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650 records · Page 32

Thermal Data-driven Model Reduction for Enhanced Battery Health Monitoring

Electric aviation faces a major challenge of avoiding potentially catastrophic consequences of the battery’s thermal runaway while keeping the weight of the battery low. Detection of early warning signals of battery failures requires accurate monitoring of the battery’s health throughout its lifespan. However, identifying the parameters of the battery from field data is notoriously difficult. We investigate this problem within the framework of modeling the temperature dynamics of a Li-ion cell during tests simulating loading in electric aircraft flights. It is found that the parameters of a higher-fidelity physics-based thermal model cannot be identified from the simulated flight data. To resolve this issue, we reduce the higher-fidelity thermal model to a model with fewer parameters. The resulting reduced-order model can predict temperature dynamics accurately and is identifiable throughout the cell’s lifespan which allows using the model’s parameters to monitor the state-of-health of the aging cell and detect anomalies in thermal behavior.

Li ion batteries

Advances in Design Capabilities for Planetary Missions from the NASA Entry Systems Modeling and Instrumentation Portfolio

The Entry Systems Modeling project (ESM) is supported by both the NASA Space Technology and the Science Mission Directorates and focuses on developing simulation tools and validated models for characterizing the performance of entry systems tailored to planetary destinations across the Solar System. ESM is organized into six technical capability areas that together address all relevant factors related to spacecraft entry, as well as some aspects of descent: Thermal Protection System (TPS) Materials; Aerothermodynamics; Entry & Descent Vehicle Dynamics; Guidance, Navigation, and Control; Vehicle Systems Analysis; and Advanced Tools and Numerical Methods. Development within the capability areas is undertaken explicitly with a focus on transition and infusion to science missions, human exploration missions, and commercial space activities. The present talk details developments that specifically impact science missions, including simulation tool capabilities that aid in mission design and model development to understand entry system performance at a given destination. Examples of the successful infusion and transition of such project outcomes to science missions also are provided. Several simulation tool development efforts within ESM have resulted in new design capabilities for missions. One such outcome is improved toolsets for mission trajectory and concept of operations design. Specifically, an initiative to couple a leading tool for entry, ascent/descent, and orbital trajectory optimization (Program to Optimize Simulated Trajectories II or POST2) to those used within the Agency for interplanetary trajectory optimization (Copernicus and Monte) has made substantial progress, with the outcomes to date promising to allow efficient trajectory optimization across mission phases. Additionally, toolchains for the evaluation of vehicle performance during entry and descent have been developed that allow assessment of multi-dimensional aeroheating on detailed vehicle geometries, characterization of deployment and inflation of parachutes, and assessment of vehicle dynamic stability during descent. These capabilities are achieved by coupling diverse sets of physics together – material response, computational fluid dynamics, radiation, and vehicle dynamics – to suitably describe complex entry and descent phenomena. Several model development and validation efforts for specific destinations and entry regimes also are underway within the ESM project. For instance, new experimental capabilities to validate radiation models at low densities/high altitudes recently have been established with project support, specifically the Low-Density Shock Tube (LDST) at the NASA Ames Research Center Electric Arc Shock Tube (EAST) facility. The LDST is being leveraged to develop improved models of shock layer kinetics and radiation in Titan atmospheres, while future studies will be conducted in the LDST and the existing high velocity shock tube to provide validation data for radiation models of Venus, Ice Giants, and Mars atmospheres. Models describing the aerothermal and thermo-structural performance of Thermal Protection System (TPS) materials has been another focus, with multiscale modeling activities on-going for the two leading TPS materials applicable to a range of entry conditions and science missions: the Phenolic-Impregnated Carbon Ablator (PICA) and woven materials like 3D Mid-Density Carbon Phenolic (3MDCP). A continual effort is made to infuse and transition outcomes from ESM simulation tool and model development activities into relevant science missions. Significant progress has been made on this front, with missions such as Dragonfly, DAVINCI, and Mars Missions benefitting from project outcomes. The groundwork also is being laid to provide insights into forward looking missions to Gas/Ice Giants as well as for potential sample returns.

