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At least 775 records · Page 43

A microchannel shell-and-tube absorber for ammonia-water absorption

A shell-and-tube absorber with microscale geometric features that yields significant volumetric heat duties is investigated. A vertically-oriented baffled shell-and-tube heat exchanger with a tightly packed tube bundle is designed to serve as the absorber for a 10.5 kW nominal cooling capacity absorption chiller. The heat and mass transfer in this absorber is investigated experimentally at operating conditions spanning a wide range of working fluid and coupling fluid flow rates and ambient temperatures. An experimental facility is fabricated to closely simulate the operating conditions in an absorption refrigeration system. Absorption heat duties in the range of 5-15 kW are measured. In addition to operating the absorber in the baseline co-current flow configuration with premixed inlet, fluid ports are provided to enable operation in counter-current flow, where the dilute solution enters from the top and vapor enters from the bottom. The performance of these two flow configurations is compared. A preliminary heat and mass transfer model is developed to quantify the local temperatures, concentrations, and mass flow rates of the solution and vapor streams along the length of the absorber. The model predictions for total heat duty agree with the experimental results within 10% for almost all the data points, with an AAD of ~3.4%. Finally, the results of this study, along with the modeling framework, can guide further development of highly compact and efficient absorbers absorption systems.

42 ENGINEERING↗

MODIS Retrieval of Dust Aerosol

The MODerate resolution Imaging Spectroradiometer (MODIS) currently aboard both the Terra and Aqua satellites produces a suite of products designed to characterize global aerosol distribution, optical thickness and particle size. Never before has a space-borne instrument been able to provide such detailed information, operationally, on a nearly global basis every day. The three years of Terra-MODIS data have been validated by comparing with co-located AERONET observations of aerosol optical thickness and derivations of aerosol size parameters. Some 8000 comparison points located at 133 AERONET sites around the globe show that the MODIS aerosol optical thickness retrievals are accurate to within the pre-launch expectations. However, the validation in regions dominated by desert dust is less accurate than in regions dominated by fine mode aerosol or background marine sea salt. The discrepancy is most apparent in retrievals of aerosol size parameters over ocean. In dust situations, the MODIS algorithm tends to under predict particle size because the reflectances at top of atmosphere measured by MODIS exhibit the stronger spectral signature expected by smaller particles. This pattern is consistent with the angular and spectral signature of non-spherical particles. All possible aerosol models in the MODIS Look-Up Tables were constructed from Mie theory, assuming a spherical shape. Using a combination of MODIS and AERONET observations, in regimes dominated by desert dust, we construct phase functions, empirically, with no assumption of particle shape. These new phase functions are introduced into the MODIS algorithm, in lieu of the original options for large dust-like particles. The results will be analyzed and examined.

Remer, Lorraine A.↗

An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer

The Terrestrial Planet Finder formation flying Interferometer (TPF-I) will be a five-spacecraft, precision formation operating near the second Sun-Earth Lagrange point. As part of technology development for TPF-I, a formation and attitude control system (FACS) is being developed that achieves the precision and functionality needed for the TPF-I formation and that will be demonstrated in a distributed, real-time simulation environment. In this paper we present an overview of FACS and discuss in detail its formation estimation, guidance and control architectures and algorithms. Since FACS is currently being integrated into a high-fidelity simulation environment, component simulations demonstrating algorithm performance are presented.

Scharf, Daniel P.↗

Influence of Triply-Charged Ions and Ionization Cross-Sections in a Hybrid-PIC Model of a Hall Thruster Discharge

