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At least 1,081 records · Page 60

The Formation and Evolution of Tessera and Insights into the Beginning of Recorded History on Venus: Geology of the Fortuna Tessera Quadrangle (V-2)

Today, and throughout its recorded history, Venus can be classified as a "one-plate planet." The observable geological record of the planet comprises only the last 1/4 or less of its overall geologic history. As shown by many authors, it started with intensive deformation in broad regions to form tessera [1-6] during the Fortunian period of history [7]. The period of tessera formation quickly changed to numerous zonal deformational belts of ridges and grooves that were followed by emplacement of vast volcanic plains (shield plains, regional plains) [7,8]. During the final epoch of the geologic history of Venus, large but isolated centers of volcanism formed extensive fields of lavas, with tectonics concentrated within fewer very prominent rift zones [8,9]. The observable changes in intensity and character of volcanism and tectonics suggest progressive changes from thin lithosphere early in the geologic history to thick lithosphere during later epochs [6,10]. We have little idea of the character of the first 3/4 of Venus' history. So, what does the earliest period of recorded history tell us about the transition from the Pre-Fortunian to the Fortunian period and what insight does this give us into this earlier period?

Head, J. W.↗

Thin Film Characterization on Cu/SnAg Solder Interface for 3D Packaging Technologies

Copper is a commonly used interconnect metal in microelectronic interconnects due to its exceptional electrical and thermal properties. Particularly in applications of the 2.5 and 3D integration, Cu is utilized in through-silicon-vias (TSVs) and flip chip interconnects between microelectronic chips for providing miniaturization, lower power and higher performance than current 2D packaging approaches. Furthermore, SnAg capped Cu pillars are a common high-density interconnect technology for flip chip bonding. For these interconnects, specific properties of the Cu surface, such as roughness and cleanliness, are an important factor in the process to ensure quality solder bumps. During electroplating, tight processing parameters must be met so that defects are avoided, and high bump uniformity is achieved. An understanding of the interactions at the solder and Cu pillar interface is needed, based on the electroplating parameters, to determine the best method for populating solder on the wafer surface. In this study, surface treatment techniques such as oxygen plasma cleaning were performed on the Cu surfaces and the SnAg plating chemistry for depositing the solder were evaluated through hull cell testing to qualitatively determine the range of current densities to investigate. It was observed that current density while plating played a large role in solder bump deposition morphology. At the higher current densities greater than 60 mA/cm 2 , bump height non-uniformity and dendritic growth are observed and at lower current densities, less than or equal to 60 mA/cm 2 , uniform, continuous bump height occurred.

36 MATERIALS SCIENCE↗

Heat flow and continental breakup: The Gulf of Elat (Aqaba)

Heat flow measurements were made in the major basins of the Gulf of Elat (Aqaba), northern Red Sea. The gulf is located at the southern portion of the Dead Sea rift which is a transform plate boundary. Gradient measurements at each site were made with a probe which allows multiple penetration of the bottom during a single deployment of the instrument. Thermal conductivity was determined by needle probe measurements on sedimentary cores. The mean heat flux, about 80 mWm(-2), is significantly above the continental mean, and probably also above that from the adjacent Sinai and Arabian continental blocks. The heat flow appears to increase from north to south. Such an increase may be related to the more advanced rifting stage of the Red Sea immediately to the south, which presently includes creation of an oceanic crust. This trend also corresponds to the general trend of the deep crustal structure in the gulf. Evidence from various geophysical fields suggest a gradual thinning of the crust towards the direction of the Red Sea where a normal oceanic crust exists. The heat flow data, together with other geophysical data, indicate a propagation of mature rifting activity from the Red Sea into the Gulf of Elat. This process is acting simultaneously with the transform motion along the Dead Sea rift.

