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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.

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267 records · Page 15

NASA Tech Briefs, February 2004

Topics include: Simulation Testing of Embedded Flight Software; Improved Indentation Test for Measuring Nonlinear Elasticity; Ultraviolet-Absorption Spectroscopic Biofilm Monitor; Electronic Tongue for Quantitation of Contaminants in Water; Radar for Measuring Soil Moisture Under Vegetation; Modular Wireless Data-Acquisition and Control System; Microwave System for Detecting Ice on Aircraft; Routing Algorithm Exploits Spatial Relations; Two-Finger EKG Method of Detecting Evasive Responses; Updated System-Availability and Resource-Allocation Program; Routines for Computing Pressure Drops in Venturis; Software for Fault-Tolerant Matrix Multiplication; Reproducible Growth of High-Quality Cubic-SiC Layers; Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites; Liquid-Crystal Thermosets, a New Generation of High-Performance Liquid-Crystal Polymers; Formulations for Stronger Solid Oxide Fuel-Cell Electrolytes; Simulation of Hazards and Poses for a Rocker-Bogie Rover; Autonomous Formation Flight; Expandable Purge Chambers Would Protect Cryogenic Fittings; Wavy-Planform Helicopter Blades Make Less Noise; Miniature Robotic Spacecraft for Inspecting Other Spacecraft; Miniature Ring-Shaped Peristaltic Pump; Compact Plasma Accelerator; Improved Electrohydraulic Linear Actuators; A Software Architecture for Semiautonomous Robot Control; Fabrication of Channels for Nanobiotechnological Devices; Improved Thin, Flexible Heat Pipes; Miniature Radioisotope Thermoelectric Power Cubes; Permanent Sequestration of Emitted Gases in the Form of Clathrate Hydrates; Electrochemical, H2O2-Boosted Catalytic Oxidation System; Electrokinetic In Situ Treatment of Metal-Contaminated Soil; Pumping Liquid Oxygen by Use of Pulsed Magnetic Fields; Magnetocaloric Pumping of Liquid Oxygen; Tailoring Ion-Thruster Grid Apertures for Greater Efficiency; and Lidar for Guidance of a Spacecraft or Exploratory Robot.

Source record↗

Assessment of the NASA Glenn 8- by 6-Foot Supersonic Wind Tunnel Supersonic Test Section for Sonic Boom and Supersonic Testing

The NASA Glenn Research Center performed a Sonic Boom Exploratory test with Boeing as an industry partner. The test was performed in the transonic test section of the 8-by 6-foot supersonic wind tunnel (8x6 SWT) in 2012. Since that test, research has been performed to validate the suitability of the supersonic test section, located upstream of the 8x6 transonic test section. This little used upstream supersonic test section can be better for certain objectives in supersonic testing and sonic boom validation. Background pressure profiles were collected in a Mach number stability test (in 2014) with a sonic boom pressure measurement rail installed in the ceiling of the smooth supersonic test section. Results from this test demonstrated favorable background pressure profiles for future sonic boom validation tests. A preliminary supersonic test section calibration was performed in 2016, followed by a detailed calibration in 2020; which also demonstrated the stable and uniform flow characteristics in the supersonic test section. The calibration test utilized the transonic array and the cone-cylinder calibration model in the smooth supersonic test section of the 8x6 SWT. Completion of the calibration prepared the facility for sonic boom assessments of the Low Boom Flight Demonstrator.

Sonic Boom↗

Determination of the Risk of Radiation-Associated Circulatory and Cancer Disease Mortality in a NASA Early Astronaut Cohort

