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NASA NTRS2010

Stiffness and Damping Coefficient Estimation of Compliant Surface Gas Bearings for Oil-Free Turbomachinery

Foil gas bearings are a key technology in many commercial and emerging Oil-Free turbomachinery systems. These bearings are non-linear and have been difficult to analytically model in terms of performance characteristics such as load capacity, power loss, stiffness and damping. Previous investigations led to an empirically derived method, a rule-of-thumb, to estimate load capacity. This method has been a valuable tool in system development. The current paper extends this tool concept to include rules for stiffness and damping coefficient estimation. It is expected that these rules will further accelerate the development and deployment of advanced Oil-Free machines operating on foil gas bearings

DellaCorte, Christopher↗

NASA NTRS1988

Rarefied-flow pitching moment coefficient measurements of the Shuttle Orbiter

An overview of the process for obtaining the Shuttle Orbiter rarefied-flow pitching moment from flight gyro data is presented. The extraction technique involves differentiation of the output of the pitch gyro after accounting for nonaerodynamic torques, such as those produced by gravity gradient and the Orbiter's auxiliary power unit and adjusting for drift biases. The overview of the extraction technique includes examples of results from each of the steps involved in the process, using the STS-32 mission as a typical sample case. The total pitching moment and moment coefficient (Cm) for that flight are calculated and compared with preflight predictions. The flight results show the anticipated decrease in Cm with increasing altitude. However, the total moment coefficient is less than predicted using preflight estimates.

Blanchard, R. C.↗

NASA NTRS1977

Low-speed power effects on advanced fighter configurations with two-dimensional deflected thrust

Wind-tunnel studies at the Langley Research Center have shown that significant increases in maximum lift coefficient and stability and decreases in drag due to lift are obtained when two-dimensional vectored thrust is used in conjuction with a close-coupled canard. The configuration tested was somewhat above the theoretical minimum drag due to lift because of the sharp leading edge on the biconvex airfoil used on the wing and canard. An effort to design a new configuration which will approach the minimum drag due to lift while maintaining high-lift configurations was completed. The resulting model will incorporate a realistic planform, airfoil section, and twist for a transonic maneuvering configuration.

Paulson, J. W., Jr.↗

DOE OSTI2020

Integrated Traction Drive Thermal Management: Keystone Project 3

The presentation was developed for the U.S. Department of Energy (DOE) Vehicle Technologies Program 2020 Annual Merit Review and Peer Evaluation Meeting. It reports on progress and accomplishments of DOE funded Integrated Traction Drive Thermal Management project. Highlighted are NREL's research accomplishments during FY 2020. Challenges associated with thermal management of integrated traction drives for electric vehicles arise due to the limited packaging space, coolant distribution, electrical connections, and ambient temperatures. For this project at NREL, research focuses on enabling thermal management technologies to support a modular, compact, self-contained integrated electric drive unit with motor and power electronics. Integration approaches, based on packaging location and coolant options for power electronics integrated with candidate motor technologies to reduce cables and connectors, are reviewed and compared using finite element analysis (FEA) tools. Automatic transmission fluid (ATF) jet impingement cooling characterization is carried out experimentally (measuring heat transfer coefficients) and using computational fluid dynamics (CFD) modeling.

47 OTHER INSTRUMENTATION↗

NASA NTRS1994

Multipole moments of stellar oscillation modes

The oscillating mass 2(exp l)-pole moment, M(sub nl), of a star in a given (normalized) oscillation mode determines the energy that can be absorbed by the mode in a tidal interaction and the power radiated by the mode in gravitational waves, both of which are proportional to (absolute value of M(sub nl))(exp 2). The coefficients in the expansion of the vector fields del(r(exp l)Y(sub lm)(theta, phi)) in terms of the displacement fields of modes of given l and m are proportional to M(sub nl). This expansion leads to a sum rule sum over n(absolute value of M(sub nl))(exp 2) = constant. For stars of weak to moderate central condensation (such as neutron stars), the f-mode is well approximated by the vector field being expanded, and therefore it takes the lion's share of the sum. Thus the multipole moments of all other modes must be small. In there numerical evaluation, it is necessary to know the shape of the eigenfunctions quite precisly, since a small f-mode contamination can significantly increase the obtained values. This contamination occurs in some `hybrid' numerical computations of neutron star oscillations with relativistic equilibrium stars and Newtonian dynamics (e.g., McDermott et al. 1988). In this case, it is due to a slight inconsistency in the models and leads to a large overestimate of the power radiated in gravitational waves by modes other than the f-mode, although their oscillation periods are nearly unaffected.