Ben-Avraham, Z.↗

Gravity Effects in Diffusive Coarsening of Bubble Lattices: von Neumann's Law

von Neumann modelled the evolution of two-dimensional soap froths as a purely diffusive phenomenon; the area growth of a given cell was found to depend only on the geometry of the bubble lattice. In the model, hexagons are stable, pentagons shrink and heptagons grow. The simplest equivalent to the area growth law is / approximately t(sub beta). The result depends on assuming (1) an incompressible gas; (2) bubble walls which meet at 120 deg and (3) constant wall thickness and curvature. Each assumption is borne out in experiments except the last one: bubble wall thickness between connecting cells varies in unit gravity because of gravity drainage. The bottom part of the soap membrane is thickened, the top part is thinned, such that gas diffusion across the membrane shows a complex dependence on gravity. As a result, experimental tests of von Neumann's law have been influenced by effects of gravity; fluid behavior along cell borders can give non-uniform wall thicknesses and thus alter the effective area and gas diffusion rates between adjacent bubbles. For area plotted as a function of time, Glazier (J.A. Glazier, S.P. Gross, and I. Stavans, Phys. Rev. A. 36, 306 (1987); J. Stavans, J.A, Glazier, Phys. Rev. Lett. 62, 1318 (1989).) suggest that in some cases their failure to observe von Neumann's predicted growth exponent ((sup beta)theor(sup =1; beta)exp(sup =0.70 + 0.10)) may have been the result of such "fluid drainage onto the lower glass plate". Additional experiments which varied plate spacing gave different beta exponents in a fashion consistent with this suggestion. During preliminary long duration experiments (approximately 100 h) aboard Spacelab-J, a low-gravity test of froth coarsening has examined (1) power law scaling of von Neumann's law (beta values) in the appropriate diffusive limits; (2) new bubble lattice dynamics such as greater fluid wetting behavior on froth membranes in low gravity; and (3) explicit relations for the gravity dependence of the second moment (or disorder parameter) governing the geometric spread in cell-sidedness around the mean of perfect hexagonal filling. By reducing the gravity-induced distortion in lattice wall thickness, the diffusion-limited regime of bubble coarsening becomes available for performing critical tests of network dynamics.

Noever, David A.↗

Design and Fabrication of Oxygen/RP-2 Multi-Element Oxidizer-Rich Staged Combustion Thrust Chamber Injectors

As part of the Combustion Stability Tool Development project funded by the Air Force Space and Missile Systems Center, the NASA Marshall Space Flight Center was contracted to assemble and hot-fire test a multi-element integrated test article demonstrating combustion characteristics of an oxygen/hydrocarbon propellant oxidizer-rich staged-combustion engine thrust chamber. Such a test article simulates flow through the main injectors of oxygen/kerosene oxidizer-rich staged combustion engines such as the Russian RD-180 or NK-33 engines, or future U.S.-built engine systems such as the Aerojet-Rocketdyne AR-1 engine or the Hydrocarbon Boost program demonstration engine. On the current project, several configurations of new main injectors were considered for the thrust chamber assembly of the integrated test article. All the injector elements were of the gas-centered swirl coaxial type, similar to those used on the Russian oxidizer-rich staged-combustion rocket engines. In such elements, oxidizer-rich combustion products from the preburner/turbine exhaust flow through a straight tube, and fuel exiting from the combustion chamber and nozzle regenerative cooling circuits is injected near the exit of the oxidizer tube through tangentially oriented orifices that impart a swirl motion such that the fuel flows along the wall of the oxidizer tube in a thin film. In some elements there is an orifice at the inlet to the oxidizer tube, and in some elements there is a sleeve or "shield" inside the oxidizer tube where the fuel enters. In the current project, several variations of element geometries were created, including element size (i.e., number of elements or pattern density), the distance from the exit of the sleeve to the injector face, the width of the gap between the oxidizer tube inner wall and the outer wall of the sleeve, and excluding the sleeve entirely. This paper discusses the design rationale for each of these element variations, including hydraulic, structural, thermal, combustion performance, and combustion stability considerations. This paper also discusses the fabrication and assembly of the injector components, including the injector body/interpropellant plate, the additive manufactured GRCop-84 faceplate, and the pieces that make up the injector elements including the oxidizer tube, an inlet to the oxidizer tube, and a facenut that includes the fuel tangential inlets and forms the initial recessed volume where oxidizer and fuel first interact. Hot-fire test results of these main injector designs in an integrated test article that includes an oxidizer-rich preburner are described in companion papers at this JANNAF meeting.

