulted in the final functional requirements. In summary, the software prototypes, functional decomposition of the ConOps and use cases, and SysML diagrams provided the basis for the CDSS requirements developed in FY21. In the upcoming year, these requirements will be refined for their final ExMC baseline review in latter FY22.

Clinical decision support↗

NASA NTRS1973

Mars - Crustal structure inferred from Bouguer gravity anomalies.

Bouguer gravity has been computed for the equatorial region of Mars by differencing free air gravity and the gravity predicted from topographic variations. The free air gravity was generated from an eighth-order set of spherical harmonic coefficients. The gravity from topographic variations was generated by integrating a two-dimensional Green's function over each contour level. The Bouguer gravity indicates crustal inhomogeneities on Mars that are postulated to be variations in crustal thickness. The Tharsis ridge is a region of thick continental type crust. The gravity data, structural patterns, topography, and surface geology of this region lead to the interpretation of the Tharsis topographic high as a broad crustal upwarp possibly associated with local formation of lower-density crustal material and subsequent rise of a thicker crust. The Amazonis region is one of several basins of relatively thin crust, analogous to terrestrial ocean basins. The Libya and Hellas basins, which are probable impact features, are also underlain by thin crust and are possible regions of mantle upwelling.

Phillips, R. J.↗

NASA NTRS1993

The compositional structure and the effects of exothermicity in a nonpremixed planar jet flame

Results are presented of direct numerical simulation (DNS) of a randomly perturbed compressible, spatially developing two-dimensional planar jet under the influence of a finite rate chemical reaction of the type F + O yields product. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the DNS generated data. It is shown that even with this idealized kinetics model the simulated results exhibit features in accord with experimental data. These results indicate that the Damkohler number is an important parameter in determining the statistical composition of the reacting field and that the results are not very sensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and variance of the product mass fraction decrease and those of the reactants' mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants' mass fractions shift towards higher values within the composition domain, indicating a lower reactedness.

Steinberger, C. J.↗

NASA NTRS1986

Combustion characteristics in the transition region of liquid fuel sprays

A number of important effects have been observed in the droplet size transition region in spray combustion systems. In this region, where the mechanism of flame propagation is transformed from diffusive to premixed dominated combustion, the following effects have been observed: (1) maxima in burning velocity; (2) extension of flammability limits; (3) minima in ignition energy; and (4) minima in NOx formation. A monodisperse aerosol generator has been used to form and deliver a well controlled liquid fuel spray to the combustion test section where measurements of ignition energy have been made. The ignition studies were performed on monodisperse n-heptane sprays at atmospheric pressure over a range of equivalence ratios and droplet diameters. A capacitive discharge spark ignition system was used as the ignition source, providing independent control of spark energy and duration. Preliminary measurements were made to optimize spark duration and spark gap, optimum conditions being those at which the maximum frequency or probability of ignition was observed. Using the optimum electrode spacing and spark duration, the frequency of ignition was determined as a function of spark energy for three overall equivalence ratios (0.6, 0.8, and 1.0) and for initial droplet diameters of 25, 40, 50, 60, and 70 micro m.

Cernansky, N. P.↗

NASA NTRS2015

Directed Design of Experiments for Validating Probability of Detection Capability of NDE Systems (DOEPOD)

Directed Design of Experiments for Validating Probability of Detection Capability of NDE Systems (DOEPOD) Manual v.1.2 The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that there is 95% confidence that the POD is greater than 90% (90/95 POD). Design of experiments for validating probability of detection capability of nondestructive evaluation (NDE) systems (DOEPOD) is a methodology that is implemented via software to serve as a diagnostic tool providing detailed analysis of POD test data, guidance on establishing data distribution requirements, and resolving test issues. DOEPOD demands utilization of observance of occurrences. The DOEPOD capability has been developed to provide an efficient and accurate methodology that yields observed POD and confidence bounds for both Hit-Miss or signal amplitude testing. DOEPOD does not assume prescribed POD logarithmic or similar functions with assumed adequacy over a wide range of flaw sizes and inspection system technologies, so that multi-parameter curve fitting or model optimization approaches to generate a POD curve are not required. DOEPOD applications for supporting inspector qualifications is included.

