Search NASA⌕ Search

SEARCH · Search NASA

Results for “Simulation Credibility”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Validation of highly reliable, real-time knowledge-based systems

Knowledge-based systems have the potential to greatly increase the capabilities of future aircraft and spacecraft and to significantly reduce support manpower needed for the space station and other space missions. However, a credible validation methodology must be developed before knowledge-based systems can be used for life- or mission-critical applications. Experience with conventional software has shown that the use of good software engineering techniques and static analysis tools can greatly reduce the time needed for testing and simulation of a system. Since exhaustive testing is infeasible, reliability must be built into the software during the design and implementation phases. Unfortunately, many of the software engineering techniques and tools used for conventional software are of little use in the development of knowledge-based systems. Therefore, research at Langley is focused on developing a set of guidelines, methods, and prototype validation tools for building highly reliable, knowledge-based systems. The use of a comprehensive methodology for building highly reliable, knowledge-based systems should significantly decrease the time needed for testing and simulation. A proven record of delivering reliable systems at the beginning of the highly visible testing and simulation phases is crucial to the acceptance of knowledge-based systems in critical applications.

Johnson, Sally C.↗

EDL Simulation Results for the Mars 2020 Landing Site Safety Assessment

The Mars 2020 rover is NASA’s next flagship mission, set to explore Mars in search of scientific evidence of past microbial life. Importantly, the rover will also, for the first time, have the ability to collect and cache rock and soil samples for retrieval and return to laboratories here on Earth. A key step in the development of the Mars 2020 mission is the selection of a suitable landing site with the largest likelihood of meeting scientific goals. This decision is a complex and critical one that requires close interaction between the scientific and engineering communities. The chosen landing site must be both scientifically interesting — providing the project with the greatest possible chance of gathering credible and defendable scientific evidence — and also safe enough to attempt a landing in the first place. Thus, arguably one of the most important undertakings of the Entry, Descent, and Landing (EDL) team, is to effectively enumerate, quantify, and communicate the landing risks to all of the stakeholders. The culmination of this effort is the Landing Site Safety Assessment, which is a review commissioned by the project, presided over by the EDL Standing Review Board, and attended by management and science stakeholders, in which the EDL team communicates their assessment of the associated landing risks and the statistical probability of a successful landing at each of the final candidate landing sites. This paper summarizes the results of high-fidelity computer simulations of the Mars 2020 EDL sequence used in this assessment. From an EDL performance perspective, all four candidates offer similar level of robustness, which is in-family with Mars Science Laboratory (MSL). However, two new features of the Mars 2020 EDL sequence – range trigger and Terrain-Relative Navigation (TRN) – dramatically enhance the capability of the EDL system to safely land at landing sites with much more rugged terrain than ever before considered. This has allowed the landing site selection for Mars 2020 to proceed in a manner that has been unprecedentedly weighted more heavily toward scientific interest and less heavily on engineering constraints. With TRN, the overall probability of success is predicted to be approximately 99% for all of the candidates.

David Way↗

Integration of In-Situ Resource Utilization Into Lunar/Mars Exploration Through Field Analogs