Garcia, C. P.↗

Local Ultrasonic Resonance Spectroscopy of Lithium Metal Batteries for Aerospace Applications

As next-generation aircraft and vehicles continue to develop, so do their associated energy demands. Lithium metal batteries are a leading candidate to fulfill this energy requirement, but these batteries are prone to internal dendrite defects that can lead to catastrophic thermal runaway events. Current battery management systems are capable of mitigating such risks, but are unable to detect such defects until thermal runaway has already begun. Various nondestructive evaluation (NDE) techniques, particularly ultrasonic NDE, can directly monitor internal battery parameters giving them the potential to detect critical defects prior to catastrophic failure. However, most of the current battery NDE research has focused on improved battery state-of-charge (SOC) and stateof- health (SOH) monitoring with little emphasis on critical defect detection. Thus, a measurement technique sensitive to subtle battery defects is needed. In addition, the complex mechanics of ultrasound in porous, thin, multilayered batteries prompt the use of physics-based simulation to guide inspections. In this work, an ultrasonic NDE technique has been developed utilizing frequency domain analysis of local battery resonances to detect the presence of battery defects. This technique is a practical extension of local ultrasonic resonance spectroscopy (LURS) – which previously required non-contact laser ultrasonics – to measurements with piezoelectric contact and immersion scan transducers. To extend the technique to work with piezoelectric transducers, ultrasonic battery measurements were compared to a sans-battery calibration measurement. Then, a linear systems deconvolution was used to eliminate the transfer functions of extraneous factors such as the transducer and electronics, leaving only the frequency-dependent battery reflection coefficient. The LURS technique was first validated on stainless steel and aluminum plates, producing reflection coefficients in line with analytical and numerical finite element modeling (FEM) results. Functioning Li-metal pouch cells were then seeded with lithium chip defects prior to LURS measurements. The presence of these defects is shown to cause a measurable shift in the battery’s through-thickness local resonances. 2D, frequency-domain poroelastic models of ultrasonic propagation in a single-cell lithium metal pouch battery were created and corroborated these findings. Thus, this work has both extended and proven the feasibility of the LURS technique in the detection of local battery defects.

Ultrasound↗

Tectonics and volcanism of Eastern Aphrodite Terra: No subduction, no spreading

Eastern Aphrodite Terra is approximately equal in size to the western North American Cordillera, from Mexico to Alaska. Its size and unique landforms make it an important area for understanding the tectonics of Venus, yet models for its formation are diametrically opposed. This region is part of the Equatorial Highlands, which was proposed as a region of lithospheric thinning, isostatic uplift, and attendant volcanism. Eastern Aphrodite Terra is dominated by circular structures within which deformation and volcanism are intimately related. These structures are marked by radial and concentric fractures, and volcanic flows that emanate from a central vent, as well as from concentric fracture sets. Cross-cutting relations between flows and concentric fracture sets indicate that outer concentric fracture sets are younger than inner fracture sets. The circular structures are joined by regional northeast- to east-trending fractures that dominantly postdate formation of the circular structures. We propose that the circular structures 'grow' outward with time. Although these structures probably represent addition of crust to the lithosphere, they do not represent significant lithospheric spreading or convergence, and the region does not mark the boundary between two distinct tectonic plates. This region is not easily explained by analogy with either terrestrial midocean rifts or subduction zones. It is perhaps best explained by upwelling of magma diapirs that blister the surface, but do not cause significant lithospheric spreading. Further study of the structural and volcanic evolution of this region using Magellan altimetry and SAR data should lead to better understanding of the tectonic evolution of this region.

Hansen, Vicki L.↗

New Eddy Current Probe for Thickness Gauging of Conductive Materials

The accurate measure of material thickness is important for many non-destructive evaluation applications. Factors such as corrosion damage can jeopardize structural integrity through material thinning and process control considerations often mandate strict limits on material dimensions. Access to the material under test can be limited to a single side and large areas may need to be examined in a small time period. In an effort to enhance the effectiveness of material thickness measurements a flux focusing eddy current probe has been developed at NASA Langley Research Center. The probe provides an accurate measure of the thickness of conducting materials from a single sided measurement. It is straight forward to use and can be easily automated for production line testing. The probe also requires only minimal instrumentation and power so that extremely portable units can be manufactured at a low cost. This new eddy current probe has been used to accurately measure the thickness of aluminum alloy plates with a resolution of greater than 0.001 in. (25 microns). Simulated corrosion damage has also been detected on both single layer and multi-layer samples. The present work will explain the output voltage dependence of the device as a function of material thickness and present experimental results for thickness gauging and corrosion detection.