Reisenegger, Andreas↗

DOE OSTI2023

Automated power-following control for nuclear thermal propulsion startup and shutdown using MOOSE-based applications

This paper describes an investigation of various automated control strategies applied to a full-core multiphysics Griffin/Bison/RELAP-7 model of a prototypical nuclear thermal propulsion system. In all cases, control is achieved by actuating control drums based on the demanded power and predicted quantities from the numerical model. One key finding is that hybrid proportional integral derivative controllers – a novel type of controller that uses both power and reactivity predicted signals – can demonstrate a level of performance rivaling that of period-generated control. The former requires parameter tuning, while the latter mostly necessitates providing reactivity coefficients and temperature rates of change, which could be very challenging to accurately measure in real-time. In addition, decay heat plays an important role in determining cooling requirements during cooldown phases. A decay heat model, accounting for burn time and throttling, was derived, and is incorporated within the model to simulate the steady-state and shutdown phases and satisfyingly follow the power demand. However, temperature overshoots and non-constant specific impulse during throttling will necessitate further improvements.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1993

Nonlinear aerodynamic modeling using multivariate orthogonal functions

A technique was developed for global modeling of nonlinear aerodynamic coefficients using multivariate orthogonal functions based on the data. Each orthogonal function retained in the model was decomposed into an expansion of ordinary polynomials in the independent variables, so that the final model could be interpreted as selectively retained terms from a multivariable power series expansion. A predicted squared-error metric was used to determine the orthogonal functions to be retained in the model; analytical derivatives were easily computed. The approach was demonstrated on the Z-body axis aerodynamic force coefficient (Cz) wind tunnel data for an F-18 research vehicle which came from a tabular wind tunnel and covered the entire subsonic flight envelope. For a realistic case, the analytical model predicted experimental values of Cz very well. The modeling technique is shown to be capable of generating a compact, global analytical representation of nonlinear aerodynamics. The polynomial model has good predictive capability, global validity, and analytical differentiability.

Morelli, Eugene A.↗

NASA NTRSDate not supplied

Evaluating the Performance of Hybrid Vehicles between LEO, Cislunar Space, and Mars

Nuclear power and electric propulsion technologies can enable a broad range of existing and future space mission concepts. This paper evaluates how these two technology classes, when combined into systems with various performance levels (and paired with a chemical propulsion system) affect vehicle sizing and mission feasibility for round-trip, opposition-class, crewed missions to Mars. The technology trade-space evaluated in this paper encompasses: various nuclear power system mass-efficiency levels (or power-specific mass), a range of output power levels available to the electric propulsion system, two electric propulsion thruster technologies (Hall and Magnetoplasmadynamic) at various characteristic specific impulse levels, and a range of propellant tank mass sizing coefficient. Each combination of the technologies is evaluated for the 2039 and the 2042 Mars mission opportunities for a range of imposed total mission duration constraints. The results show that synergies between technology performance levels exist and that increasing the performance of some parameters might have undesired consequences for the trajectory and vehicle. It was found that increasing the mass-efficiency of the nuclear power system is broadly beneficial, resulting in lower vehicle masses and enabling shorter mission durations. However, increasing the specific impulse of a thruster or increasing the available power level do not always yield a net benefit to the vehicle or mission; since increasing the specific impulse or power level (holding power system mass-efficiency constant) tends to decrease the vehicle thrust-to-mass ratio. Furthermore, the results show that mission feasibility is highly dependent on the mission duration; the required technology performance level to enable a mission is relaxed as the mission duration increases. Given the optimally sized vehicles resulting from the trade-space for a crewed mission to Mars, this paper also evaluates the impact of aggregating the Mars mission vehicle in Low-Earth Orbit and transferring it to the Mars mission departure node (using the on-board power and propulsion systems). The trade-space for this portion of the analysis includes the option of in-space vehicle refueling at the Mars mission departure node. The results show that on-orbit refueling can relax the required technology performance levels to achieve lower launch masses and orbit-raising durations at the cost of increased architecture complexity and risk.