The sensitivity of xenon ionization rates to collision cross-sections is studied within the framework of a hybrid-PIC model of a Hall thruster discharge. A revised curve fit based on the Drawin form is proposed and is shown to better reproduce the measured crosssections at high electron energies, with differences in the integrated rate coefficients being on the order of 10% for electron temperatures between 20 eV and 30 eV. The revised fit is implemented into HPHall and the updated model is used to simulate NASA's HiVHAc EDU2 Hall thruster at discharge voltages of 300, 400, and 500 V. For all three operating points, the revised cross-sections result in an increase in the predicted thrust and anode efficiency, reducing the error relative to experimental performance measurements. Electron temperature and ionization reaction rates are shown to follow the trends expected based on the integrated rate coefficients. The effects of triply-charged xenon are also assessed. The predicted thruster performance is found to have little or no dependence on the presence of triply-charged ions. The fraction of ion current carried by triply-charged ions is found to be on the order of 1% and increases slightly with increasing discharge voltage. The reaction rates for the 0→III, I→III, and II→III ionization reactions are found to be of similar order of magnitude and are about one order of magnitude smaller than the rate of 0→II ionization in the discharge channel.

Hall Thrusters↗

Are Current SEE Test Procedures Adequate for Modern Devices and Electronics Technologies?

Believe it or not, this has been a simplistic look at starting a checklist for SEE testing. Given a memory that has 68 operating modes, when a SEU occurs that changes the mode, just how do you determine what's going on? Laser and microbeam tests can help, but not easily for modern packaged devices. Expanding this approach to other more complex devices such as ADCs or processors as well as analog devices should be considered. The recommendation is to use the existing text standards as the starting point. Just make your own checklist for the device/technology/issues being considered. At HEART 2007, we presented some of the burgeoning challenges associated with single event effect(SEE) testing of modern commercial memories: a) Package, device complexity, test fixture, and data analysis issues were discussed; b) "Complete" SEE Characterization would take 15 years; c) Qualification test costs have a greater than 4 times increase over the last decade. In this talk, we continue to explore the roles of technology with an emphasis on the existing SEE Test Procedures and some of the concerns related to modern devices. The primary objective of the briefing is to provide some overarching guidance concerning the many considerations involved in the formulation of a SEE test plan provided in a " Checklist" format.we note that there is no such thing as a complete check list and that the best approach is to develop a flexible test plan that takes into account the device type and functions, the device technology, circuit and package design, and, of course, test facility and beam characteristics.

LaBel, Kenneth A.↗

Cost Estimates of Roll-to-Roll Production of Organic Light Emitting Devices for Lighting

White organic light emitting devices (WOLEDs) offerdistinct advantages as solid state lighting sources, including high energy efficiency, superior color quality,and a flexible, thin profile that can accommodate a vast array of possible fixture designs. Recent advances in device lifetime and high speed deposition suggest that mass production of WOLED panels is approaching an inflection point. To understand the tradeoffs in the volume manufacturing of WOLED lighting panels, in this work, we estimate the cost of white WOLED panel production based on vacuum and vapor phase deposition in a roll-to-roll production line envisioned to yield an annual capacity of at least 6 × 10 6 m 2 . Assuming a WOLED operating luminance at 10 klm/m 2 , we anticipate a $\$12.5$ /klm cost of a WOLED light engine that includes the cost of the current driverand packaging. With incremental reduction in material and driver costs and improved luminance, the costof WOLED lighting can be reduced to $\$6.3$ /klm in thenear term, potentially positioning WOLEDs for use innumerous premium lighting applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum machine learning with differential privacy

Abstract Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach’s success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

97 MATHEMATICS AND COMPUTING↗

Hyper Suprime-Cam Legacy Archive

Abstract We present the launch of the Hyper Suprime-Cam Legacy Archive (HSCLA), a public archive of processed, science-ready data from the Hyper Suprime-Cam (HSC). HSC is an optical wide-field imager installed at the prime focus of the Subaru Telescope and has been in operation since 2014. While ∼1/3 of the total observing time of HSC has been used for the Subaru Strategic Program (SSP), the remainder of the time is used for Principal Investigator (PI)-based programs. We have processed the data from these PI-based programs and make the processed, high-quality data available to the community through HSCLA. The current version of HSCLA includes data taken in the first year of science operation, 2014. We provide both individual and coadd images as well as photometric catalogs. The photometric catalog from the coadd is loaded to the database, which offers a fast access to the large catalog. There are other online tools such as an image browser and an image cutout tool and they will be useful for science analyses. The coadd images reach 24–27th magnitudes at 5σ for point sources and cover approximately 580 square degrees in at least one filter with 150 million objects in total. We perform extensive quality assurance tests and verify that the photometric and astrometric quality of the data is good enough for most scientific explorations. However, the data are not without problems and users are referred to the list of known issues before exploiting the data for science. All the data and documentations can be found at the data release site, 〈https://hscla.mtk.nao.ac.jp/〉.