Justin Haskins

Hubble Space Telescope 2004 Battery Update

Battery cell wear out mechanisms and signatures are examined and compared to orbital data from the six on-orbit Hubble Space Telescope (HST) batteries, and the Flight Spare Battery (FSB) Test Bed at Marshall Space Flight Center (MSFC), which is instrumented with individual cell voltage monitoring. The on-orbit HST batteries were manufactured on an expedited basis after the Challenger Shuttle Disaster in 1986. The original design called for the HST to be powered by six 50 Ah Nickel Cadmium batteries, which would have required a shuttle mission every 5 years for battery replacement. The decision to use NiH2 instead has resulted in a longer life battery set which was launched with HST in April 1990, with a design life of 7 years that has now exceeded 14+ years of orbital cycling. This chart details the specifics of the original HST NiH2 cell design. The HST replacement batteries for Service Mission 4, originally scheduled for Spring 2005, are currently in cold storage at NASA Goddard Space Flight Center (GSFC). The SM4 battery cells utilize slurry process electrodes having 80% porosity.

Hollandsworth, Roger

Control of Thermo-Acoustics Instabilities: The Multi-Scale Extended Kalman Approach

"Multi-Scale Extended Kalman" (MSEK) is a novel model-based control approach recently found to be effective for suppressing combustion instabilities in gas turbines. A control law formulated in this approach for fuel modulation demonstrated steady suppression of a high-frequency combustion instability (less than 500Hz) in a liquid-fuel combustion test rig under engine-realistic conditions. To make-up for severe transport-delays on control effect, the MSEK controller combines a wavelet -like Multi-Scale analysis and an Extended Kalman Observer to predict the thermo-acoustic states of combustion pressure perturbations. The commanded fuel modulation is composed of a damper action based on the predicted states, and a tones suppression action based on the Multi-Scale estimation of thermal excitations and other transient disturbances. The controller performs automatic adjustments of the gain and phase of these actions to minimize the Time-Scale Averaged Variances of the pressures inside the combustion zone and upstream of the injector. The successful demonstration of Active Combustion Control with this MSEK controller completed an important NASA milestone for the current research in advanced combustion technologies.

Dzu K Le

Ultra-High-Temperature Ceramics Evaluated for Aeropropulsion Use

Ultra-high-temperature ceramics (UHTC) are a group of materials consisting of zirconium diboride (ZrB2) or hafnium diboride (HfB2) plus silicon carbide (SiC), and in some instances, carbon (C). They offer a combination of properties that make them candidates for airframe leading edges on sharp-bodied reentry vehicles. These UHTCs perform well in the environment for such applications (i.e., air at low pressures). The purpose of this study at the NASA Glenn Research Center was to examine three of these materials under conditions more representative of a propulsion environment: that is, higher oxygen partial pressure and total pressure. Relatively long, multiple-exposure cycles were emphasized. We completed an in-house study of ZrB2 plus 20 vol% SiC (abbreviated as ZS), ZrB2 plus 14 vol% SiC and 30 vol% C (ZSC), and SCS-9a SiC fiber-reinforced ZrB2 plus 20 vol% SiC (ZSS). HfB2-based compositions were not included in the study because of their high cost. The capability of UHTC for propulsion applications must be compared with that of mature, available, and commercially used ceramics such as silicon nitride (e.g., AS-800) to put things in proper perspective. In terms of mechanical properties, UHTCs fall short in terms of strength and fracture toughness. At about 1300 C, the creep resistance of ZS appears to be superior to the creep resistance reported for AS-800. However, the stress rupture life for Si3N4 under stress and temperature conditions similar to those used in this study is measured in hundreds of hours. Because of oxidation, ZS could not achieve such lives. In terms of oxidation resistance, acceptable amounts of material recession in 1 hour to thousands of hours, depending on the specific propulsion application, are on the order of 100 to 300 mm. This converts to an acceptable range of parabolic recession rate constants kp" of approximately less than or equal to 10(exp -1) to 10(exp -2) square millimeters per hour for a 1-hr application. For a 100-hr application, an acceptable range of kp" would be less than or equal to those values divided by 100. For the more oxidation resistant ZS material, measured parabolic recession rate constants were 4.7 x 10(exp -3) millimeters per hour at 1327 C, 7.8 x 10(exp -2) square millimeters per hour at 1627 C, and 1.3 millimeters per hour at 1927 C. Thus, recession rate constants for ZS are acceptable at 1327 C for a 1-hr application, but here silicon nitride is a superior material. At 1627 C, ZS oxidation is marginal for a 1-hr application, but dimensional growth would be an issue. In a 100-hr application, ZS cannot be considered at any temperature. Our cursory examination of thermal shock, both from a theoretical and experimental viewpoint, indicated that the ZS and ZSC UHTCs are inferior to AS-800 silicon nitride. On the basis of this limited study, UHTCs are not ready to be considered as aeropropulsion materials for any applications longer than a few minutes. Current materials suffer from aggressive oxidation and moisture attack (Quynhgiao Nguyen, NASA Glenn, and Raymond C. Robinson, QSS Group, Inc., Cleveland, OH, 2002, private communication), and they are susceptible to thermal shock. For long-term propulsion applications, major improvements in environmental durability are needed. Work is in progress to improve the oxidation resistance of UHTC materials.