Of the many possible health challenges posed during extended exploratory missions to space, the effects of space radiation on cardiovascular disease and cancer are of particular concern. There are unique challenges to estimating those radiation risks; care and appropriate and rigorous methodology should be applied when considering small cohorts such as the NASA astronaut population. The objective of this work was to determine if there was sufficient evidence for excess risk of cardiovascular disease and cancer in early NASA astronaut cohorts. NASA astronauts in selection groups 1-7 were chosen; this relatively homogeneous cohort consists of 73 white males, who unlike today's astronauts, maintained similar smoking and drinking habits to the general US population, and have published radiation doses. The participants flew in space on missions Mercury through Shuttle and received space radiation doses between 0-74.1 milligrays. Cause of death information was obtained from the Lifetime Surveillance of Astronaut Health (LSAH) program at NASA Johnson Space Center. Mortality was compared with the US male population. Trends of mortality with dose were assessed using a logistic model, fitted by maximum likelihood. Only 32 (43.84 percent) of the 73 early astronauts have died. Standard mortality ratios (SMRs) for cancer (n=7, SMR=43.4, 95 percent CI 17.8, 84.9), all circulatory disease (n=7, SMR=33.2, 95 percent CI 13.7, 65.0), and ischemic heart disease (IHD) (n=5, SMR=40.1, 95 percent CI 13.2, 89.4) were significantly lower than for the US white male population. For cerebrovascular disease, the upper confidence interval for SMR included 100, indicating it was not significantly different from the US population (n=2, SMR = 77.0, 95 percent CI 9.4, 268.2). The power of the study is low and remains below 10 percent even when risks 10 times those reported in the literature are assumed. Due to small sample size, there is currently insufficient statistical power to evaluate space radiation exposure effects on mortality in NASA astronauts. In addition to a comprehensive longitudinal study of NASA astronauts, a research strategy of low dose epidemiology data integration with cell and animal studies should be utilized for space radiation risk assessment in the astronauts.

Elgart, S. R.↗

Hippocampal place-cell firing during movement in three-dimensional space

"Place" cells of the rat hippocampus are coupled to "head direction" cells of the thalamus and limbic cortex. Head direction cells are sensitive to head direction in the horizontal plane only, which leads to the question of whether place cells similarly encode locations in the horizontal plane only, ignoring the z axis, or whether they encode locations in three dimensions. This question was addressed by recording from ensembles of CA1 pyramidal cells while rats traversed a rectangular track that could be tilted and rotated to different three-dimensional orientations. Cells were analyzed to determine whether their firing was bound to the external, three-dimensional cues of the environment, to the two-dimensional rectangular surface, or to some combination of these cues. Tilting the track 45 degrees generally provoked a partial remapping of the rectangular surface in that some cells maintained their place fields, whereas other cells either gained new place fields, lost existing fields, or changed their firing locations arbitrarily. When the tilted track was rotated relative to the distal landmarks, most place fields remapped, but a number of cells maintained the same place field relative to the x-y coordinate frame of the laboratory, ignoring the z axis. No more cells were bound to the local reference frame of the recording apparatus than would be predicted by chance. The partial remapping demonstrated that the place cell system was sensitive to the three-dimensional manipulations of the recording apparatus. Nonetheless the results were not consistent with an explicit three-dimensional tuning of individual hippocampal neurons nor were they consistent with a model in which different sets of cells are tightly coupled to different sets of environmental cues. The results are most consistent with the statement that hippocampal neurons can change their "tuning functions" in arbitrary ways when features of the sensory input or behavioral context are altered. Understanding the rules that govern the remapping phenomenon holds promise for deciphering the neural circuitry underlying hippocampal function.

Non-NASA Center↗

Compendium of NASA data base for the global tropospheric experiment's Pacific Exploratory Mission West-B (PEM West-B)

This compendium describes aircraft data that are available from NASA's Pacific Exploratory Mission West-B (PEM West-B). PEM West is a component of the International Global Atmospheric Chemistry's (IGAC) East Asia/North Pacific Regional Study (APARE) project. Objectives of PEM West are to investigate the atmospheric chemistry of ozone over the northwest Pacific -- natural budgets and the impact of anthropogenic/continental sources; and to investigate sulfur chemistry -- continental and marine sulfur sources. The PEM West program encompassed two expeditions. PEM West-A was conducted in September 1991 during which the predominance of tropospheric air was from mid-Pacific (marine) regions, but (at times) was modified by Asian outflow. PEM West-B was conducted during February 1994, a period characterized by maximum Asian outflow. Results from PEM West-A and B are public domain. PEM West-A data are summarized in NASA TM 109177 (published February 1995). Flight experiments were based at Guam, Hong Kong, and Japan. This document provides a representation of NASA DC-8 aircraft data that are available from NASA Langley's Distributed Active Archive Center (DAAC). The DAAC includes numerous other data such as meteorological and modeling products, results from surface studies, satellite observations, and sonde releases.