Tanaka, Masayuki↗

Large Space Shuttle Flight Experiment

It appears practical to challenge the Orbiter DAP with a large, attached structure. The definition of this capability is a fundamental step in the development of nearly all large space systems currently under consideration. Experiment features may be incorporated that apply to control systems for large space systems such as modal damping devices. In a relatively simple deployable structure, the correlation of flight test results with ground test and analysis should provide a basis for extrapolation to more complex structures. Initial experiment concepts will provide a starting point for the examination of antenna feed mast requirements with the objective changing the design to produce a representative test article. Correlation of construction operations with ground simulations will provide for better task and time-line definition. EVA needs to be a direct benefit to the conduct of the experiment. Early consideration of safety issues is a precaution against defining an unacceptable experiment concept. Integration of many objectives seems feasible and is generally perceived as the only way to justify a relatively expensive experiment.

Jenkins, L. M.↗

Astrophysics science operations in the Great Observatories era

Plans for Astrophysics science operations during the decade of the nineties are described from the point of view of a scientist who wishes to make a space-borne astronomical observation or to use archival astronomical data. 'Science Operations' include the following: proposal preparation, observation planning and execution, data collection, data processing and analysis, and dissemination of results. For each of these areas of science operations, we derive technology requirements for the next ten to twenty years. The scientist will be able to use a variety of services and infrastructure, including the 'Astrophysics Data System.' The current status and plans for these science operations services are described.

Riegler, Guenter R.↗

Cryogenic Optical Systems and Instrumentation IX (AM 116) Newly Modified Cryogenic Optical Test Facility at the Marshall Space Flight Center

Marshall Space Flight Center (MSFC) has maintained and operated a world-class x-ray optics and detector testing facility known as the X-ray Calibration Facility (XRCF) since the mid 1970's. The ground test and calibration of the Chandra X-ray Observatory optics and detectors were successfully completed at the XRCF in 1997. The beginning of the Next Generation Space Telescope (NGST) development programs (NMSD, SBMD, AMSD, etc.) and the establishment of the Space Optics Manufacturing Technology Center at MSFC have led to an XRCF modification. In 1999 the facility was upgraded to perform cryogenic testing of lightweight visible optics (without compromising the existing x-ray testing capability). A thermal enclosure capable of 20 degrees Kelvin and vibration isolated instrumentation mount were added. A vacuum-compatible five-axis motion table was modified to operate under cryogenic conditions. Optics up to two meters in diameter with radii of curvature of up to twenty meters can be accommodated. Facility characterization tests and one NGST program mirror test have been completed to date. By July 2000, two other mirrors will be tested. Optical wavefront measurements were made at < 35 degrees Kelvin with several instruments located at the test mirror's radius of curvature. The current wavefront measuring instruments include a Shack-Hartman wavefront sensor, a point diffraction interferometer, a point spread function-measuring device, and a radius of curvature measuring instrument. A vibration insensitive phase shifting interferometer is planned for future optical testing. This paper will present a brief history of the facility, a discussion of its current x-ray optic testing capabilities, and a complete description of the new capabilities in the visible optical testing regime.