Stanley R Levine

Bosch Carbon Catalyst Regeneration in Water I: Bosch Carbon Removal from Reacted Beads Utilizing Mechanical Agitation

The ability to recover oxygen from metabolic carbon dioxide is crucial for crewed long duration missions in which the atmosphere must be recycled. Two physiochemical methods are primarily employed for this purpose: the Bosch process and the Sabatier reaction. This paper focuses on the Bosch process. It utilizes hydrogen in the presence of a catalyst to form water and solid carbon out of metabolic carbon dioxide. The solid carbon product deposits onto the catalyst and eventually causes reactor over pressurization issues. Multiple methods are currently being investigated to regenerate the catalyst’s surface and break up the pressure causing carbon clogs. This paper explores whether water and mechanical abrasion would work to remove Bosch carbon by testing multiple washing conditions. The different washing conditions involved agitation intensity, heating, duration, and volume of water. It was found that it is possible to break up the clumps of carbon formed in the reactor through agitation with room temperature water in one hour and shows promise for completely cleaning the carbon off the beads’ surface.

Agitation

Hydrofluoroether (HFE) Cleaning Fluid Replacement and Qualification

This NASA Engineering and Safety Center (NESC) Technical Assessment Report addresses the urgent need to identify, test, and qualify replacement cleaning solvents and technologies following 3M’s decision to discontinue production of hydrofluoroether (HFE) products, including Novec HFE-7100, by the end of 2025. HFE-7100 is widely used across NASA for precision cleaning of ground and flight hardware, especially in oxygen system components, and as a heat transfer fluid in high-power-density thermal control systems. The assessment evaluates commercially available replacement solvents, alternative cleaning technologies, and their compatibility with NASA’s operational requirements. Key findings include the identification of viable solvent replacements, their performance in contaminant removal, materials compatibility, and oxygen system safety. The report also explores novel cleaning approaches, including aqueous, supercritical CO₂, cryogenic aerosol, plasma, UV-ozone, magnetically optimized fluids, and induced charge active filtration, highlighting their merits, limitations, and readiness for NASA adoption. The NESC provides recommendations for solvent selection, facility adaptation, and continued technology maturation to ensure mission continuity and regulatory compliance.

Alternative Cleaning Technologies

International Space Station Lithium-Ion Battery Status

When originally launched, the International Space Station (ISS) primary Electric Power System (EPS) used Nickel-Hydrogen (Ni-H2) batteries to store electrical energy. The electricity for the space station is generated by its solar arrays, which charge batteries during insolation for subsequent discharge during eclipse. The Ni-H2 batteries were designed to operate for ten years at a 35 percent depth of discharge (DOD) maximum during normal operation in a Low Earth Orbit. For service beyond that period, upgraded Li-Ion Orbital Replacement Units (ORUs) were designed. These are the largest Li-Ion batteries ever utilized for a human rated spacecraft. With the oldest 12 Ni-H2 battery ORUs cycling since September 2006, the first set of six was replaced by Li-Ion batteries in December 2016; the second set of six is planned for replacement in September 2018. This paper will include an overview of the ISS Li-Ion battery system architecture, on-orbit status of the first 6 batteries, start up of the second 6 batteries, and the status of the Li-Ion cell and ORU life cycle testing.

