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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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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Possible Influences of Air Pollution, Dust and Sandstorms on the Indian Monsoon

In Asian monsoon countries, such as China and India, human health and safety problems caused by air pollution are becoming increasingly serious, due to the increased loading of atmospheric pollutants from waste gas emissions and from rising energy demand associated with the rapid pace of industrialization and modernization. Meanwhile, uneven distribution of monsoon rain associated with flash floods or prolonged drought, has caused major loss of human life and damage to crops and.property with devastating societal impacts. Historically, air-pollution and monsoons research are treated as separate problems. However recent studies have suggested that the two problems may be intrinsically linked and need to be studied jointly. Fundamentally, aerosols can affect precipitation through radiative effects cif suspended particles in the atmosphere (direct effect) and/or by interfering and changing: the cloud and precipitation formation processes (indirect effect). Based on their optical properties, aerosols can be classified into two types.: those that absorb solar radiation, and those that do not. Both types of aerosols scatter sunlight and reduce the amount of solar radiation from reaching the Earth's surface, causing it to cool. The surface cooling increases atmospheric stability and reduces convection potential, Absorbing aerosols, however, in addition to cooling the surface, can heat the atmosphere. The heating of the atmosphere may reduce the amount of low clouds by increased evaporation in cloud drops. The heating, however, may induce rising motion, enhance low-level moisture, convergence and, hence, increases rainfall, The latent heating from enhanced rainfall may excite feedback processes in the large-scale circulation, further amplify.the initial response to aerosol heating and producing more rain. Additionally, aerosols can increase the concentration of cloud condensation nuclei (CCN), increase cloud amount and decrease coalescence and collision rates, leading to reduced precipitation. However, in the presence of increasing moist and warm air, the reduced coalescence/collision may lead to supercooled drops at higher altitudes where ice precipitation falls and melts. The latent heat release from freezing aloft and melting below implies greater upward heat transport in polluted clouds and invigorate deep convection. In this way, aerosols may lead to increased local convection. Hence, depending on the ambient large-scale conditions and dynamical feedback processes, aerosols' effect on precipitation can be positive, negative or mixed. In the Asian monsoon and adjacent regions, the aerosol forcing and responses of the water cycle are even more complex, Both direct and indirect effects may take place locally and simultaneously, interacting with each other. in addition to local effects, monsoon rainfall may be affected by aerosols transported from other regions and intensified through large-scale circulation and moisture feedback. Thus, dust transported by the large-scale circulation from the adjacent deserts to northern India may affect rainfall over the Bay of Bengal; sulphate and black carbon front industrial pollution in central, southern China and northern India may affect the rainfall regime over the Korean peninsula and Japan; organic and black carbon front biomass burning from Indo-China may modulate the pre-monsoon rainfall regime over southern China and coastal regions, contributing to variability in differential heating and cooling of the atmosphere and to the land-sea thermal contrast. During the pre-monsoon season and monsoon breaks, it has been suggested that radiative forcing by absorbing aerosols have nearly the same order of magnitude as the forcing due to latent heating from convection and surface fluxes. The magnitude of the total aerosol radiative cooling due to sulphates and soot is of the order of 20-40 W/m2 over the Asian monsoon land region in the pre-monsoon season, compared to about 1-2 W/m2 for global warng. However, the combined forcing at the surface and in the atmosphere, including all species. if aerosols, and details of aerosol mixing, and impacts on the energy and water cycles in the monsoon land regions, are not well known.

Lau, William K. M.↗
NASA NTRSDate not supplied

Surface Instability of Liquid Propellants in Microgravity During Pulsed Settling Operations