Eng, Ronnie↗

Evolution of NASA's Near-Earth Tracking and Data Relay Satellite System (TDRSS)

NASA's Tracking and Data Relay Satellite System (TDRSS) is now in its 23rd year of operations and its spacecraft fleet includes three second-generation spacecraft launched since the year 2000; a figure illustrates the first generation TDRSS spacecraft. During this time frame the TDRSS has provided communications relay support to a broad range of missions, with emphasis on low-earth-orbiting (LEO) spacecraft that include unmanned science spacecraft (e.g., Hubble Space Telescope), and human spaceflight (Space Shuttle and Space Station). Furthermore, the TDRSS has consistently demonstrated its uniqueness and adaptability in several ways. First, its S- and K-band services, combined with its multi-band/steerable single-access (SA) antennas and ground-based configuration flexibility, have permitted the mission set to expand to unique users such as scientific balloons and launch vehicles. Second, the bent-pipe nature of the system has enabled the introduction of new/improved services via technology insertion and upgrades at each of the ground terminals; a specific example here is the Demand Access Service (DAS), which, for example, is currently providing science-alert support to NASA science missions Third, the bent-pipe nature of the system, combined with the flexible ground-terminal signal processing architecture has permitted the demonstration/vaIidation of new techniques/services/technologies via a real satellite channel; over the past 10+ years these have, for example, included demonstrations/evaluations of emerging modulation/coding techniques. Given NASA's emerging Exploration plans, with missions beginning later this decade and expanding for decades to come, NASA is currently planning the development of a seamless, NASA-wide architecture that must accommodate missions from near-earth to deep space. Near-earth elements include Ground-Network (GN) and Near-Earth Relay (NER) components and both must efficiently and seamlessly support missions that encompass: earth orbit, including dedicated science missions and lunar support/cargo vehicles; earth/moon transit; lunar in-situ operations; and other missions within approximately 2 million km of earth (e.g., at the sun/earth libration points). Given that the NER is an evolution of TDRSS, one element of this NASA-wide architecture development activity is a trade study of future NER architecture candidates. The present paper focuses on trade study aspects associated with the NER, highlights study elements, and provides representative interim results.

Flaherty, Roger↗

Telemedicine in Space Flight - Summary of a NASA Workshop

The Exploration Medical Capability Element of the Human Research Program at NASA Johnson Space Center hosted the Telemedicine Workshop in January 2011 to discuss the medical operational concept for a crewed mission to a near-Earth asteroid (NEA) and to identify areas for future work and collaboration. With the increased likelihood of a medical incident on a long duration exploration mission to a near-Earth asteroid, as well as the fact that there will likely be limited medical capabilities and resources available to diagnose and treat medical conditions, it is anticipated that a more structured use of telemedicine will become highly desirable. The workshop was convened to solicit expert opinion on current telemedicine practices and on medical care in remote environments. Workshop Objectives: The workshop brought together leaders in telemedicine and remote medicine from The University of Texas Medical Branch, Henry Ford Hospital, Ontario Telemedicine Network, U.S. Army Institute of Surgical Research, University of Miami, American Telemedicine Association, Doctors Without Borders, and the Pan American Health Organization. The primary objectives of the workshop were to document the medical operations concept for a crewed mission to a NEA, to determine gaps between current capabilities and the capabilities outlined in the operations concept, to identify research required to close these gaps, and to discuss potential collaborations with external-to-NASA organizations with similar challenges. Summary of Discussions and Conclusions: The discussions held during the workshop and the conclusions reached by the workshop participants were grouped into seven categories: Crew Medical Officers, Patient Area in Spacecraft, Training, Electronic Medical Records, Intelligent Care Systems, Consultation Protocols, Prophylactic Surgical Procedures, and Data Prioritization. The key points discussed under each category will be presented.