Nuclear Electric Propulsion↗

DOE OSTI2024

Carrier confinement and alloy disorder exacerbate Auger–Meitner recombination in AlGaN ultraviolet light-emitting diodes

The quantum efficiency of AlGaN ultraviolet light-emitting diodes declines (droops) at increasing operating powers due to Auger–Meitner recombination (AMR). Using first-principles density-functional theory, we show that indirect AMR mediated by electron–phonon coupling and alloy disorder can induce bulk C coefficients as large as ~10 –31 cm 6 /s. Furthermore, we find that the confinement of carriers by polarization fields within quantum wells severely relaxes crystal-momentum conservation, which exacerbates the rate of AMR over radiative recombination by an order of magnitude relative to the bulk. Furthermore, this results in a striking decrease in quantum efficiency at high power. Suppressing polarization fields and jointly increasing the well width would greatly mitigate AMR and efficiency droop.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Leveraging Natural Language Processing and Generative Models in Molecular Chemistry: Property Prediction and Novel Compound Generation

The accurate prediction of molecular properties is important for the rational design and the advancement of green chemistry and sustainable materials research. However, the predictive power of traditional computational chemistry methods is limited due to computational restrictions. Here, in this study, we examine an alternative approach to the accurate prediction of properties of organic compounds: natural language processing (NLP)-based molecular embedding. Using viscosity, partition coefficient (log P), and enthalpy of vaporization as test properties through a survey of comprehensive datasets comprising 5695 data points for viscosity, 25 870 data points for log P, and 2296 data points for enthalpy of vaporization. These are important properties for the design of greener, safer, and sustainable chemical processes. Models were trained using NLP methods such as Mol2vec and fine-tuned ChemBERTa, and results were compared with traditional input featurization techniques such as Morgan fingerprints and quantum chemistry derived sigma profiles and DFT features. Among the various machine learning models, Mol2vec demonstrated superior predictive capabilities, achieving the highest correlation coefficient (R 2 = 0.945) and lowest RMSE (0.106 mPa s) for viscosity, as well as high accuracy for log P and enthalpy of vaporization predictions. These findings establish the Mol2vec featurization technique, graph-convolutional neural networks (GCNN), and fine-tuned ChemBERTa model as powerful tools for predictive modeling of organic compounds properties, offering a significant improvement over previously used featurization techniques and opening up strategies for very-high-throughput computational screening. Finally, we integrated ML models with hybrid language-model-based generative adversarial networks (LM-GAN) to generate novel molecular sequences with desirable properties for different research applications. The ability to computationally design solvents with lower viscosity, lower log P, and lower enthalpy of vaporization offers a data-driven route to accelerating the discovery of sustainable alternatives to traditionally toxic solvents.

ChemBERTa↗

DOE OSTI2022

Mass transfer coefficients, kL, and air-CO2 ingassing rates in 3.4 m2 and 1-acre raceway ponds.

The US DOE 2016 Billion Ton Update (Langholtz 2016) projected that CO2 in flue-gas from power plants or similar sources would limit U.S. algal biofuel potential to under 5 billion gallons gasoline equivalent (gge) per year, due to lack of sufficient land, water and other requirements near such flue gas sources. 2nd generation carbon capture technologies are proposed to overcome this constraint (Davis 2017), and could expand this resource potential nearly 10-fold, assuming CO2 costs near the future, 2025 DOE NETL, goal of $40/metric ton CO2. An alternative pathway is the direct uptake of air CO2 into the algal ponds through an increase in the air-CO2 transfer rate resulting from the reaction of CO2 with hydroxide ions. However, such a ‘chemical enhancement’ in mass transfer depends on a high pH in the culture, and, by extension, the ability of microalgae to maintain high rates of carbon assimilation under such conditions. Abiotic experiments characterized the air-CO2 mass-transfer rate in 1-acre and 3.4 m2 raceway ponds as a function of pH, with rates approaching 10 g C/m2-day at pH 12 in the brackish water tested, equivalent to a biomass productivity potential of near 20 g AFDW/m2-day (@ 0.47 g C/g AFDW). The mass transfer rate was found to be nearly independent of the mass-transfer coefficient, indicating that at turbulence levels achievable in typical raceway ponds, the system is reaction rate, rather than diffusion limited. In biotic trials with an unknown green microalga, biomass productivity in ponds receiving CO2 from only direct surface air-CO2 exchange averaged 5 +/- 0.5 g AFDW/m2-day in August - September central California conditions, about half-that of experimental controls fertilized with supplemental CO2. pH in the air-only treatment reached a maximum of 10.5, supporting a model predicted air-CO2 ingassing rate between 2-3 g C/m2-day, consistent with the observed biomass carbon assimilation rate. Results suggest that unique alkaliphilic strains are required if reliant on direct in-pond air-CO2 transfer for algal inorganic carbon supply, and that reaching an economically viable biomass productivity will require strains that thrive at pH 11 and above.