Pulsing reaction control system (RCS) thrusters, vent valves, or other propulsion devices can preserve propellant resources in space, but this operation also effectively introduces a vibration to the vehicle. When the vibration is perpendicular to the liquid propellant surface, Faraday waves may be generated at the liquid-vapor interface. These Faraday instabilities can perturb or break up the liquid surface of cryogenic tanks, leading to inefficiencies in thermal management or even ullage collapse. Drawing from theory and experiments, an engineering model defining the allowable design regions for pulsed settling in microgravity was assembled and verified with computational fluid dynamics (CFD) simulations. A traditional settling metric, the Bond number, was also overlaid in the model to indicate which duty cycles were insufficient to overcome surface tension and aggregate propellant. Mission planners and engineers can consult the tool to rapidly evaluate the stability of a liquid-vapor interface given the pulse frequency and the excitation acceleration. Expressions developed for Faraday waves induced by a sinusoidal forcing input at standard gravity were found to provide excellent predictive capabilities for pulsed, or rectangular, waveforms in the absence of a consistent gravitational acceleration. This study extends the usage of these equations to an alternative forcing function and microgravity environments for the purpose of estimating natural frequencies, surface mode shapes, surface wave amplitudes, and the onset of droplet ejection. CFD simulations with the Loci/STREAM-VoF (Volume of Fluid) solver were initially validated against experimental results in standard gravity. Discrete points on the design map were then investigated with CFD and confirmed that the engineering model reliably indicates surface stability and most Faraday wave characteristics without requiring higher-fidelity tools. The engineering model is highly extensible and can be adapted for various propellant fill fractions, fluid properties, and tank sizes.

Faraday Waves↗
NASA NTRSDate not supplied

Surface Instability of Liquid Propellants in Microgravity During Pulsed Settling Operations

Pulsing reaction control system (RCS) thrusters, vent valves, or other propulsion devices can preserve propellant resources in space, but this operation also effectively introduces a vibration to the vehicle. When the vibration is perpendicular to the liquid propellant surface, Faraday waves may be generated at the liquid-vapor interface. These Faraday instabilities can perturb or break up the liquid surface of cryogenic tanks, leading to inefficiencies in thermal management or even ullage collapse. Drawing from theory and experiments, an engineering model defining the allowable design regions for pulsed settling in microgravity was assembled and verified with computational fluid dynamics (CFD) simulations. A traditional settling metric, the Bond number, was also overlaid in the model to indicate which duty cycles were insufficient to overcome surface tension and aggregate propellant. Mission planners and engineers can consult the tool to rapidly evaluate the stability of a liquid-vapor interface given the pulse frequency and the excitation acceleration. Expressions developed for Faraday waves induced by a sinusoidal forcing input at standard gravity were found to provide excellent predictive capabilities for pulsed, or rectangular, waveforms in the absence of a consistent gravitational acceleration. This study extends the usage of these equations to an alternative forcing function and microgravity environments for the purpose of estimating natural frequencies, surface mode shapes, surface wave amplitudes, and the onset of droplet ejection. CFD simulations with the Loci/STREAM-VoF (Volume of Fluid) solver were initially validated against experimental results in standard gravity. Discrete points on the design map were then investigated with CFD and confirmed that the engineering model reliably indicates surface stability and most Faraday wave characteristics without requiring higher-fidelity tools. The engineering model is highly extensible and can be adapted for various propellant fill fractions, fluid properties, and tank sizes.

Faraday Waves↗
NASA NTRS1980

Experimental and analytical transonic flutter characteristics of a geared-elevator configuration

The flutter model represented the aft fuselage and empennage of a proposed supersonic transport airplane and had an all movable horizontal tail with a geared elevator. It was tested mounted from a sting in the transonic dynamics tunnel. Symmetric flutter boundaries were determined experimentally at Mach numbers from 0.7 to 1.14 for a geared elevator configuration (gear ratio of 2.8 to 1.0) and an ungeared elevator configuration (gear ratio of 1.0 to 1.0). Gearing the elevator increased the experimental flutter dynamic pressures about 20 percent. Flutter calculations were made for the geared elevator configuration by using two analytical methods based on subsonic lifting surface theory. Both methods analyzed the stabilizer and elevator as a single, deforming surface, but one method also allowed the elevator to be analyzed as hinged from the stabilizer. All analyses predicted lower flutter dynamic pressures than experiment with best agreement (within 12 percent) for the hinged elevator method. Considering the model as mounted from a flexible rather than rigid sting in the analyses, had only a slight effect on the flutter results but was significant in that a sting related vibration mode was identified as a potentially flutter critical mode.