Barsten, K. N.↗

Behavior of Triple Langmuir Probes in Non-Equilibrium Plasmas

The triple Langmuir probe is an electrostatic probe in which three probe tips collect current when inserted into a plasma. The triple probe differs from a simple single Langmuir probe in the nature of the voltage applied to the probe tips. In the single probe, a swept voltage is applied to the probe tip to acquire a waveform showing the collected current as a function of applied voltage (I-V curve). In a triple probe three probe tips are electrically coupled to each other with constant voltages applied between each of the tips. The voltages are selected such that they would represent three points on the single Langmuir probe I-V curve. Elimination of the voltage sweep makes it possible to measure time-varying plasma properties in transient plasmas. Under the assumption of a Maxwellian plasma, one can determine the time-varying plasma temperature T(sub e)(t) and number density n(sub e)(t) from the applied voltage levels and the time-histories of the collected currents. In the present paper we examine the theory of triple probe operation, specifically focusing on the assumption of a Maxwellian plasma. Triple probe measurements have been widely employed for a number of pulsed and timevarying plasmas, including pulsed plasma thrusters (PPTs), dense plasma focus devices, plasma flows, and fusion experiments. While the equilibrium assumption may be justified for some applications, it is unlikely that it is fully justifiable for all pulsed and time-varying plasmas or for all times during the pulse of a plasma device. To examine a simple non-equilibrium plasma case, we return to basic governing equations of probe current collection and compute the current to the probes for a distribution function consisting of two Maxwellian distributions with different temperatures (the two-temperature Maxwellian). A variation of this method is also employed, where one of the Maxwellians is offset from zero (in velocity space) to add a suprathermal beam of electrons to the tail of the main Maxwellian distribution (the bump-on-the-tail distribution function). For a range of parameters in these non-Maxwellian distributions, we compute the current collection to the probes. We compare the distribution function that was assumed a priori with the distribution function one would infer when applying standard triple probe theory to analyze the collected currents. For the assumed class of non-Maxwellian distribution functions this serves to illustrate the effect a non-Maxwellian plasma would have on results interpreted using the equilibrium triple probe current collection theory, allowing us to state the magnitudes of these deviations as a function of the assumed distribution function properties.

Polzin, Kurt A.↗

Durability Characterization of Low Ice Adhesion and Impact Resistance Coatings

Glaze, rime and mixed icing conditions can cause significant variation in aerodynamic performance, fuel efficiency, and flight safety. For commercial aircraft, active icing mitigation strategies are utilized to enable safe flight within icing conditions according to the FAR Part 25/29 Appendix C icing envelope. For general aviation and unmanned aerial vehicles that cannot support active anti-icing technologies, avoidance is the only recourse. Passive approaches have been investigated to reduce weight and energy consumption for active systems and to expand the operational envelope for smaller aircraft. Coatings are one passive method to reduce or mitigate ice accretion on frontal surfaces of commercial aircraft with the greatest region of interest being wing leading edges. Aircraft wing leading edges represent an extreme environment. Durability must be considered for any material to be applied as a coating in this area. Currently, there are no specifications regarding coating durability of a low ice adhesion material applied on the wing leading edge. Therefore, a reasonable starting point is to use the durability specifications put forth for an aircraft external coating. Besides the tests called out in these specifications, others were included such as Taber abrasion to simulate wear and erosion. Beyond durability, performance metrics with regards to adhesion strength of accreted in-flight (i.e., impact) icing are central to determine coating usefulness. Determination of this property though is particularly challenging and only a few facilities have the capability to quantify this. An instrument at NASA Langley Research Center [Adverse Environment Rotary Test Stand Jr., (AERTS Jr.)], based on the AERTS system at The Pennsylvania State University, allows for screening numerous coatings subjected to the icing environment. To establish a benchmark for comparison with research coatings, a state-of-the-art (SOA) commercial aircraft coating was subjected to an array of salient durability and performance experiments. The same tests were conducted using a baseline epoxy (BE) resin formulation that demonstrated some initial promising results for comparison. Results from this initial screening will be discussed herein.