09 BIOMASS FUELS↗

DOE OSTI2023

Enhancement of operational Flexibility of Power Plants Using IN740

Headers are crucial components within diverse industries, especially in the energy sector, as they enable the efficient transfer of fluids. The selection of materials for headers is determined by their specific applications; for example, Grade 91 and Grade 92 steels are commonly utilized. In our research, we recommend the adoption of INCONEL alloy 740 due to its exceptional robustness and heat-resistant characteristics. One critical parameter in header systems is the heat transfer coefficient, which directly influences the efficiency of heat exchange processes and can thereby impact the structural integrity of the headers. This coefficient is closely linked with factors such as the Nusselt number, which is influenced by fluid flow characteristics and thermal properties. The flow direction within headers, whether unidirectional or multidirectional—significantly affects the overall dynamics of heat transfer. This research focuses on exploring the behavior of headers, a specific pipeline system component, using ANSYS simulation software. The study aims to predict heat transfer and mechanical behavior within headers under various conditions through steady-state and transient simulations (parts 1 and 2 of the report). Key parameters such as heat transfer coefficient, velocity, and temperature are examined with the goal of optimizing header design. Part 3 of the report addresses the critical yet underexplored relationship between pressure drop and heat transfer coefficients in the transient flow regime within headers, specifically focusing on smooth horizontal circular tubes. Limited experimental work has been conducted in this area, prompting the need for comprehensive analysis. By leveraging machine learning techniques, this research aims to establish a correlation between pressure drop and heat transfer across various flow conditions, including laminar, transient, quasi-turbulent, and turbulent regimes. The data utilized for this analysis were meticulously gathered from existing literature, capturing simultaneous measurements of pressure drops and heat transfer. Part 4: In the context of power plants, header pipes are essential components that significantly influence system performance by facilitating the collection and distribution of steam. This report highlights the critical role of header pipes in enhancing reliability, efficiency, and overall power plant performance. A key aspect of this investigation is shape optimization, which aims to maximize performance while minimizing material usage. By focusing on shape optimization, this research contributes to improved efficiency and a reduced environmental footprint for power plant installations. The methodology developed in this study emphasizes optimizing header shapes to decrease reliance on expensive alloy materials and lower maintenance costs. Furthermore, a case study was conducted using a header from an operational power plant to validate the proposed optimization techniques. Finally, part 5 addresses the challenges associated with flexible operations in boiler systems, the study outlines several strategies for enhancing the durability and reliability of steam headers. Key approaches include material selection, which involves utilizing advanced materials with superior high-temperature properties and enhanced fatigue resistance to extend the lifespan of steam headers. Design modifications are also recommended, focusing on implementing changes that mitigate thermal stress and cyclic loading to reduce the likelihood of failures under varying operating conditions. Additionally, the study emphasizes the importance of regular inspection and monitoring by establishing rigorous protocols to detect early signs of damage, allowing for timely maintenance and minimizing the risks of catastrophic failures. Furthermore, operational guidelines are developed to minimize the frequency and severity of thermal transients, ensuring stable and efficient operations. Collectively, these strategies provide a robust framework for overcoming the unique challenges posed by flexible operation in boiler systems, ultimately contributing to improved reliability and performance in power plant operations. Through this comprehensive approach, the study not only enhances the understanding of pressure drop and heat transfer relationships but also promotes advancements in design and operation that will benefit the entire power generation industry.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS2005