Ruhlin, C. L.↗
DOE OSTI2018

Photostable and efficient upconverting nanocrystal-based chemical sensors

Chemical sensing in living systems demands optical sensors that are bright, stable, and sensitive to the rapid dynamics of chemical signaling. Lanthanide-doped upconverting nanoparticles (UCNPs) efficiently convert near infrared (NIR) light to higher energy emission and allow biological systems to be imaged with no measurable background or photobleaching, and with reduced scatter for subsurface experiments. Despite their advantages as imaging probes, UCNPs have little innate chemical sensing ability and require pairing with organic fluorophores to act as biosensors, although the design of stable UCNP-fluorophore hybrids with efficient upconverted energy transfer (UET) has remained a challenge. Here, we report Yb 3+ - and Er 3+ -doped UCNP-fluorophore conjugates with UET efficiencies up to 88%, and photostabilities 100-fold greater by UET excitation than those of the free fluorophores under direct excitation. Despite adding distance between Er 3+ donors and organic acceptors, thin inert shells significantly enhance overall emission without compromising UET efficiency. This can be explained by the large increase in quantum yield of Er 3+ donors at the core/shell interface and the large number of fluorophore acceptors at the surface. Sensors excited by UET show increases in photostability well beyond those reported for other methods for increasing the longevity of organic fluorophores, and those covalently attached to UCNP surface polymers show greater chemical stability than those directly coordinated to the nanocrystal surface. Furthermore by conjugating other fluorescent chemosensors to UCNPs, these hybrids may be extended to a series of NIR-responsive biosensors for quantifying the dynamic chemical populations critical for cell signaling.

36 MATERIALS SCIENCE↗
NASA NTRS1999

Origin and Reactivity of the Martian Soil: A 2003 Micromission

The role of water in the development of the martian surface remains a fundamental scientific question. Did Mars have one or more "warm and wet" climatic episodes where liquid water was stable at the surface? If so, the mineral phases present in the soils should be consistent with a history of aqueous weathering. More generally, the formation of hydrated mineral phases on Mars is a strong indicator of past habitable surface environments. The primary purpose of this investigation is to help resolve the question of whether such aqueous indicators are present on Mars by probing the upper meter for diagnostic mineral species. According to Burns [1993], the formation of the ferric oxides responsible for the visible color of Mars are the result of dissolution of Fe (+2) phases from basalts followed by aqueous oxidation and precipitation of Fe" mineral assemblages. These precipitates likely included iron oxyhydroxides such as goethite (a-FeOOH) and lepidocrocite (g-FeOOH), but convincing evidence for these phases at the surface is still absent. The stability of these minerals is enhanced beneath the surface, and thus we propose a subsurface search for hydroxylated iron species as a test for a large-scale chemical weathering process based on interactions with liquid water. It is also possible that the ferric minerals on Mars are not aqueous alteration products of the rocks. A chemical study of the Pathfinder landing site concluded that the soils are not directly derived from the surrounding rocks and are enhanced in Mg and Fe. The additional source of these elements might be from other regions of Mars and transported by winds, or alternatively, from exogenic sources. Gibson [1970] proposed that the spectral reflectivity of Mars is consistent with oxidized meteoritic material. Yen and Murray [1998] further extend Gibson's idea and show, in the laboratory, that metallic iron can be readily oxidized to maghemite and hematite under present-day martian surface conditions (in the absence of liquid water). A test for a meteoritic component of the soil can be conducted, as described below, by searching for the presence of Ni at the martian surface. The average abundance of nickel in an Fe-Ni meteorite is about 7% and, if present at measurable levels in the soil, would be indicative of an exogenic contribution. In addition, it may be possible to directly search for mineral phases common in meteorites. An understanding of the formation and evolution of the martian soil would not be complete without addressing the unusual reactivity discovered by the Viking Landers The presence of an inorganic oxidant, possibly one produced as a results of photochemical processes, is the most widely accepted explanation of the Viking results. Are these chemical species simply adsorbed on soil grains, or have they reacted with the metal oxide substrates and altered the mineral structures? Could a completely different (non-photochemical) process be responsible for the soil reactivity? The various ideas for the nature of this putative oxidant could be constrained by a measurement of the change in reactivity with depth. Different compositions will have different lifetimes and mobilities and thus will have different vertical profiles. Because the oxidizing compounds are believed to actively destroy organic molecules, determination of the reactivity gradient also has significant implications for the search for life on Mars. A DS2-based microprobe system can be instrumented for a 2003 micromission to investigate the origin and reactivity of the martian soil. These measurements would provide invaluable information regarding the climate history and exobiological potential of the planet. The NMR, X ray and chemiresistor measurement approach described embodies a highly synergistic and general set of soil interrogation methods for elements, compounds, and crystal structures and can also be applied to other geologic questions of interest. For example, if the capability for precise targeting of the probes is available, then in-situ investigations of suspected evaporite and hydrothermal deposits would be possible with the same set of instruments. Additional information is contained in the original.