The NASA project to develop In-Situ Resource Utilization (ISRU) technologies, in partnership with commercial and international collaborators, has achieved full system demonstrations of oxygen production using native regolith simulants. These demonstrations included robotic extraction of material from the terrain, sealed encapsulation of material in a pressurized reactor; chemical extraction of oxygen from the material in the form of water, and the electrolysis of water into oxygen and hydrogen for storage and reuse. These successes have provided growing confidence in the prospects of ISRU oxygen production as a credible source for critical mission consumables in preparation for and during crewed missions to the moon and other destinations. Other ISRU processes, especially relevant to early lunar exploration scenarios, have also been shown to be practical, including the extraction of subsurface volatiles, especially water, and the thermal processing of surface materials for civil engineering uses and for thermal energy storage. This paper describes these recent achievements and current NASA ISRU development and demonstration activity. The ability to extract and process resources at the site of exploration into useful products such as propellants, life support and power system consumables; and radiation and rocket exhaust plume debris shielding, known as In-Situ Resource Utilization or ISRU, has the potential to significantly reduce the launch mass, risk, and cost of robotic and human exploration of space. The incorporation of ISRU into missions can also significantly influence technology selection and system development in other areas such as power, life support, and propulsion. For example. the ability to extract or produce large amounts of oxygen and/or water in-situ could minimize the need to completely close life support air and water processing system cycles, change thermal and radiation protection of habitats, and influence propellant selection for ascent vehicles and surface propulsive hoppers. While concepts and even laboratory work on evaluating and developing ISRU techniques such as oxygen extraction from lunar regolith have been going on since before the Apollo 11 Moon landing, no ISRU system has ever flown in space, and only recently have ISRU technologies been developed at a scale and at a system level that is relevant to actual robotic and human mission applications. Because ISRU hardware and systems have never been demonstrated or utilized before on robotic or human missions, architecture and mission planners and surface system hardware developers are hesitant to rely on ISRU products and services that are critical to mission and system implementation success. To build confidence in ISRU systems for future missions and assess how ISRU systems can best influence and integrate with other surface system elements, NASA, with international partners, are performing analog field tests to understand how to take advantage of ISRU capabilities and benefits with the minimum of risk associated with introducing this game-changing approach to exploration. This paper will describe and review the results of four analog field tests (Moses Lake in 6/08, Mauna Kea in 11/08. Flagstaff in 9/09; and Mauna Kea in 1/10) that have begun the process of integrating ISRU into robotic and human exploration systems and missions, and propose future ISRU-related analog field test activities that can be performed in collaboration with international space agencies.

Sanders, Gerald B.↗

Probabilistic Modeling of the Renal Stone Formation Module

The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.

kidney stones↗

Highlights of Space Weather Tools and Resources at the Community Coordinated Modeling Center

In this presentation, we showcase a diverse array of tools and resources offered by the Community Coordinated Modeling Center (CCMC) to advance space weather research and support space weather services. Highlights include the Run-on-Request (RoR) and continuous run simulation services, the multi-purpose integrated Space Weather Analysis (iSWA) system (has been used for space weather monitoring, anomaly resolution, and education), space weather event database DONKI, the validation tool called CAMEL, and various scoreboard activities serving as model validation efforts before a space weather event/condition occurs (this type of pre-event validation enhances the accuracy and credibility of space weather predictions from the community). In addition, CCMC’s is an active participant providing strong support for NASA’s Heliophysics Big Year activities. Above all, our team welcomes collaborations in the broad range of áreas. Through this presentation, we aim to inspire engagement and collaboration among latinoamerican scientific communities and CCMC.

Yihua Zheng↗

Comments on "The Sensitivity Study of Radiative-Convective Equilibrium in the Tropics with a Convective Resolving Model"

In general, there are two broad scientific objectives when using cloud resolving models (CRMs or cloud ensemble models-CEMs) to study tropical convection. The first one is to use them as a physics resolving models to understand the dynamic and microphysical processes associated with the tropical water and energy cycles and their role in the climate system. The second approach is to use the CRMs to improve the representation of moist processes and their interaction with radiation in large-scale models. In order to improve the credibility of the CRMs and achieve the above goals, CRMs using identical initial conditions and large-scale influences need to produce very similar results. Two CRMs produced different statistical equilibrium (SE) states even though both used the same initial thermodynamic and wind conditions. Sensitivity tests to identify the major physical processes that determine the SE states for the different CRM simulations were performed. Their results indicated that atmospheric horizontal wind is treated quite differently in these two CRMs. The model that had stronger surface winds and consequently larger latent and sensible heat fluxes from the ocean produced a warmer and more humid modeled thermodynamic SE state. In addition, the domain mean thermodynamic state is more unstable for those experiments that produced a warmer and more humid SE state. Their simulated wet (warm and humid) SE states are thermally more stable in the lower troposphere (from the surface to 4-5 km in altitude). The large-scale horizontal advective effects on temperature and water vapor mixing ratio are needed when using CRMs to perform long-term integrations to study convective feedback under specified large-scale environments. In addition, it is suggested that the dry and cold SE state simulated was caused by enhanced precipitation but not enough surface evaporation. We find some problems with the interpretation of these three phenomena.