International Space Station

The thermal engine of Venus: Implications from the impact crater distribution

Questions concerning the state of Venus' volcanological activity are currently under investigation. These questions were raised by the imaging radar and altimetric data obtained by the Magellan spacecraft, which began mapping Venus in Sept. 1990. Clues about the answers to these questions are provided by the nature and distribution of impact craters on the surface of Venus. Statistical tests show that the distribution of craters on Venus cannot be distinguished from a completely spatially random population. Further, the majority of craters look relatively pristine; only about 5 percent of the observed craters appear to be embayed or flooded by lavas. The simplest interpretation of these observations is a model in which the impact craters lie on a surface that has been undisturbed by volcanological and tectonic processes since the time the surface was formed. Counting up the number of craters and estimating the rate at which meteoroids strike the surface then gives an age for the venusian surface of 500 million years; in this model the volcanic activity since that time has been essentially nil. This scenario is described as a 'production' model, or perhaps more appropriately, a 'catastrophic' model.

Phillips, Roger J.

Thermal Analysis of the Advanced Modular Power Systems (AMPS) Power Electronic Modules

In an effort to transform future space power system architectures and operations, the Advanced Modular Power Systems (AMPS) project is currently developing an interface standard for power electronic modules to enable modular architectures for space power systems. Each architecture would consist of one or more modular electronic units (MEU) that would comprise of a tailored combination of modules. The standard currently comprises modules enabling switchgear, power conversion, and data interfacing. The objective of the AMPS project is to enable the modularity and interchangeability of different architectures using these standardized modules in hopes of reducing complexity and cost, increasing inherent redundancy and reliability, and minimizing power system redesign for future programs. A key enabler to these future modular architectures will be the thermal management system, which has to contend with acquiring heat from the electronics modules at the card level and then transporting that heat to the radiator of the larger system. The focus of this paper, therefore, will be the thermal design and analysis of multiple AMPS power electronics modules and the development of their thermal-vacuum test.

Modular Power Electronics

Photophoretic Propulsion Enabling Mesosphere Exploration NIAC Phase I Final Report

This Phase I report presents a comprehensive study on photophoretic flyers—innovative, ultralight, solar-powered vehicles that harness photophoretic forces generated via Knudsen pumping to achieve sustained flight in the mesosphere (50–80 km altitude). By integrating advanced materials such as nanocardboard— characterized by its extremely low areal density (~1 g/m²) and high bending stiffness—with ultrathin light-absorbing coatings, the project converts incident solar radiation directly into a directed thrust. Extensive experimental investigations, coupled with high-fidelity computational fluid dynamics (CFD) simulations using ANSYS Fluent, validate the concept across various three-dimensional geometries, including spherical, conical, and rocket-shaped configurations. These simulations bridge the gap between free-molecular and continuum flow regimes, demonstrating that optimized designs can generate lift forces sufficient to support kilogram-scale payloads even in low-pressure environments. At the heart of this innovation is the use of Knudsen pumping, where temperature gradients across porous surfaces induce directional gas flow, creating a modest overpressure that provides lift. The report introduces an analytical framework that interpolates between the well-known low-Reynolds number drag regime and the high-Reynolds number momentum theory. This model accurately predicts lift based on design parameters such as microchannel dimensions, porous wall geometry, areal density, and nozzle exit area. For instance, simulations indicate that 10-meter-scale structures with carefully engineered porous walls can achieve the necessary pressure differential to support scientifically significant payloads (~1 kg). The study also explores a hybrid propulsion approach that combines solar buoyancy with photophoretic lift. Initially, solar heating creates a buoyant force that elevates the flyer to mesospheric altitudes. Once in the optimal pressure range, the photophoretic mechanism—powered by Knudsen pumping—takes over as the primary source of lift, ensuring stable, long-duration flight. This dual-mode operation not only facilitates the deployment of photophoretic flyers but also broadens the potential applications for mesospheric exploration. In addition to propulsion, the report investigates the integration of photophoretic thrusters for trajectory control of existing research balloons in the upper stratosphere. By dynamically adjusting the nozzle orientation and controlling the flow-through velocity, these thrusters provide precise maneuverability, enabling the flyers to counteract atmospheric disturbances and adjust their flight paths in real time. For example, a photophoretic thruster approximately 7.5 by 7.5 meters in size could be unfolded below a payload gondola of a 60 million-cubic-foot zero-pressure balloon. Such a thruster can provide horizontal speed control of approximately 1 m/s using only sunlight and no moving parts (except those needed to track the Sun and control the jet direction). Importantly, photophoretic thrusters operate more efficiently at higher altitudes, which is complementary to known trajectory control techniques, such as propellers and tethered wings, which are more effective at lower altitudes. Finally, the report identifies three scientific research thrusts where mesospheric aircraft technology can have a profound impact: atmospheric tides, characterization of gravity waves, and investigation of mesospheric instabilities. Overall, the findings of this Phase I project represent a significant advancement in photophoretic propulsion technology. By demonstrating that large-scale, ultralight structures can be powered solely by solar radiation—via carefully engineered Knudsen pumping—this work lays a robust foundation for scalable, near-space flight architectures. Future refinements in material fabrication, structural optimization, and integrated trajectory control are expected to further enhance performance, paving the way for operational demonstrations that could revolutionize atmospheric science, remote sensing, and communication networks.