Yen, Albert S.↗
NASA NTRS2014

Lithium-Air Cell Development

Lithium-air (Li-air) primary batteries have a theoretical specific capacity of 11,400 Wh/kg, the highest of any common metal-air system. NASA is developing Li-air technology for a Mobile Oxygen Concentrator for Spacecraft Emergencies, an application which requires an extremely lightweight primary battery that can discharge over 24 hours continuously. Several vendors were funded through the NASA SBIR program to develop Li-air technology to fulfill the requirements of this application. New catalysts and carbon cathode structures were developed to enhance the oxygen reduction reaction and increase surface area to improve cell performance. Techniques to stabilize the lithium metal anode surface were explored. Experimental results for prototype laboratory cells are given. Projections are made for the performance of hypothetical cells constructed from the materials that were developed.

Lithium-air↗
DOE OSTI2021

Toward Optimizing Electrospun Nanofiber Fuel Cell Catalyst Layers: Polymer–Particle Interactions and Spinnability

We investigate the effect of the poly(acrylic acid) (PAA) carrier polymer concentration on the microstructure and rheological properties of catalyst inks for electrospun polymer–electrolyte membrane fuel-cell catalyst layers. Characterization of an ink microstructure using oscillatory shear rheology showed that the catalyst particles (platinum on carbon) are significantly agglomerated in the absence of PAA or an ionomer. Both the ionomer and PAA promoted the stability of the particles against agglomeration via electrosteric stabilization by adsorbing onto the particle surface. Increasing the PAA concentration increased the stability of the particles (or reduced the agglomerated structure) due to increasing PAA coverage onto the free surface area of the particles. However, beyond a certain increase in concentration, PAA was found to predominantly remain as an excess free polymer in the ink due to an insufficient free/available surface area on the particles for further PAA coverage. Extensional rheology measurements demonstrated that PAA enhances the extensional viscosities of the inks. Consequently, increasing the PAA concentration in the ink promoted the evolution of uniform nanofibers. However, beyond a certain concentration, a significant increase in the shear viscosities of the inks led to defective fiber morphologies because of the onset of flow instabilities. Electrochemical performance comparisons between catalyst layers with different PAA concentrations showed maximum performance at the PAA concentration that led to the least agglomerated structure of the catalyst, most uniform fiber morphologies, and low concentrations of free (non-adsorbing) PAA in the electrode. These results provide a rationale for optimization of electrospun catalyst nanofibers for both spinnability and electrochemical performance.

25 ENERGY STORAGE↗
DOE OSTI2018

Phenyl radical + propene: a prototypical reaction surface for aromatic-catalyzed 1,2-hydrogen-migration and subsequent resonance-stabilized radical formation

The C 9 H 11 potential energy surface (PES) was experimentally and theoretically explored because it is a relatively simple, prototypical alkylaromatic radical system. Although the C 9 H 11 PES has already been extensively studied both experimentally (under single-collision and thermal conditions) and theoretically, new insights were made in this work by taking a new experimental approach: flash photolysis combined with time-resolved molecular beam mass spectrometry (MBMS) and visible laser absorbance. The C 9 H 11 PES was experimentally accessed by photolytic generation of the phenyl radical and subsequent reaction with excess propene (C 6 H 5 + C 3 H 6 ). The overall kinetics of C 6 H 5 + C 3 H 6 was measured using laser absorbance with high time-resolution from 300 to 700 K and was found to be in agreement with earlier measurements over a lower temperature range. Five major product channels of C 6 H 5 + C 3 H 6 were observed with MBMS at 600 and 700 K, four of which were expected: hydrogen (H)-abstraction (measured by the stable benzene, C 6 H 6 , product), methyl radical (CH 3 )-loss (styrene detected), H-loss (phenylpropene isomers detected) and radical adduct stabilization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Composition-Dependent Reconstructions of Titanium Oxide Clusters and Cu(111) Support via Cluster-Adatom Interactions