Wincheski, Buzz↗

Benchmarking the QUAD4/TRIA3 element

The QUAD4 and TRIA3 elements are the primary plate/shell elements in NASTRAN. These elements enable the user to analyze thin plate/shell structures for membrane, bending and shear phenomena. They are also very new elements in the NASTRAN library. These elements are extremely versatile and constitute a substantially enhanced analysis capability in NASTRAN. However, with the versatility comes the burden of understanding a myriad of modeling implications and their effect on accuracy and analysis quality. The validity of many aspects of these elements were established through a series of benchmark problem results and comparison with those available in the literature and obtained from other programs like MSC/NASTRAN and CSAR/NASTRAN. Never-the-less such a comparison is never complete because of the new and creative use of these elements in complex modeling situations. One of the important features of QUAD4 and TRIA3 elements is the offset capability which allows the midsurface of the plate to be noncoincident with the surface of the grid points. None of the previous elements, with the exception of bar (beam), has this capability. The offset capability played a crucial role in the design of QUAD4 and TRIA3 elements. It allowed modeling layered composites, laminated plates and sandwich plates with the metal and composite face sheets. Even though the basic implementation of the offset capability is found to be sound in the previous applications, there is some uncertainty in relatively simple applications. The main purpose of this paper is to test the integrity of the offset capability and provide guidelines for its effective use. For the purpose of simplicity, references in this paper to the QUAD4 element will also include the TRIA3 element.

Pitrof, Stephen M.↗

Impact of Cirrus Crystal Shape on Solar Spectral Irradiance: A Case Study for Subtropical Cirrus

Profiles of in situ measurements of ice crystal size distribution of subtropical cirrus were used to calculate solar spectral irradiances above and below the clouds. Spheres and nonspherical ice crystal habits (columns, hollows, plates, bullets, and aggregates) were assumed in the calculations. The simulation results were compared to irradiance measurements from the NASA Solar Spectral Flux Radiometer. The microphysical and radiation data were collected by three aircraft during CRYSTAL-FACE. Two cirrus cases (optical thickness of about 1 and 7) from two mission dates (26 and 23 July 2002) were investigated in detail. The measured downwelling and upwelling irradiance spectra above the cirrus could mostly be reproduced by the radiation model to within +/- 5-10% for most ice crystal habits. Below the cirrus the simulations disagreed with the measured irradiances due to surface albedo variability along the flight track, and nonoptimal colocation between the microphysical and irradiance measurements. The impact of shape characteristics of the crystals was important for the reflected irradiances above the optically thin cirrus, especially for small solar zenith angles, because in this case single-scattering dominated the solar radiation field. For the cirrus of moderate optical thickness the enhanced multiple scattering tended to diminish particular shape features caused by nonspherical single-scattering. Within the ice absorption bands the shape-related differences in the absorption characteristics of the individual nonspherical ice crystals were amplified if multiple scattering prevailed. Furthermore, it was found that below the cloud the shape sensitivity of the downwelling irradiance spectra is larger compared to the nonsphericity effects on reflected irradiances above the cirrus. Finally, it was shown that the calculated cirrus solar radiative forcing could vary by as much as 26% depending on the ice crystal habit.