Tao, W.-K.↗

Integrated Modeling and Simulation Verification, Validation, and Accreditation Strategy for Exploration Systems Mission Directorate

Models and simulations (M&S) are critical resources in the exploration of space. They support program management, systems engineering, integration, analysis, test, and operations and provide critical information and data supporting key analyses and decisions (technical, cost and schedule). Consequently, there is a clear need to establish a solid understanding of M&S strengths and weaknesses, and the bounds within which they can credibly support decision-making. Their usage requires the implementation of a rigorous approach to verification, validation and accreditation (W&A) and establishment of formal process and practices associated with their application. To ensure decision-making is suitably supported by information (data, models, test beds) from activities (studies, exercises) from M&S applications that are understood and characterized, ESMD is establishing formal, tailored W&A processes and practices. In addition, to ensure the successful application of M&S within ESMD, a formal process for the certification of analysts that use M&S is being implemented. This presentation will highlight NASA's Exploration Systems Mission Directorate (ESMD) management approach for M&S W&A to ensure decision-makers receive timely information on the model's fidelity, credibility, and quality.

Hale, Joseph P.↗

The atmospheric effects of stratospheric aircraft. Report of the 1992 Models and Measurements Workshop. Volume 1: Workshop objectives and summary

This Workshop on Stratospheric Models and Measurements (M&M) marks a significant expansion in the history of model intercomparisons. It provides a foundation for establishing the credibility of stratospheric models used in environmental assessments of chlorofluorocarbons, aircraft emissions, and climate-chemistry interactions. The core of the M&M comparisons involves the selection of observations of the current stratosphere (i.e., within the last 15 years): these data are believed to be accurate and representative of certain aspects of stratospheric chemistry and dynamics that the models should be able to simulate.

Prather, Michael J.↗

The atmospheric effects of stratospheric aircraft. Report of the 1992 Models and Measurements Workshop. Volume 2: Comparisons with global atmospheric measurements

This Workshop on Stratospheric Models and Measurements (M&M) marks a significant expansion in the history of model intercomparisons. It provides a foundation for establishing the credibility of stratospheric models used in environmental assessments of chlorofluorocarbons, aircraft emissions, and climate-chemistry interactions. The core of the M&M comparisons involves the selection of observations of the current stratosphere (i.e., within the last 15 years): these data are believed to be accurate and representative of certain aspects of stratospheric chemistry and dynamics that the models should be able to simulate.

Prather, Michael J.↗

The atmospheric effects of stratospheric aircraft. Report of the 1992 Models and Measurements Workshop. Volume 3: Special diagnostic studies

This Workshop on Stratospheric Models and Measurements (M&M) marks a significant expansion in the history of model intercomparisons. It provides a foundation for establishing the credibility of stratospheric models used in environmental assessments of chlorofluorocarbons, aircraft emissions, and climate-chemistry interactions. The core of the M&M comparisons involves the selection of observations of the current stratosphere (i.e., within the last 15 years): these data are believed to be accurate and representative of certain aspects of stratospheric chemistry and dynamics that the models should be able to simulate.

Prather, Michael J.↗

Sleep Disruption Medical Intervention Forecasting (SDMIF) Module for the Integrated Medical Model

The NASA Integrated Medical Model (IMM) assesses the risk, including likelihood and impact of occurrence, of all credible in-flight medical conditions. Fatigue due to sleep disruption is a condition that could lead to operational errors, potentially resulting in loss of mission or crew. Pharmacological consumables are mitigation strategies used to manage the risks associated with sleep deficits. The likelihood of medical intervention due to sleep disruption was estimated with a well validated sleep model and a Monte Carlo computer simulation in an effort to optimize the quantity of consumables. METHODS: The key components of the model are the mission parameter program, the calculation of sleep intensity and the diagnosis and decision module. The mission parameter program was used to create simulated daily sleep/wake schedules for an ISS increment. The hypothetical schedules included critical events such as dockings and extravehicular activities and included actual sleep time and sleep quality. The schedules were used as inputs to the Sleep, Activity, Fatigue and Task Effectiveness (SAFTE) Model (IBR Inc., Baltimore MD), which calculated sleep intensity. Sleep data from an ISS study was used to relate calculated sleep intensity to the probability of sleep medication use, using a generalized linear model for binomial regression. A human yes/no decision process using a binomial random number was also factored into sleep medication use probability. RESULTS: These probability calculations were repeated 5000 times resulting in an estimate of the most likely amount of sleep aids used during an ISS mission and a 95% confidence interval. CONCLUSIONS: These results were transferred to the parent IMM for further weighting and integration with other medical conditions, to help inform operational decisions. This model is a potential planning tool for ensuring adequate sleep during sleep disrupted periods of a mission.