Mass-selected cluster deposition and scanning tunneling microscopy (STM) were used to investigate the surface structure and thermal stability of Ti 3 O y (y = 5, 6) clusters on a Cu(111) surface. STM imaging shows that the substoichiometric Ti 3 O 5 clusters aggregate into large dendritic assemblies at step edges, while the stoichiometric Ti 3 O 6 clusters are highly dispersed as single or small groupings of clusters. Cluster deposition also results in extensive reconstruction of the Cu(111) surface. The Ti 3 O 5 /Cu(111) surface exhibits one Cu-layer deep pits that are ringed by cluster assemblies that nucleate and grow at the perimeter step edges. By comparison, the Ti 3 O 6 /Cu(111) surface consists of irregular step edges and small one Cu-layer islands that are decorated with clusters. The restructuring of the Cu(111) surface is attributed to strong Cu-cluster interactions that release Cu adatoms from the step edges. This mechanism is supported by density functional theory (DFT) calculations, which predict that the Cu adatom attachment to the clusters is energetically favorable. Annealing the surfaces at elevated temperatures (400-700 K) results in higher densities of irregular steps, pits and isolated Cu islands as well as increased cluster aggregation. In conclusion, this work highlights adatom-cluster interactions as another manifestation of strong cluster-support interactions that can significantly alter the nature of the oxide-metal interface.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Anomalous stability of non-van der Waals bonded B4C nanosheets through surface reconstruction

Boron carbide (B4C) has been well studied both theoretically and experimentally in its bulk form due to its exceptional hardness and use as a high-temperature thermoelectric. However, the properties of its two-dimensional nanosheets are not well established. In this paper, using van der Waals-corrected density-functional theory simulations, we show that bulk B4C can be cleaved along different directions to form B4C nanosheets with low formation energies. We find that there is minimal dependence of formation energies on cleavage planes and surface terminations, even though the bulk is not van der Waals layered. This anomalous stability of B4C nanosheets is found to be a result of surface reconstructions that are unique to B-rich systems. While the density of states of the bulk B4C indicate that it is a semiconductor, the B4C nanosheets are found to be predominantly metallic. We attribute this metallic behavior to a redistribution of charges on the surface bonds of the films. The Seebeck coefficients of the B4C films remain comparable to those of the bulk and are nearly constant as a function of temperature. Our results provide guidance for experimental synthesis efforts and future application of B4C nanosheets in nanoelectronic and thermoelectric applications.

Physics↗
DOE OSTI2020

Pt-Ligand single-atom catalysts: tuning activity by oxide support defect density

The support–metal interaction is an important element of heterogeneous catalyst design and is particularly critical for the rapidly growing field of single-atom catalysts (SACs). In this work, we investigate the impact of varying the defect density of the titania support on metal–organic Pt SACs for hydrosilylation reactions. Pt SACs are decorated on the powder titania support, employing a metal–ligand interaction with a dipyridyl-tetrazine ligand (DPTZ). The single-atom nature of Pt is verified by X-ray absorption spectroscopy (XAS) on both pristine and defective titania surfaces. These Pt species have a +2 oxidation state and are stabilized by bonding with DPTZ, surface oxygen, and residual chloride from the metal precursor. The catalytic activity is evaluated for the alkene hydrosilylation reaction and it is discovered that the activity of Pt-ligand is positively correlated with the defect density of the titania support. The turn-over number (TON) is calculated to be 12 530 for Pt SACs on a defective surface, which is significantly higher than Pt SACs on a pristine titania surface (830) for the same reaction period (10 min) under the same conditions (70 °C). We ascribe the high activity of Pt SACs on defective titania surfaces to two aspects: the coordination of Pt with more chloride than on pristine titania surfaces, which shortens the induction period of the reaction, and the preferential dispersion of Pt–DPTZ units on defective regions of titania surfaces, allowing facile contact between Pt sites and reactants. The supported Pt–DPTZ SACs show high stability through multiple cycles of batch reactions. This work demonstrates an efficient approach to improve the activity and stability of SACs by optimizing the metal–support interaction, which can also be applied to other oxide surfaces to further develop next-generation heterogeneous single-atom catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2011

Engine Yaw Augmentation for Hybrid-Wing-Body Aircraft via Optimal Control Allocation Techniques

Asymmetric engine thrust was implemented in a hybrid-wing-body non-linear simulation to reduce the amount of aerodynamic surface deflection required for yaw stability and control. Hybrid-wing-body aircraft are especially susceptible to yaw surface deflection due to their decreased bare airframe yaw stability resulting from the lack of a large vertical tail aft of the center of gravity. Reduced surface deflection, especially for trim during cruise flight, could reduce the fuel consumption of future aircraft. Designed as an add-on, optimal control allocation techniques were used to create a control law that tracks total thrust and yaw moment commands with an emphasis on not degrading the baseline system. Implementation of engine yaw augmentation is shown and feasibility is demonstrated in simulation with a potential drag reduction of 2 to 4 percent. Future flight tests are planned to demonstrate feasibility in a flight environment.