A Feasibility Study for Simultaneous Measurements of Water Vapor and Precipitation Parameters using a Three-frequency Radar

The radar return powers from a three-frequency radar, with center frequency at 22.235 GHz and upper and lower frequencies chosen with equal water vapor absorption coefficients, can be used to estimate water vapor density and parameters of the precipitation. A linear combination of differential measurements between the center and lower frequencies on one hand and the upper and lower frequencies on the other provide an estimate of differential water vapor absorption. The coupling between the precipitation and water vapor estimates is generally weak but increases with bandwidth and the amount of non-Rayleigh scattering of the hydrometeors. The coupling leads to biases in the estimates of water vapor absorption that are related primarily to the phase state and the median mass diameter of the hydrometeors. For a down-looking radar, path-averaged estimates of water vapor absorption are possible under rain-free as well as raining conditions by using the surface returns at the three frequencies. Simulations of the water vapor attenuation retrieval show that the largest source of error typically arises from the variance in the measured radar return powers. Although the error can be mitigated by a combination of a high pulse repetition frequency, pulse compression, and averaging in range and time, the radar receiver must be stable over the averaging period. For fractional bandwidths of 20% or less, the potential exists for simultaneous measurements at the three frequencies with a single antenna and transceiver, thereby significantly reducing the cost and mass of the system.

Meneghini, R.↗

DOE OSTI2022

Impact of nuclear data covariance libraries on uncertainty quantification of sodium cooled fast reactor simulation

Uncertainty quantification in core modelling to assess reactor performance is a regular practice to identify design safety limits. Best-estimate plus uncertainty (BEPU) methods are commonly used to propagate uncertainties to core responses from input parameters, characterized by variance-covariance libraries. This study evaluates the impact of different covariance libraries on the uncertainty associated with core safety parameters and their propagation through reactor transient modelling for a metallic core (ABR-1000). The COMAC-1.0, COMMARA-2.0, and COMMARA-2.1 covariance libraries are used to propagate nuclear data uncertainties to neutron feedback coefficients using the Generalized Perturbation Theory, then through transient safety analyses to establish the confidence interval for safety performance of the reactor using stochastic sampling. The considered transients include Unprotected Transient Over Power and Unprotected Loss Of Flow. Most influential nuclide and reaction pairs in different variance-covariance libraries are identified and their impact on the uncertainty of safety parameters are evaluated. Significant differences were observed between uncertainties from COMAC compared to COMMARA libraries. Uncertainties from COMMARA libraries were consistently larger than COMAC for all cases. For structure, coolant density feedback coefficients and control rod worth, total nuclear data uncertainties were approximately 50% larger for COMMARA than COMAC. Differences were also observed in identification of top contributors of uncertainty in terms of reaction-cross sections. For instance, largest contribution to total uncertainty of radial expansion coefficient from COMMARA-2.0 and 2.1 originates from Na{sup 23} P1 Elastic cross section (0.81%) but from Pu{sup 239} Fission (0.53%) with COM C-1.0. Such differences are evaluated in this research for all quantities of interest. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Interdiffusion and Formation of Intermetallic Compounds in High-Temperature Power Electronics Substrate Joints Fabricated by Transient Liquid Phase Bonding