Gregory, Gerald L.↗

Compendium of NASA data base for the Global Tropospheric Experiment's Pacific Exploratory Mission West-A (PEM West-A)

This compendium describes aircraft data that are available from NASA's Pacific Exploratory Mission West-A (PEM West-A). PEM West is a component of the International Global Atmospheric Chemistry's (IGAC) East Asia/North Pacific Regional Study (APARE) project. The PEM- West program encompassed two expeditions to study contrasting meteorological regimes in the Pacific. Objectives of PEM West are to investigate the atmospheric chemistry of ozone over the northwest Pacific -- natural budgets and the impact of anthropogenic sources; and to investigate sulfur chemistry -- continental versus marine sulfur sources. PEM West-A was conducted in September 1991 during which the predominance of tropospheric air is from the mid-Pacific (marine) regions, but (at times) is modified/mixed with Asian continental outflow. PEM West-B was conducted during February 1994, a period characterized by maximum continental outflow. PEM-B data (not included) will become public domain during the Summer of 1995. PEM West-A flight experiments were based at Japan, Hong Kong, and Guam. This document provides a representation of NASA DC-8 aircraft data that are available from NASA Langley's Distributed Active Archive Center (DAAC), which include numerous data such as meteorological observations, modeling products, results from surface studies, satellite observations, and sonde releases.

Gregory, G. L.↗

Interface Consistency: Phase I Results & Phase II Status

Future exploration missions will rely on designing and developing vehicles and complex systems from within NASA and through multiple external commercial partners to meet mission goals. Despite existing consistency-related agency requirements, NASA’s approach to commercial spaceflight development encourages providers’ flexibility and innovation. This strategy is resulting in significant design diversity across Artemis vehicles. Design best practices and guidelines champion interface consistency to promote mental model development and knowledge transfer. However, research investigating the benefits of consistency is mixed, and little is known about its role in complex systems. Determining the level of risk that system diversity presents is difficult, as there is no established method for quantifying the degree of consistency within and across interfaces, nor is there information about the differential impacts of different types of inconsistency. Phase I of this project (Characterization and Measurement) served as a starting point to better understand the construct of consistency, its application, and the range of studies and methods for measuring it. The project team created a taxonomy of consistency to apply to interfaces as a framework to guide the development of tools to assess intersystem consistency. Checklist and cognitive walkthrough methods were developed for use by human factors (HF) and human-computer interaction (HCI) experts. The Intersystem Consistency Scale (ICS) was developed for interface evaluations with crew. A pilot study evaluated the methods’ ability to distinguish differences between Artemis-like prototype pairs exhibiting either high or low design consistency. In addition, click errors and time on task were collected within the ICS (crew-like) group. Results from our exploratory analysis and lessons learned from the pilot study will be discussed. The project team will also present the status of Phase II (Risk Assessment, Standards and Guidelines). This includes incorporating feedback to redesign the assessment tools, and inputs from displays and training Subject Matter Experts to update tasks and prototype designs. The team will present the risk assessment study design to identify the types and levels of inconsistency that pose the greatest risk to performance. Plans to apply these results toward agency standards and guideline recommendations will also be discussed.

Human-Computer Interaction↗

Directionally Sensitive Silicon Radiation Sensor (VCELL)

Sensors are a mission critical element in many NASA programs and require some very unique properties such as small size, low power, high reliability, low weight. Low cost sensors offer the possibility of technology transfer to the public domain for commercial applications. One sensor application that is important to many NASA programs is the ability to point at a radiation source, such as the sun. Such sensors may be an integral part of the guidance and control systems in space platforms and in remote exploratory vehicles. Sun/solar pointing is also important for ground-based systems such as solar arrays. These systems are not required to be small and lightweight. However, if a sensor with a sun pointing capability was developed that is very small, rugged, lightweight and at the same time low cost, it certainly could be used in existing and perhaps many new ground based applications. The objective of the VCELL (Directionally Sensitive Silicon Radiation Sensor) research is to develop a new and very unique silicon based directionally sensitive radiation sensor which can be fabricated using conventional monolithic IC technologies and which will meet the above requirements. The proposed sensor is a novel silicon chip that is directionally sensitive to incident radiation, providing azimuth and elevation information on the incident radiation. The resulting sensor chip will be appropriate for integration into a silicon IC or useful in a hybrid structure to be interfaced with a standard IEEE 1451 bus interface IC to create an Intelligent Sensor. It is presently estimated that it will require about three man-years of effort to complete the VCELL research and development. This includes the optical, electrical, mechanical and silicon fabrication and testing as well as computer simulations and theoretical analysis and modeling including testing in simulated space environments. This report summarizes the sensor research completed this summer as part of the Summer Faculty Fellowship Program. The primary effort was focused on activity necessary to fabricate prototype sensor.