Lewandowski, Beth↗

Dynamical and Trace Gas Responses of the Quasi-Biennial Oscillation to Increased CO2

Long-term projections of the Quasi-Biennial Oscillation (QBO) remain uncertain. Using the high-top \Middle Atmosphere" (MA) version of the NASA Goddard Institute for Space Studies (GISS) ModelE (E2.2-AP), we show that increased CO2 reduces the QBO period and weakens its amplitude, consistent with results from recent multimodel studies. The amplitude response is asymmetric, with the easterly phase weakening more than the westerly phase. Results from both coupled atmosphere{ocean and climatologically fixed sea surface temperature simulations link the period response to changes in parameterized convective gravity wave fluxes, whereas the amplitude changes are more closely tied to changes in tropical upwelling. Comparisons of simulations with and without ozone-dynamical feedbacks reveal that ozone feedbacks increase the QBO amplitude and period in pre-industrial control simulations, and reduce the response of the amplitude to increased CO2. The response of stratospheric tracers to projected changes in the QBO is also investigated. Similarity between results using fully interactive (trace gas and aerosol) versus linearized ozone chemical mechanisms suggests that the QBO response to CO2 does not depend on additional chemical feedbacks beyond those associated with ozone, which implies that projected QBO changes may be credibly represented using simpli fied stratospheric ozone schemes.

GISS Model E2.2-AP↗

Characterization of the Space Shuttle Ascent Debris using CFD Methods

After video analysis of space shuttle flight STS-107's ascent showed that an object shed from the bipod-ramp region impacted the left wing, a transport analysis was initiated to determine a credible flight path and impact velocity for the piece of debris. This debris transport analysis was performed both during orbit, and after the subsequent re-entry accident. The analysis provided an accurate prediction of the velocity a large piece of foam bipod ramp would have as it impacted the wing leading edge. This prediction was corroborated by video analysis and fully-coupled CFD/six degree of freedom (DOF) simulations. While the prediction of impact velocity was accurate enough to predict critical damage in this case, one of the recommendations of the Columbia Accident Investigation Board (CAIB) for return-to-flight (RTF) was to analyze the complete debris environment experienced by the shuttle stack on ascent. This includes categorizing all possible debris sources, their probable geometric and aerodynamic characteristics, and their potential for damage. This paper is chiefly concerned with predicting the aerodynamic characteristics of a variety of potential debris sources (insulating foam and cork, nose-cone ablator, ice, ...) for the shuttle ascent configuration using CFD methods. These aerodynamic characteristics are used in the debris transport analysis to predict flight path, impact velocity and angle, and provide statistical variation to perform risk analyses where appropriate. The debris aerodynamic characteristics are difficult to determine using traditional methods, such as static or dynamic test data, due to the scaling requirements of simulating a typical debris event. The use of CFD methods has been a critical element for building confidence in the accuracy of the debris transport code by bridging the gap between existing aerodynamic data and the dynamics of full-scale, in-flight events.

Murman, Scott M.↗

Improved Analysis of GW150914 Using a Fully Spin-Precessing Waveform Model

This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015 [Abbott et al. Phys. Rev. Lett. 116, 061102 (2016).]. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] presented parameter estimation of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and an 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here, we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [Abbott et al. Phys. Rev. Lett. 116, 241102 (2016).], and we quote updated component masses of 35(+5)(-3) solar M; and 30(+3)(-4) solar M; (where errors correspond to 90 symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate is less than 0.65 and a secondary spin estimate is less than 0.75 at 90% probability. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here, we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.

Abbott, B. P.↗

Present Status of Lunar Regolith Simulants, Workshop Overview and Objectives

As NASA embarks on a new phase of Space Exploration aiming at establishing a long- term human presence on the Moon and Mars, we face some immediate challenges in the development of tbe technologies that will take us there. Among these challenges, the lack of accepted reference materials that simulate the lunar soil and regolith is a significant one that must be addressed now. The workshop organized today focuses on defining these materials for the use of NASA and other organizations involved in research and development efforts of lunar technologies. The range of these technologies is vast and so is the variety of lunar materials. The gathering of experts from a large number of disciplines is a pre-requisite to achieve a credible consensus on this issue and be able to make the right recommendations for NASA management as they consider solutions to the development and usage of these specific materials.