Wendisch, Manfred↗

Direct Electrolytic Deposition of Mats of Mn(x)O(y) Nanowires

Mats of free-standing manganese oxide (MnxOy) nanowires have been fabricated as experimental electrode materials for rechargeable electrochemical power cells and capacitors. Because they are free-standing, the wires in these mats are electrochemically accessible. The advantage of the mat-of-nanowires configuration, relative to other configurations of electrode materials, arises from the combination of narrowness and high areal number density of the wires. This combination offers both high surface areas for contact with electrolytes and short paths for diffusion of ions into and out of the electrodes, thereby making it possible to charge and discharge at rates higher than would otherwise be possible and, consequently, to achieve greater power densities. The nanowires are fabricated in an electrolytic process in which there is no need for an electrode binder material. Moreover, there is no need to incorporate an electrically conductive additive into the electrode material; the only electrically conductive material that must be added is a thin substrate contact film at the anchored ends of the nanowires. Hence, the mass fraction of active electrode material is close to 100 percent, as compared with about 85 percent in conventional electrodes made from a slurry of active electrode material, binder, and conductive additive pressed onto a metal foil. The locations and sizes of the nanowires are defined by holes in templates in the form of commercially available porous alumina membranes. In experiments to demonstrate the present process, alumina membranes of various pore sizes and degrees of porosity were used. First, a film of Au was sputtered onto one side of each membrane. The membranes were then attached, variously, to carbon tape or a gold substrate by use of silver or carbon paste. Once thus attached, the membranes were immersed in a plating solution comprising 0.01 M MnSO4 + 0.03 M (NH4)2SO4. The pH of the solution was kept constant at 8 by addition of H2SO4 or NH4OH as needed. Mn(x)O(y) nanowires were potentiostatically electrodeposited in the pores in the alumina templates. Depending on the anodic deposition potentials, Mn(x)O(y) was deposited in various oxidation states [divalent (Mn3O4), trivalent (Mn2O3), or tetravalent (MnO2)]. The Mn(x)O(y) wires were made free-standing (see figure) by dissolving the alumina templates, variously, in KOH or NaOH at a concentration of 20 volume percent.

Myung, Nosang↗

Solar Tests of Aperture Plate Materials for Solar Thermal Dish Collectors

If a malfunction occurs in a solar thermal point-focus distributed receiver power plant while a concentrator is pointed at the Sun, motion of the concentrator may stop. As the Sun moves relative to the Earth, the spot of concentrated sunlight then slowly walks off the receiver aperture, across the receiver face plate, and perhaps across adjacent portions of the concentrator. Intense local heating by the concentrated sunlight may damage or destroy these parts. The behavior of various materials under conditions simulating walk-off of a parabolic dish solar collector were evaluated. Each test consisted of exposure to concentrated sunlight at a peak flux density of about 7000 kW/square meter for 15 minutes. Types of materials tested included graphite, silicon carbide, silica, various silicates, alumina, zirconia, aluminum, copper, steel, and polytetrafluoroethylene. The only material that neither cracked nor melted was grade G-90 graphite. Grade CS graphite, a lower cost commercial grade, cracked half-way across, but did not fall apart. Both of these grades are medium-grain extruded graphites. A graphite cloth (graphitized polyacrylonitrile) showed fair performance when tested as a single thin ply; it might be useful as a multi-ply assembly. High purity slipcast silica showed some promise also.

Jaffe, L. D.↗

Solar tests of aperture plate materials for solar thermal dish collectors

If a malfunction occurs in a solar thermal point-focus distributed receiver power plant while a concentrator is pointed at the sun, motion of the concentrator may stop. As the sun moves relative to the earth, the spot of concentrated sunlight then slowly walks off the receiver aperture, across the receiver face plate, and perhaps across adjacent portions of the concentrator. Intense local heating by the concentrated sunlight may damage or destroy these parts. The behavior of various materials under conditions simulating walk-off of a parabolic dish solar collector were evaluated. Each test consisted of exposure to concentrated sunlight at a peak flux density of about 7000 kW/square meter for 15 minutes. Types of materials tested included graphite, silicon carbide, silica, various silicates, alumina, zirconia, aluminum, copper, steel, and polytetrafluroethylene. The only material that neither cracked nor melted was grade G-90 graphite. Grade CS graphite, a lower cost commercial grade, cracked half-way across, but did not fail apart. Both of these grades are medium-grain extruded graphites. A graphite cloth (graphitized polyacrylonitrile) showed fair performance when tested as a single thin ply; it might be useful as a multi-ply assembly. High purity slipcast silica showed some promise also.