Koy B. Cook↗

An Exploratory Exercise in Taguchi Analysis of Design Parameters: Application to a Shuttle-to-space Station Automated Approach Control System

The chief goals of the summer project have been twofold - first, for my host group and myself to learn as much of the working details of Taguchi analysis as possible in the time allotted, and, secondly, to apply the methodology to a design problem with the intention of establishing a preliminary set of near-optimal (in the sense of producing a desired response) design parameter values from among a large number of candidate factor combinations. The selected problem is concerned with determining design factor settings for an automated approach program which is to have the capability of guiding the Shuttle into the docking port of the Space Station under controlled conditions so as to meet and/or optimize certain target criteria. The candidate design parameters under study were glide path (i.e., approach) angle, path intercept and approach gains, and minimum impulse bit mode (a parameter which defines how Shuttle jets shall be fired). Several performance criteria were of concern: terminal relative velocity at the instant the two spacecraft are mated; docking offset; number of Shuttle jet firings in certain specified directions (of interest due to possible plume impingement on the Station's solar arrays), and total RCS (a measure of the energy expended in performing the approach/docking maneuver). In the material discussed here, we have focused on single performance criteria - total RCS. An analysis of the possibility of employing a multiobjective function composed of a weighted sum of the various individual criteria has been undertaken, but is, at this writing, incomplete. Results from the Taguchi statistical analysis indicate that only three of the original four posited factors are significant in affecting RCS response. A comparison of model simulation output (via Monte Carlo) with predictions based on estimated factor effects inferred through the Taguchi experiment array data suggested acceptable or close agreement between the two except at the predicted optimum point, where a difference outside a rule-of-thumb bound was observed. We have concluded that there is most likely an interaction effect not provided for in the original orthogonal array selected as the basis for our experimental design. However, we feel that the data indicates that this interaction is a mild one and that inclusion of its effect will not alter the location of the optimum.

Deal, Don E.↗

Exploring Applications of Machine Learning for Wildfire Monitoring and Detection using Unmanned Aerial Vehicles

Wildfires are increasing in frequency and severity around the world, including the United States. The losses caused by wildfires could be mitigated if high-risk areas, hotspots, and flare-ups could be monitored continuously, such as through the use of Unmanned Aerial Vehicles (UAVs). This paper documents exploratory efforts using machine learning to determine efficient flight paths for UAVs and to detect wildfires using image classification. On path planning, three machine learning techniques—Genetic Algorithm, Simulated Annealing, and Dynamic Programming—were explored. Genetic Algorithm was found to be an effective approach for path planning for wildfire monitoring and surveillance by UAVs. For a scenario of 25 locations in a circular arrangement, the algorithm was able to return the optimal path. The accuracy and execution time was found to be sensitive to the algorithm hyperparameters selected, which was especially evident in scenarios with hundreds or thousands of locations. Simulated Annealing was also found to be an effective approach for UAV path planning, with a major benefit of avoiding getting trapped in local minima and being straightforward to implement. Like Genetic Algorithm, the performance of Simulated Annealing was also found to be sensitive to the algorithm hyperparameters selected. By comparison, Dynamic Programming guarantees optimality for any number of locations, but it was found to be less practical in terms of execution time for scenarios with more than about a couple dozen locations. On wildfire detection, image classification using deep learning with a convolutional neural network was explored. Transfer learning was found to be a useful technique to efficiently train deep learning models. Also, it was determined that GPU processing can increase training speed by an order of magnitude, which enables significantly faster development. For a validation test set of 500 images, there were only two false negatives and zero false positives. These results demonstrate that detecting wildfires in static cameras using machine learning is feasible and establish a baseline for using images captured by UAVs in flight for wildfire detection.