Power electronics packages typically comprise a dielectric substrate bonded to a metal layer and attached to heat sinks using a low-thermal-conductivity solder. These multiple layers increase the effective thermal resistance of the package and are responsible for package failures under cyclic thermal loads. Bonding the aluminum nitride dielectric layer (AlN) directly to a low coefficient of thermal expansion (CTE) aluminum silicon carbide (AlSiC) cold plate using copper-aluminum (Cu-Al) transient liquid phase (TLP) bonding has been shown to improve the mechanical reliability of the power electronic packages while making the package more compact by bringing the cooling solutions closer to the devices. This study aims to characterize the Cu-Al bonds formed during the TLP bonding of AlSiC with three different power electronics substrates: pure aluminum nitride (AlN), aluminum (DBA), and copper (DBC). The material compositions and microstructures of the bonds were analyzed using scanning electron microscopy (SEM), x-ray spectroscopy (EDS), confocal scanning acoustic microscopy (C-SAM), and x-ray diffraction (XRD). ..alpha..-Al solid compound was identified as the dominant phase in AlN-AlSiC and Al-AlSiC, with a notable presence of SiC particles. In contrast, three intermetallic phases - ..theta..-CuAl2, ..eta..-CuAl, and ..gamma..'- Cu9Al4 - were observed in the Cu-AlSiC bond. A computational solid-state diffusion model was developed to predict the intermetallic compounds (IMCs) formed during Cu-Al TLP bonding in each system, which supported the observation that an initial Cu volume fraction of 20 % in the material layers produced a final bond composition of >95 % Al with minimal IMC growth. However, increased Cu concentrations produced higher concentration gradients, leading to increased growth of IMCs, Kirkendall voids, and interstitial cracks.

DIRECT ENERGY CONVERSION↗

DOE OSTI2020

Non-linear flow modes of identified particles in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}} $ = 5.02 TeV

The pT-differential non-linear flow modes, v 4,22 , v 5,32 , v 6,33 and v 6,222 for π ± , K ± , K$^0_S$ , $p + \bar{p}, Λ + \bar{Λ}$ and &straightphi;-meson have been measured for the first time at $\sqrt{s_{NN}}$ = 5.02 TeV in Pb-Pb collisions with the ALICE detector at the Large Hadron Collider. The results were obtained with a multi-particle technique, correlating the identified hadrons with reference charged particles from a different pseudorapidity region. These non-linear observables probe the contribution from the second and third order initial spatial anisotropy coefficients to higher flow harmonics. All the characteristic features observed in previous p T -differential anisotropic flow measurements for various particle species are also present in the non-linear flow modes, i.e. increase of magnitude with increasing centrality percentile, mass ordering at low p T and particle type grouping in the intermediate p T range. Hydrodynamical calculations (iEBE-VISHNU) that use different initial conditions and values of shear and bulk viscosity to entropy density ratios are confronted with the data at low transverse momenta. These calculations exhibit a better agreement with the anisotropic flow coefficients than the non-linear flow modes. These observations indicate that non-linear flow modes can provide additional discriminatory power in the study of initial conditions as well as new stringent constraints to hydrodynamical calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Diffusion and Solvation Dynamics of Ions in Water: Beyond the Brownian Approximation

The coupled dynamics of ions and water molecules in their first hydration shell impact a variety of processes including ion diffusion, selective ion transport in water-filled nanopores, and the kinetics of ion-pairing, ion adsorption, and metal-ligand binding reactions. In this work, we study these coupled dynamics for alkali metals (Li, Na, K, Rb, Cs), alkaline Earth metals (Mg, Ca, Sr, Ba), and chloride through the lens of their dependence on ion isotopic mass. Results are validated against previous measurements of the isotopic mass-dependence of ion diffusion coefficients in water and previous ab initio calculations of ion high-frequency dynamics in water. We find that the vibrational power spectra of ions in water consistently exhibit either two or three peaks, i.e., ions have several rattling frequencies within their solvations shells as previously reported for a subset of the species examined here. These frequencies have different sensititivies to isotopic mass that may serve as signatures of ion solvation processes (such as the tendency of ions to orient their first-shell water molecules) and that also may relate to Hofmeister-like effects including the relative affinity of different metals for ribonucleic acid (RNA).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1969

Testing the Fraunhofer line discriminator by sensing fluorescent dye

The experimental Fraunhofer Line Discriminator (FLD) has detected increments of Rhodamine WT dye as small as 1 ppb in 1/2 meter depths. It can be inferred that increments considerably smaller than 1 ppb will be detectable in depths considerably greater than 1/2 meter. Turbidity of the water drastically reduces luminescence or even completely blocks the transmission of detectable luminescence to the FLD. Attenuation of light within the water by turbidity and by the dye itself are the major factors to be considered in interpreting FLD records and in relating luminescence coefficient to dye concentration. An airborne test in an H-19 helicopter established feasibility of operating the FLD from the aircraft power supply, and established that the rotor blades do not visibly affect the monitoring of incident solar radiation.

Stoertz, G. E.↗