Generazio, Edward R.↗

NASA NTRSDate not supplied

Reversibly Assembled Microparticles for Sustained Applications on the Moon and Mars

A sustained presence in any extra-terrestrial environment will require the capability to generate materials, goods, and ultimately vehicles, construction supplies and habitats to be tenable. As an example, NASA, in collaboration with Made In Space, Inc., recently reported the results of extensive research toward enabling3D printing in space. The extensive characterization and comparison of 3D printed articles suggested that, overall, articles generated in the International Space Station microgravity environment were comparable to those generated on Earth. The benefit of in-space manufacturing can be increased through utilization of recyclable materials. A recent analysis of a hypothetical 1,100 day round trip mission to Mars determined that significant mass savings and increase in mission probability of success could be achieved through in-space manufacturing with recyclable materials. NASA’s project ESPUR (Enabling Sustained Presence Using Recyclables), through support from NASA Langley’s Innovative Research and Development Fund, is investigating novel, polymer-coated, epoxy microparticle systems as an enabling technology to realize in-space manufacturing using recyclable feedstocks. Building from previously reported results, further progress toward synthesis of the polymer coating containing click chemical functionalities will be described here. Finite elemental analysis (FEA) has been utilized, in light of scale-free/small world considerations in an effort to identify compositions most likely to yield robust macroscopic geometries. Initial results will be described here. Finally, potential mass savings and life cycle of this recyclable materials technology will be discussed.

Click Chemistry↗

NASA NTRS1980

Aerodynamic aspects of shock containing jet plumes

Aerodynamic and acoustic measurements of shock-free and shock-containing plumes were acquired for several supersonic free-jet model nozzles. The purpose was to investigate important features of the broadband shock noise generation process. The aerodynamic measurements include the variation of shock cell spacing and strength as a function of nozzle pressure ratio, and longitudinal turbulent-mass-flux axial development as determined by a hot-film probe. In addition, correlations of the hot-film probe with a near-field microphone were obtained. These measurements provide useful information concerning the relation of peak shock noise frequency and level with variations in shock cell spacing and strength. In general, it is shown that a distinction must be made between plumes containing weak and strong imbedded shocks. Strong shocks diminish the level of emitted shock noise and influence the behavior of the jet mixing noise process. The probable location and spectral content for the shock-shear layer interaction mechanism is indicated by the correlations. Numerical inviscid plume comparisons with experimental data are also included.

Seiner, J. M.↗

NASA NTRS2016

Precision Landing and Hazard Avoidance Doman

The Precision Landing and Hazard Avoidance (PL&HA) domain addresses the development, integration, testing, and spaceflight infusion of sensing, processing, and GN&C functions critical to the success and safety of future human and robotic exploration missions. PL&HA sensors also have applications to other mission events, such as rendezvous and docking. Autonomous PL&HA builds upon the core GN&C capabilities developed to enable soft, controlled landings on the Moon, Mars, and other solar system bodies. Through the addition of a Terrain Relative Navigation (TRN) function, precision landing within tens of meters of a map-based target is possible. The addition of a 3-D terrain mapping lidar sensor improves the probability of a safe landing via autonomous, real-time Hazard Detection and Avoidance (HDA). PL&HA significantly improves the probability of mission success and enhances access to sites of scientific interest located in challenging terrain. PL&HA can also utilize external navigation aids, such as navigation satellites and surface beacons. Advanced Lidar Sensors High precision ranging, velocimetry, and 3-D terrain mapping Terrain Relative Navigation (TRN) TRN compares onboard reconnaissance data with real-time terrain imaging data to update the S/C position estimate Hazard Detection and Avoidance (HDA) Generates a high-resolution, 3-D terrain map in real-time during the approach trajectory to identify safe landing targets Inertial Navigation During Terminal Descent High precision surface relative sensors enable accurate inertial navigation during terminal descent and a tightly controlled touchdown within meters of the selected safe landing target.

Robertson, Edward A.↗

NASA NTRS1985

Interactions between large space power systems and low-Earth-orbit plasmas

There is a growing tendency to plan space missions that will incorporate very large space power systems. These space power systems must function in the space plasma environment, which can impose operational limitations. As the power output increases, the operating voltage also must increase and this voltage, exposed at solar array interconnects, interacts with the local plasma. The implications of such interactions are considered. The available laboratory data for biased array segment tests are reviewed to demonstrate the basic interactions considered. A data set for a floating high voltage array test was used to generate approximate relationships for positive and negative current collection from plasmas. These relationships were applied to a hypothetical 100 kW power system operating in a 400 km, near equatorial orbit. It was found that discharges from the negative regions of the array are the most probable limiting factor in array operation.