Wildfire management↗

Algorithms and Libraries

This exploratory study initiated our inquiry into algorithms and applications that would benefit by latency tolerant approach to algorithm building, including the construction of new algorithms where appropriate. In a multithreaded execution, when a processor reaches a point where remote memory access is necessary, the request is sent out on the network and a context--switch occurs to a new thread of computation. This effectively masks a long and unpredictable latency due to remote loads, thereby providing tolerance to remote access latency. We began to develop standards to profile various algorithm and application parameters, such as the degree of parallelism, granularity, precision, instruction set mix, interprocessor communication, latency etc. These tools will continue to develop and evolve as the Information Power Grid environment matures. To provide a richer context for this research, the project also focused on issues of fault-tolerance and computation migration of numerical algorithms and software. During the initial phase we tried to increase our understanding of the bottlenecks in single processor performance. Our work began by developing an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. Based on the results we achieved in this study we are planning to study other architectures of interest, including development of cost models, and developing code generators appropriate to these architectures.

Dongarra, Jack↗

Underwater Multi-Node Radio Communication Solutions for Planetary Exploration

The exploration of the presumably life harboring subsurface ocean of Europa will provide scientists with extensive new knowledge in the search for extraterrestrial life. A highly miniaturized payload is required to penetrate a narrow passage through the thick ice crust covering Europa's surface. Underwater wireless communications may be the most viable means of communication for such exploratory missions, accounting for size and weight restrictions. This presents a challenge to achieve satisfactory data rates and a range that permits autonomous underwater vehicles (AUVs) to communicate within their region of operation, as well as with a surface lander or orbiter. This work presents thorough prototype experimentation on an underwater communication system established between several nodes using RF signals. During an eight-week internship experience at NASA's Ames Research Center in September-October 2014, our team developed a Europa exploration mission concept, built representative hardware, and carried out tests to assess the feasibility of key aspects of the concept. Experiments demonstrating the viability of RF communication underwater comprised inspecting the effect of depth and horizontal distance on signal strength as well as the optimum positioning of antennas. To test the system's performance, two submersibles were designed and built. A commercially available remotely operated vehicle (ROV) was also modified and used as a main communication node. The two submersibles were wirelessly connected and accommodated sensors capable of characterizing water properties and equipped with 2.4 GHz, 1 mW transceivers to communicate the measured data. The communication procedure is that the main communication node requests the collected data from the two submersibles when in range and receives it instantly through RF. This work models what may take place during an actual mission to Europa. The developed mission concept involved a hybrid communication system consisting of acoustic and RF signals to enhance the capability of the nodes to communicate over greater distances. The AUVs will need to avoid obstacles and maneuver around to collect data based on predefined algorithms. Thus, they will be provided with two positioning systems; the inertial navigation system, backed with an acoustic positioning system to mitigate drift. The AUVs divide the ocean into planes and explore along circular paths increasing in diameter with depth. Moreover, they make use of miniaturized sensors to map the surrounding environment. In this paper, the ROV and the submersibles are described, along with sections explaining the mechanism of communication and the testing procedures conducted to yield results.

Europa↗

Exploring Earth's Interface with Space: The Scientific Case for a Satellite Mission to the Lower Thermosphere-Ionosphere Transition Region