Knudsen Pump

Radiation-Resistant Ti/BN Coatings: Insights From 171 Days Exposure to Space Radiation and Atomic Oxygen in Low Orbit

Atmospheric Plasma Spray (APS) and Vacuum Plasma Spray (VPS) techniques were used to develop Ti/2 vol.% hBN coatings, for extreme space environments and tested aboard the International Space Station as part of the MISSE-17 (Materials International Space Station Experiments) program. The coatings were exposed to atomic oxygen, space radiation, and low-orbit thermal cycling. VPS coatings showed a 56% increase in microhardness, a 26% rise in elastic modulus, minimal porosity and crack density changes compared to APS coatings. The change in mechanical properties is attributed to the formation of TiO, TiO₂ and TiN from nitrogen retention, alongside radiation-induced dislocations, which enhanced surface hardening. The oxidation of titanium led to the formation of TiO and TiO₂, while boron nitride was retained and underwent transmutation in VPS coatings. XPS and EDS analyses confirmed the enhanced space-environment resistance of VPS coatings, making them ideal for long-term spacecraft protection in lunar and Martian conditions.

Abhijith Kunneparambil Sukumaran

Diamond-Loaded Polyimide Aerogel Scattering Filters and Their Applications in Astrophysical and Planetary Science Observations

Infrared-blocking, aerogel-based scattering filters have a broad range of potential applications in astrophysics and planetary science instruments in the far-infrared, sub-millimeter, and microwave regimes. This paper demonstrates the ability of conductively-loaded, polyimide aerogel filters to meet the mechanical and science instrument requirements for several experiments, including the Cosmology Large Angular Scale Surveyor (CLASS), the Experiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM), and the Sub-millimeter Solar Observation Lunar Volatiles Experiment (SSOLVE). Thermal multi-physics simulations of the filters predict their performance when integrated into a cryogenic receiver. Prototype filters have survived cryogenic cycling to 4 K with no degradation in mechanical properties. Measurement of total hemispherical reflectance and transmittance, as well as cryogenic tests of the aerogel filters in a full receiver context, allow estimates of the integrated infrared emissivity of the filters. Knowledge of the emissivity will help instrument designers incorporate the filters into future experiments in planetary science, astrophysics, and cosmology.