Miranda L Beaudry↗

Testing of Liquid Metal Components for Nuclear Surface Power Systems

The Early Flight Fission Test Facility (EFF-TF) was established by the Marshall Space Flight Center (MSFC) to provide a capability for performing hardware-directed activities to support multiple in-space nuclear reactor concepts by using a non-nuclear test methodology. This includes fabrication and testing at both the module/component level and near prototypic reactor configurations. The EFF-TF is currently supporting an effort to develop an affordable fission surface power (AFSP) system that could be deployed on the Lunar surface. The AFSP system is presently based on a pumped liquid metal-cooled (Sodium-Potassium eutectic, NaK-78) reactor design. This design was derived from the only fission system that the United States has deployed for space operation, the Systems for Nuclear Auxiliary Power (SNAP) 10A reactor, which was launched in 1965. Two prototypical components recently tested at MSFC were a pair of Stirling power conversion units that would be used in a reactor system to convert heat to electricity, and an annular linear induction pump (ALIP) that uses travelling electromagnetic fields to pump the liquid metal coolant through the reactor loop. First ever tests were conducted at MSFC to determine baseline performance of a pair of 1 kW Stirling convertors using NaK as the hot side working fluid. A special test rig was designed and constructed and testing was conducted inside a vacuum chamber at MSFC. This test rig delivered pumped NaK for the hot end temperature to the Stirlings and water as the working fluid on the cold end temperature. These test were conducted through a hot end temperature range between 400 to 550C in increments of 50 C and a cold end temperature range from 30 to 70 C in 20 C increments. Piston amplitudes were varied from 6 to 1 1mm in .5 mm increments. A maximum of 2240 Watts electric was produced at the design point of 550 hot end, 40 C cold end with a piston amplitude of 10.5mm. This power level was reached at a gross thermal efficiency of 28%. A baseline performance map was established for the pair of 1kW Stirling convertors. The performance data will then be used for design modification to the Stirling convertors. The ALIP tested at MSFC has no moving parts and no direct electrical connections to the liquid metal containing components. Pressure is developed by the interaction of the magnetic field produced by the stator and the current which flows as a result of the voltage induced in the liquid metal contained in the pump duct. Flow is controlled by variation of the voltage supplied to the pump windings. Under steady-state conditions, pump performance is measured for flow rates from 0.5-4.3 kg/s. The pressure rise developed by the pump to support these flow rates is roughly 5-65 kPa. The RMS input voltage (phase-to-phase voltage) ranges from 5-120 V, while the frequency can be varied arbitrarily up to 60 Hz. Performance is quantified at different loop temperature levels from 50 C up to 650 C, which is the peak operating temperature of the proposed AFSP reactor. The transient response of the pump is also evaluated to determine its behavior during startup and shut-down procedures.

Polzin, Kurt A.↗

An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer

The Terrestrial Planet Finder formation flying Interferometer (TPF-I) will be a five-spacecraft, precision formation operating near a Sun-Earth Lagrange point. As part of technology development for TPF-I, a formation and attitude control system (FACS) is being developed that achieves the precision and functionality associated with the TPF-I formation. This FACS will be demonstrated in a distributed, real-time simulation environment. In this paper we present an overview of the FACS and discuss in detail its constituent formation estimation, guidance and control architectures and algorithms. Since the FACS is currently being integrated into a high-fidelity simulation environment, component simulations demonstrating algorithm performance are presented.

Terrestrial Planet Finder (TPF)↗

Optimization of the Carbon Dioxide Removal Assembly (CDRA-4EU) in Support of the International Space System and Advanced Exploration Systems

The Life Support Systems Project (LSSP) under the Advanced Exploration Systems (AES) program builds upon the work performed under the AES Atmosphere Resource Recovery and Environmental Monitoring (ARREM) project focusing on the numerous technology development areas. The Carbon Dioxide (CO2) removal and associated air drying development efforts are focused on improving the current state-of-the-art system on the International Space Station (ISS) utilizing fixed beds of sorbent pellets by seeking more robust pelletized sorbents, evaluating structured sorbents, and examining alternate bed configurations to improve system efficiency and reliability. A component of the CO2 removal effort utilizes a virtual Carbon Dioxide Removal Assembly, revision 4 (CDRA-4) test bed to test a large number of potential operational configurations with independent variations in flow rate, cycle time, heater ramp rate, and set point. Initial ground testing will provide prerequisite source data and provide baseline data in support of the virtual CDRA. Once the configurations with the highest performance and lowest power requirements are determined by the virtual CDRA, the results will be confirmed by testing these configurations with the CDRA-4EU ground test hardware. This paper describes the initial ground testing of select configurations. The development of the virtual CDRA under the AES-LSS Project will be discussed in a companion paper.

Knox, James C.↗