Taylor, Brian R.↗
NASA NTRS2011

Engine Yaw Augmentation for Hybrid-Wing-Body Aircraft via Optimal Control Allocation Techniques

Asymmetric engine thrust was implemented in a hybrid-wing-body non-linear simulation to reduce the amount of aerodynamic surface deflection required for yaw stability and control. Hybrid-wing-body aircraft are especially susceptible to yaw surface deflection due to their decreased bare airframe yaw stability resulting from the lack of a large vertical tail aft of the center of gravity. Reduced surface deflection, especially for trim during cruise flight, could reduce the fuel consumption of future aircraft. Designed as an add-on, optimal control allocation techniques were used to create a control law that tracks total thrust and yaw moment commands with an emphasis on not degrading the baseline system. Implementation of engine yaw augmentation is shown and feasibility is demonstrated in simulation with a potential drag reduction of 2 to 4 percent. Future flight tests are planned to demonstrate feasibility in a flight environment.

Taylor, Brian R.↗
NASA NTRS1998

Dynamics of Liquids in Edges and Corners (DYLCO): IML-2 Experiment for the BDPU

Knowledge of the behavior of fluids possessing free surfaces is important to many fluid systems, particularly in space, where the normally subtle effects of surface wettability play a more dramatic and often surprising role. DYLCO for the IML-2 mission was proposed as a simple experiment to probe the particular behavior of capillary surfaces in containers of irregular cross section. Temperature control was utilized to vary the fluid-solid contact angle, a questionable thermodynamic parameter of the system, small changes in which can dramatically influence the configuration, stability, and flow of a capillary surface. Container shapes, test fluid, and temperature ranges were selected for observing both local changes in interface curvature as well as a global change in fluid orientation due to a critical wetting phenomenon. The experiment hardware performed beyond what was expected and fluid interfaces could be readily digitized post flight to show the dependence of the interface curvature on temperature. For each of the containers tested surfaces were observed which did not satisfy the classic equations for the prediction of interface shape with constant contact angle boundary condition. This is explained by the presence of contact angle hysteresis arising from expansion and contraction of the liquid during the heating and cooling steps of the test procedure. More importantly, surfaces exceeding the critical surface curvature required for critical wetting were measured, yet no wetting was observed. These findings are indeed curious and pose key questions concerning the role of hysteresis for this critical wetting phenomena. The stability of such surfaces was determined numerically and it is shown that stability is enhance (reduced) when a surface is in its 'advancing' ('receding') state, The analysis shows complete instability as the critical wetting condition is reached. The case of ideal dynamic wetting is addressed analytically in detail with results of significant flow characteristics presented in closed form. The solutions indicate a square root of T dependence of the capillary 'rise' rate which is corroborated by drop tower tests. The analysis clearly shows that infinite time is necessary for surfaces to reorient at the critical wetting transition.

Langbein, D.↗
NASA NTRS1949

Stability derivatives at supersonic speeds of thin rectangular wings with diagonals ahead of tip Mach lines

The investigation includes steady and accelerated vertical and longitudinal motions and steady rolling, yawing, sideslipping, and pitching for Mach numbers and aspect ratios greater than those for which the Mach line from the leading edge of the tip section intersects the trailing edge of the opposite tip section. The stability derivatives are derived with respect to principal body axes and then transformed to a system of stability axes. Theoretical results are obtained, by means of the linearized theory, for the surface-velocity-potential functions, surface-pressure distributions, and stability derivatives for various motions at supersonic speeds of thin flat rectangular wings without dihedral. In the case of yawing, a treatment for the infinitely long wing which takes account of the spanwise variation in the stream Mach number is extended to the finite wing, and a plausible, although not rigorous, solution is obtained for the wing tip effects.

Harmon, Sidney M↗