Kyle R Helson

Parabolic Deformable Mirror Project Development and Device Characterization

Existing state-of-the-art wavefront sensing and control setups for the imaging of exoplanets utilize two high-actuator count flat deformable mirrors (DMs) to control both phase and amplitude aberrations. One of the objectives of the Exoplanet Spectroscopy (ExoSpec) project at Goddard Space Flight Center (GSFC) is to improve upon this regime through the development of parabolic deformable mirrors (PDMs), which can address several of the key limitations in existing setups. Specifically, the need for flat DMs to be located in conjugate pupil planes drives unique packaging challenges that can be overcome by allowing the off-axis imaging elements to be controllable as well. In addition, simulations show that the use of deformable powered elements will increase the overall controllable bandwidth, up to 35% over 5-12 lambda/D. To pursue this effort, the ExoSpec group has begun testing a first-generation parabolic DM, which is already informing a second generation design. This paper will provide a comprehensive update on its characterization, including influence function measurements, linearity analysis, closed-loop wavefront control performance, and thermal stability assessment.

spectroscopy

Radiation sensitivity of quartz crystal oscillators experiment for the Long Duration Exposure Facility (LDEF)

Factors determining the radiation sensitivity of quartz crystal oscillators were studied on NASA's LDEF. Quartz materials were examined in the transmission electron microscope (TEM) and classified as to their sensitivity to radiation damage by establishing the rate of damage caused by the electron beam in the microscope. Two types of materials, i.e., swept premium Q quartz and natural quartz were chosen because clear differences were observed in their response to the electron beam in the TEM studies. Quartz resonators were then fabricated from them, tested for frequency stability over a greater than 6 mo. period and flown on the LDEF satellite. After retrieval (more than 7 yrs in space) the stability of the resonators was again determined. All of the space exposed resonators fabricated with swept premium Q material exhibited a frequency shift above that of the control resonators: none of the resonators fabricated from the natural quartz materials exhibited such a shift. The significant differences observed between the two types of materials in both the ground-based TEM studies and the space radiation induced frequency changes suggest that there may be a correlation between the two observations.

J. S. Ahearn

Influential Factors for Liquid Acquisition Device Screen Selection for Cryogenic Propulsion Systems

This paper presents the influential factors which govern screen selection for liquid acquisition devices (LADs) operating in microgravity conditions for future in-space cryogenic propulsion engines and cryogenic propellant depots. Space flight requirements, which include mass flow rate, acceleration level and direction, and thermal environment, dictate screen selection for a particular mission. The five influential factors include bubble point pressure, flow-through-screen pressure drop, wicking rate, screen compliance, and material compatibility. Governing equations and analytical models for these parameters are developed from first principles. A comprehensive survey of the historical data on coarser LAD meshes over four decades of work is conducted, and liquid hydrogen data for finer Dutch Twill meshes (325 x 2300, 450 x 2750, 510 x 3600) from recently concluded experiments is also presented to validate analytical models. Each of these parameters is measurable from ground based tests, making it facile to predict flight system performance. Therefore analytical models in this paper will be valuable for future LAD designs for both cryogenic and storable propulsion systems. Additionally, analysis will be given on the impact of the factors on liquid hydrogen systems.

Fuel Depot

Comparison and Application of Battery Modeling Methods for Conceptual Electric Aircraft

Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.

power

IUS materials outgassing condensation effects on sensitive spacecraft surfaces

Four materials used on the inertial upper state (IUS) were subjected to vacuum conditions and heated to near-operational temperatures (93 to 316 C), releasing volatile materials. A fraction of the volatile materials were collected on 25 C solar cells, optical solar reflectors (OSR's) or aluminized Mylar. The contaminated surfaces were exposed to 26 equivalent sun hours of simulated solar ultraviolet (UV) radiation. Measurements of contamination deposit mass, structure, reflectance and effects on solar cell power output were made before and after UV irradiation. Standard total mass loss - volatile condensible materials (TML - VCM) tests were also performed. A 2500 A thick contaminant layer produced by EPDM rubber motor-case insulation outgassing increased the solar absorptance of the OSR's from 0.07 to 0.14, and to 0.18 after UV exposure. An 83,000 A layer caused an increase from 0.07 to 0.21, and then the 0.46 after UV exposure. The Kevlar-epoxy motor-case material outgassing condensation raised the absorptance from 0.07 to 0.13, but UV had no effect. Outgassing from multilayer insulation and carbon-carbon nozzle materials did not affect the solar absorptance of the OSR's.

C. R. Mullen