Stevens, N. J.↗

NASA NTRSDate not supplied

Overview of Micrometeoroid and Orbital Debris Analysis Process for Mars Sample Return Earth Entry System

Introduction: Micrometeoroid and orbital debris (MMOD) risk analyses for the Mars Sample Return (MSR) Earth Entry System (EES) have been significantly more rigorous than previously flown missions because of its categorization as a Class V restricted return mission. This means the returned samples present significant concern for biogenic contamination. These analyses seek to determine if a micrometeoroid or orbital debris strike would result in loss of containment assurance and are summarized in the flowchart in Fig. 1. Methodology: The mission is considered in two MMOD phases: a pre-release phase where the EES is protected by a Micrometeoroid Protection System (MMPS) and a post-release phase called “free-flight” where the EES is exposed directly to the MMOD environment. These phases correspond to interplanetary cruise and imminent re-entry, respectively. To inform the MMPS design, a 30-shot high velocity impact testing (HVIT) series on candidate configurations at NASA White Sands Test Facility was completed in the summer of 2022. Sample post-shot images are shown in Fig 2 [1]. These data are used to baseline the MMPS design and to tune the hydrocode simulations. ALE3D, CTH, and SPHC are the hydrocodes that simulate physics of high-speed impacts [2]. Results generated with these populate a penetration depth versus energy space beyond the testable velocity regime of HVIT (~7 km/s). The penetration depth versus energy space data are used to define a critical projectile diameter function called a Ballistic Limit Equation (BLE), where the projectile “criticality” is determined by zone dependent failure criteria defined a-priori [3]. For example, the nose of the heatshield has a failure criterion of 50% TPS penetration, assigned because the landing loads are concentrated on that region and no substructure damage is permitted. The BLEs for each vehicle material zone are input into the BUMPER 3 code, along with the vehicle surface mesh and the corresponding space environment model, to calculate a probability of penetration or number of penetrations. The environment models, MEM3 for MM and ORDEM 3.2 for OD, simulate the meteoroid environment from 0.2 to 2 au based on the Grün flux equation, and the debris environment up to 40,000 km altitude from Earth surface, respectively [4,5]. Presentation Focus: The presentation or poster will present the results to-date focusing on the full risk analysis process flow seen in Fig. 1. Details on the derivation of the failure criteria will be discussed, along with HVIT results and how these influenced the MMPS configuration baseline decision. Further, results of hydrocode simulations will be presented and the tuning to HVIT outputs will be described. Finally, the strategies that direct the BLE formulation will be reviewed, specifically, for the EES elements that are most exposed to the MMOD environment.

mmod↗

NASA NTRS1993

Statistics of highly magnified gravitational images in clusters of galaxies. I - Implications for the clusters. II - Implications for the sources

A study is presently conducted of the probability distribution of observing images of background galaxies that are gravitationally lensed in the form of elongated arcs by clusters of galaxies, as a function of arc width, curvature radius, and the elongation's orientation. An upper limit is obtained on the size of the cores which is smaller than cluster core radii obtained for the gas from the X-ray surface brightness. It is argued that lensing clusters tend to be elongated along the line of sight; projection effects will enhance surface density. In the second part of this work, it is shown that the number of arcs expected in lensing clusters is primarily dependent on the angular size of the sources, since lower magnification is required to generate an arc of fixed length for a larger source.

Miralda-Escude, Jordi↗

NASA NTRS2012

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows.

Drozda, Tomasz G.↗

NASA NTRS2008

The Solid Rocket Motor Slag Population: Results of a Radar-Based Regressive Statistical Evaluation