Sibille, L.↗

Aerodynamic Analysis of Multistage Turbomachinery Flows in Support of Aerodynamic Design

This paper summarizes the state of 3D CFD based models of the time average flow field within axial flow multistage turbomachines. Emphasis is placed on models which are compatible with the industrial design environment and those models which offer the potential of providing credible results at both design and off-design operating conditions. The need to develop models which are free of aerodynamic input from semi-empirical design systems is stressed. The accuracy of such models is shown to be dependent upon their ability to account for the unsteady flow environment in multistage turbomachinery. The relevant flow physics associated with some of the unsteady flow processes present in axial flow multistage machinery are presented along with procedures which can be used to account for them in 3D CFD simulations. Sample results are presented for both axial flow compressors and axial flow turbines which help to illustrate the enhanced predictive capabilities afforded by including these procedures in 3D CFD simulations. Finally, suggestions are given for future work on the development of time average flow models.

Adamczyk, John J.↗

Evaluation of Improvements to the TRMM Microwave Rain Algorithm

Improvements made to the Version 5 TRMM passive microwave rain retrieval algorithm (2A-12) are evaluated using independent data. Surface rain rate estimates from the Version 5 TRMM TMI (2A-12), PR (2A-25) and TMI/PR Combined (2B-31) algorithms and ground-based radar estimates for selected coincident subset datasets in 1998 over Melbourne and Kwajalein show varying degrees of agreement. The surface rain rates are then classified into convective and stratiform rain types over ocean, land, and coastal areas for more detailed comparisons to the ground radar measurements. These comparisons lead to a better understanding of the relative performances of the current TRMM rain algorithms. For example, at Melbourne more than 80% of the radar-derived rainfall is classified as convective rain. Convective rain from the TRMM rain algorithms is less than that from ground radar measurements, while TRMM stratiform rain is much greater. Rain area coverage from 2A-12 is also in reasonable agreement with ground radar measurements, with about 25% more over ocean and 25% less over land and coastal areas. Retrieved rain rates from the improved (Version 6) 2A-12 algorithm will be compared to 2A-25, 2B-31, and ground-based radar measurements to evaluate the impact of improvements to 2A-12 in Version 6. An important improvement to the Version 6 2A-12 algorithm is the retrieval of Q1/Q2 (latent heating/drying) profiles in addition to the surface rain rate and hydrometeor profiles. In order to ascertain the credibility of the new products, retrieved Q1/Q2 profiles are compared to independent ground-based estimates. Analyses of dual-Doppler radar data in conjunction with coincident rawinsonde data yield estimates of the vertical distributions of diabatic heating/drying at high horizontal resolution for selected cases over the Kwajalein and LBA field sites. The estimated vertical heating/drying structures appear to be reasonable. Comparisons of Q1/Q2 profiles from Version 6 2A-12 and the ground-based estimates are in progress. Retrieved Q1/Q2 structures will also be compared to MM5 hurricane simulations for selected cases. The results of these intercomparisons will be presented at the conference.

Yang, Song↗

Orbit Determination Toolbox

The Orbit Determination Toolbox is an orbit determination (OD) analysis tool based on MATLAB and Java that provides a flexible way to do early mission analysis. The toolbox is primarily intended for advanced mission analysis such as might be performed in concept exploration, proposal, early design phase, or rapid design center environments. The emphasis is on flexibility, but it has enough fidelity to produce credible results. Insight into all flight dynamics source code is provided. MATLAB is the primary user interface and is used for piecing together measurement and dynamic models. The Java Astrodynamics Toolbox is used as an engine for things that might be slow or inefficient in MATLAB, such as high-fidelity trajectory propagation, lunar and planetary ephemeris look-ups, precession, nutation, polar motion calculations, ephemeris file parsing, and the like. The primary analysis functions are sequential filter/smoother and batch least-squares commands that incorporate Monte-Carlo data simulation, linear covariance analysis, measurement processing, and plotting capabilities at the generic level. These functions have a user interface that is based on that of the MATLAB ODE suite. To perform a specific analysis, users write MATLAB functions that implement truth and design system models. The user provides his or her models as inputs to the filter commands. The software provides a capability to publish and subscribe to a software bus that is compliant with the NASA Goddard Mission Services Evolution Center (GMSEC) standards, to exchange data with other flight dynamics tools to simplify the flight dynamics design cycle. Using the publish and subscribe approach allows for analysts in a rapid design center environment to seamlessly incorporate changes in spacecraft and mission design into navigation analysis and vice versa.

Carpenter, James R.↗