Jaffe, L. D.↗

Solar tests of aperture plate materials for solar thermal dish collectors

If a malfunction occurs in a solar thermal point-focus distributed receiver power plant while a concentrator is pointed at the sun, motion of the concentrator may stop. As the sun moves relative to the earth, the spot of concentrated sunlight then slowly walks off the receiver aperture, across the receiver face plate, and perhaps across adjacent portions of the concentrator. Intense local heating by the concentrated sunlight may damage or destroy these parts. The behavior of various materials under conditions simulating walk-off of a parabolic dish solar collector were evaluated. Each test consisted of exposure to concentrated sunlight at a peak flux density of about 7000 kW/square meter for 15 minutes. Types of materials tested included graphite, silicon carbide, silica, various silicates, alumina, zirconia, aluminum, copper, steel, and polytetrafluoroethylene. The only material that neither cracked nor melted was grade G-90 graphite. Grade CS graphite, a lower cost commercial grade, cracked half-way across, but did not fall apart. Both of these grades are medium-grain extruded graphites. A graphite cloth (graphitized polyacrylonitrile) showed fair performance when tested as a single thin ply; it might be useful as a multi-ply assembly. High purity slipcast silica showed some promise also.

Jaffe, L. D.↗

A variational approach to the study of capillary phenomena

The problem of determining the free surface of a liquid in a capillary tube, and of a liquid drop, sitting first on a horizontal plane and then on more general surfaces is considered. With some modifications, the method applies to the study of pendent drops and of rotating drops as well. The standard capillary problem, i.e. the determination of the free surface of a liquid in a thin tube of general cross section, which resuls from the simultaneous action of surface tension, boundary adhesion and gravity is discussed. It turns out that in this case the existence of the solution surface depends heavily on the validity of a simple geometric condition about the mean curvature of the boundary curve of the cross section of the capillary tube. Some particular examples of physical interest are also be discussed. Liquid drops sitting on or hanging from a fixed horizontal plane are discussed. The symmetry of the solutions (which can actually be proved, as consequence of a general symmetrization argument) now plays the chief role in deriving both the existence and the regularity of energy-minimizing configurations. When symmetry fails (this is the case, for example, when the contact angle between the drop and the plate is not constant, or when the supporting surface is not itself symmetric), then more sophisticated methods must be used. Extensions in this direction are outlined.

Emmer, M.↗

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Nicholson, S.↗

The realuminizing of the 7-meter-diameter solar simulator collimating mirror

This paper describes the modification of a three-electron-beam (EB) gun system for vacuum depositing a highly reflective aluminum coating on a 7.01-m (23-ft) -diam nickel-plated aluminum collimating mirror. The mirror is part of the JPL 7.62-m space simulator that was recently modernized with a new high vacuum pumping system, solar lamp power supplies, solar optic lens system, and refurbished collimating mirror. The 7.01-m 12,700-kg (14-ton) spherical collimating mirror was removed from this facility for replating with 381 micron (0.015 in.) of electroless nickel and polished to a specular finish for realuminizing. The space chamber served as the vacuum coating vessel for the realuminizing coating process. The mirror is the primary reflector for the solar simulation system and the aluminized reflective surface is its most critical performance element. The uniformity of thickness and high reflectivity of the coating in visible and near-ultraviolet (UV) light governs the accuracy of the beam for solar testing. The uniformity of the thin-film thickness also controls the durability of the mirror over time. The mirror was polished to a 64-percent reflectivity with a uniformity of 1.5 percent. The performance goal for the aluminizing was 89 percent with +/- 0.5-percent variation over the mirror.

Noller, E. W.↗

Local instability of centrally loaded columns of channel section and Z-section

Charts are presented for the coefficients in formulas for the critical compressive stress at which cross-sectional distortion begins in a thin-wall member with either a channel section or a Z-section with identical flanges. The energy method of Timoshenko was used in the theoretical calculations required for the construction of the charts. The deflection equations were carefully selected to give good accuracy. The calculation of the critical compressive stress at stresses beyond the elastic range is briefly discussed. In order to demonstrate the use of the formulas and the charts in engineering calculations, two illustrative problems are included.

ELASTICITY↗