The ESA-NASA Lower Thermosphere-Ionosphere Science (ENLoTIS) Working Group was formed in May 2022 to cooperatively explore future lower thermosphere-ionosphere (LTI) satellite mission concepts, targeting very low altitudes (100-200 km) with in situ sampling of relevant geophysical parameters associated with the neutral atmosphere, the ionosphere’s plasma, electromagnetic fields, and energetic particles, which, together with modeling, would enable significant advancements in the understanding of neutral-ion interactions and other related science and space weather topics in this critical region of Geospace. The LTI region has been identified as one of considerable interest to both NASA and ESA. Most recently, the Daedalus mission study was carried out under the remit of ESA’s Earth Observation Programmes (EOP) Directorate competitive Earth Explorer 10 pre-feasibility (Phase 0) activities. Furthermore, many NASA studies have also focused on the LTI region, including both directed missions with dipping spacecraft, such as the initial TIMED dual-satellites and the GEC constellation, as well as numerous highly-rated Explorer proposals targeting the LTI. Although the Daedalus mission was not selected, the ESA Advisory Committee on Earth Observation (ACEO) ranked it highly on scientific grounds and encouraged further study activities to mature the concept, exploring potential international collaboration. Subsequent bilateral discussions with NASA’s Science Mission Directorate (SMD) noted that such a concept was in alignment with the 2020 SMD science plan – Science 2020-2024: A Vision for Scientific Excellence – along with other complimentary activities within the NASA Heliophysics Division. Building on NASA’s and ESA’s long history of very successful collaborations, this mutual interest in LTI science led to the establishment of a new inter-agency and cross-discipline science connection, linking the ESA EOP Climate Action, Sustainability and Science Department and the NASA Heliophysics Division. Initial exploratory discussions led to the formation of the ENLoTIS Working Group, which was directed to explore the science case behind a potential joint LTI mission. Members of the ENLoTIS Working Group are listed below, consisting of 7 scientists from ESA Member and Cooperating States and 7 scientists from the United States. The working group held 3 “in person” meetings over the course of 18 months, interspersed with regular virtual meetings on a more frequent basis. This report constitutes their chief findings and recommendations.

thermosphere↗

Reforming and decomposition of glucose in an aqueous phase

Exploratory experiments have been carried out to study the decomposition of glucose, a typical carbohydrate, in a high temperature-high pressure water reactor. The objective of the study was to examine the feasibility of such a process to decompose cellulosic waste materials in long-term space missions. At temperatures below the critical point of water, glucose decomposed to form liquid products and char. Little gas was noted with or without reforming catalysts present. The rate of the primary glucose reaction increased significantly with temperature. Partial identification of the liquid phase was made and the C:H:O ratios determined for both the liquid and solid products. One of the more interesting results from this study was the finding that when glucose was injected into a reactor held at the critical temperature (and pressure) of water, no solid products formed. Gas production increased, but the majority of the carbon was found in soluble furans (and furan derivatives). This significant result is now being investigated further.

Amin, S.↗

A manufacturing database of advanced materials used in spacecraft structures

Cost savings opportunities over the life cycle of a product are highest in the early exploratory phase when different design alternatives are evaluated not only for their performance characteristics but also their methods of fabrication which really control the ultimate manufacturing costs of the product. In the past, Design-To-Cost methodologies for spacecraft design concentrated on the sizing and weight issues more than anything else at the early so-called 'Vehicle Level' (Ref: DOD/NASA Advanced Composites Design Guide). Given the impact of manufacturing cost, the objective of this study is to identify the principal cost drivers for each materials technology and propose a quantitative approach to incorporating these cost drivers into the family of optimization tools used by the Vehicle Analysis Branch of NASA LaRC to assess various conceptual vehicle designs. The advanced materials being considered include aluminum-lithium alloys, thermoplastic graphite-polyether etherketone composites, graphite-bismaleimide composites, graphite- polyimide composites, and carbon-carbon composites. Two conventional materials are added to the study to serve as baseline materials against which the other materials are compared. These two conventional materials are aircraft aluminum alloys series 2000 and series 7000, and graphite-epoxy composites T-300/934. The following information is available in the database. For each material type, the mechanical, physical, thermal, and environmental properties are first listed. Next the principal manufacturing processes are described. Whenever possible, guidelines for optimum processing conditions for specific applications are provided. Finally, six categories of cost drivers are discussed. They include, design features affecting processing, tooling, materials, fabrication, joining/assembly, and quality assurance issues. It should be emphasized that this database is not an exhaustive database. Its primary use is to make the vehicle designer aware of some of the most important aspects of manufacturing associated with his/her choice of the structural materials. The other objective of this study is to propose a quantitative method to determine a Manufacturing Complexity Factor (MCF) for each material being contemplated. This MCF is derived on the basis of the six cost drivers mentioned above plus a Technology Readiness Factor which is very closely related to the Technology Readiness Level (TRL) as defined in the Access To Space final report. Short of any manufacturing information, our MCF is equivalent to the inverse of TRL. As more manufacturing information is available, our MCF is a better representation (than TRL) of the fabrication processes involved. The most likely application for MCF is in cost modeling for trade studies. On-going work is being pursued to expand the potential applications of MCF.

Bao, Han P.↗