Solid rocket motor (SRM) slag has been identified as a potential source of man-made orbital debris. The possibility that SRMs (in addition to generating dust particles in the sub-millimeter range) may generate particles up to centimeters in size has caused concern regarding their contribution to the debris environment. Returned surfaces from space do not have sufficient area or exposure time to provide a clear picture of the SRM millimeter and centimeter debris population. Currently, radar observation is probably the only way to collect data showing the debris contribution from SRMs. Such observation is used to sample the debris environment, but it is difficult to obtain accurate orbital elements for the detected debris objects. NASA has developed several models to describe the different orbital debris populations, based on assumed debris production mechanisms to create clouds of debris objects that can be propagated in time. The NASA model, LEGEND (LEO-to-GEO Environment Debris), functions as a time-tested debris model for most debris sources. However, the current LEGEND model does not include contributions from the SRM population. An SRM model has recently been developed by NASA, based on purely theoretical details of SRM production and known SRM launches, but verification with hard data is needed. Because the detections of individual SRM objects cannot be deterministically separated from the total debris observed by radar, the validation of the SRM model can only be done by combining it with the LEGEND breakup model and comparing it with data. By applying observational constraints, the degree of SRM slag contribution to the environment may be estimated. This serves as an observationally sound method from which to calibrate a purely theoretical model into something more realistic. For this study, we use the populations observed by the Haystack radar from 1996 to present. For the SRM debris, we use a historical database of SRM launches, propellant masses, and estimated locations and times of tailoff to produce and propagate the SRM debris clouds. Comparisons with radar data from the ensuing years were made, and the SRM model was altered with respect to size and mass production of slag particles to reflect the populations estimated from the data. The result is a model SRM population that fits within the bounds of the observed environment and estimates of the production and contribution of SRM debris to the environment.

Horstman, Matthew F.↗

NASA NTRS2018

Assessment and Verification of SLS Block 1-B Exploration Upper Stage State and Stage Disposal Performance

One of the SLS Navigation System's key performance requirements is a constraint on the payload system's delta-v allocation to correct for insertion errors due to vehicle state uncertainty at payload separation. The SLS navigation team has developed a Delta-Delta-V analysis approach to assess the effect on trajectory correction maneuver (TCM) design needed to correct for navigation errors. This approach differs from traditional covariance analysis based methods and makes no assumptions with regard to the propagation of the state dynamics. This allows for consideration of non-linearity in the propagation of state uncertainties. The Delta-Delta-V analysis approach re-optimizes perturbed SLS mission trajectories by varying key mission states in accordance with an assumed state error. The state error is developed from detailed vehicle 6-DOF Monte Carlo analysis or generated using covariance analysis. These perturbed trajectories are compared to a nominal trajectory to determine necessary TCM design. To implement this analysis approach, a tool set was developed which combines the functionality of a 3-DOF trajectory optimization tool, Copernicus, and a detailed 6-DOF vehicle simulation tool, Marshall Aerospace Vehicle Representation in C (MAVERIC). In addition to delta-v allocation constraints on SLS navigation performance, SLS mission requirement dictate successful upper stage disposal. Due to engine and propellant constraints, the SLS Exploration Upper Stage (EUS) must dispose into heliocentric space by means of a lunar fly-by maneuver. As with payload delta-v allocation, upper stage disposal maneuvers must place the EUS on a trajectory that maximizes the probability of achieving a heliocentric orbit post Lunar fly-by considering all sources of vehicle state uncertainty prior to the maneuver. To ensure disposal, the SLS navigation team has developed an analysis approach to derive optimal disposal guidance targets. This approach maximizes the state error covariance prior to the maneuver to develop and re-optimize a nominal disposal maneuver (DM) target that, if achieved, would maximize the potential for successful upper stage disposal. For EUS disposal analysis, a set of two tools was developed. The first considers only the nominal pre-disposal maneuver state, vehicle constraints, and an a priori estimate of the state error covariance. In the analysis, the optimal nominal disposal target is determined. This is performed by re-formulating the trajectory optimization to consider constraints on the eigenvectors of the error ellipse applied to the nominal trajectory. A bisection search methodology is implemented in the tool to refine these dispersions resulting in the maximum dispersion feasible for successful disposal via lunar fly-by. Success is defined based on the probability that the vehicle will not impact the lunar surface and will achieve a characteristic energy (C3) relative to the Earth such that it is no longer in the Earth-Moon system. The second tool propagates post-disposal maneuver states to determine the success of disposal for provided trajectory achieved states. This is performed using the optimized nominal target within the 6-DOF vehicle simulation. This paper will discuss the application of the Delta-Delta-V analysis approach for performance evaluation as well as trajectory re-optimization so as to demonstrate the system's capability in meeting performance constraints. Additionally, further discussion of the implementation of assessing disposal analysis will be provided.

Patrick, Sean↗