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NASA NTRS1986

An analytical method for predicting CMOS SRAM upsets with application to asymmetrical memory cells

An analytical method was developed to predict the heavy-ion-induced upset rate of static random access memory (SRAM) cells. The method was applied to the design of a memory with asymmetrical cells where the goal was to increase the upset rate in order to increase the number of observed upsets in a space environment. The asymmetry is achieved by increasing the drain area of selected transistors in the cell. Results from the analytical model for a space environment indicate the upset rate for the experimental asymmetrical cell (17.2 upsets/1 kbit-year) will be 4.7 times larger than the upset rate for the minimum-geometry balanced cell (3.6 upsets/1 kbit-year). The asymmetrical SRAM was designed into a test chip intended for the Combined Release and Radiation Effects Satellite (CRRES).

Buehler, Martin G.↗

NASA NTRS1987

Analytical solutions for static elastic deformations of wire ropes

This paper develops closed-form solutions for extension of twisted wire ropes subjected to axial forces for two different end conditions. The analytical results are compared with the corresponding numerical results obtained by Costello and Phillips. A close agreement between the two establishes validity of the analytical solutions. Finally, an expression for the effective rigidity modulus of the wire ropes is obtained in terms of the helix angle and the number of helical wires in the rope for each of the two end conditions.

Kumar, K.↗

NASA NTRS1987

Analytical and experimental investigation of mistuning in propfan flutter

An analytical and experimental investigation of the effects of mistuning on propfan subsonic flutter was performed. The analytical model is based on the normal modes of a rotating composite blade and a three-dimensional subsonic unsteady lifting surface aerodynamic theory. Theoretical and experimental results are compared for selected cases at different blade pitch angles, rotational speeds, and free-stream Mach numbers. The comparison shows a reasonably good agreement between theory and experiment. Both theory and experiment showed that combined mode shape, frequency, and aerodynamic mistuning can have a beneficial or adverse effect on blade damping depending on Mach number. Additional parametric results showed that alternative blade frequency mistuning does not have enough potential for it to be used as a passive flutter control in propfans similar to the one studied. It can be inferred from the results that a laminated composite propfan blade can be tailored to optimize its flutter speed by selecting the proper ply angles.

Kaza, Krishna Rao V.↗

NASA NTRS1987

Albedos of homogeneous semi-infinite canopies - Comparison of two-stream analytic and numerical solutions

The albedo of plant canopies is treated as a problem in radiative transfer. Albedos calcualted from an iterative multistream numerical model are compared with those calculated with an analytic two-stream solution. With the assumption of a randomly homogeneous distribution of leaf positions and orientations and isotropic scattering by individual leaves, the single-scattering albedo of the canopy can be found analytically. This single-scattering solution is incorporated into the two-stream solution and used to benchmark the multistream numerical model in the single-scattering limit. Relative errors so established in the multistream model are O(0.3 percent) or less. The two-stream model is also found to be remarkably accurate, with the error in multiply scattered radiation O(5 percent) or less, corresponding to absolute errors in visible albedo of less than 0.001 and near-infrared albedo of less than or equal to 0.01. Thus the two-stream model should be adequate for many purposes, such as climate modeling, provided the assumptions of homogeneous canopy and isotropic scattering are not too unrealistic.

Dickinson, Robert E.↗

NASA NTRS1985

An experimental and analytical investigation of isolated rotor flap-lag stability in forward flight

For flap-lag stability of isolated rotors, experimental and analytical investigations are conducted in hover and forward flight on the adequacy of a linear quasi-steady aerodynamics theory with dynamic inflow. Forward flight effects on lag regressing mode are emphasized. Accordingly, a soft inplane hingeless rotor with three blades is tested at advance ratios as high as 0.55 and at shaft angles as high as 20 deg. The 1.62-m model rotor is untrimmed with an essentially unrestricted tilt of the tip path plane. By computerized symbolic manipulation, an analytical model is developed in substall to predict stability margins with mode indentification. It also predicts substall and stall regions to help explain the correlation between theory and data. The correlation shows both the strengths and weaknesses of the data and theory, and promotes further insights into areas in which further study is needed in substall and stall.

Gaonkar, Gopal H.↗

NASA NTRS1987

Analytical caustic surfaces

This document discusses the determination of caustic surfaces in terms of rays, reflectors, and wavefronts. Analytical caustics are obtained as a family of lines, a set of points, and several types of equations for geometries encountered in optics and microwave applications. Standard methods of differential geometry are applied under different approaches: directly to reflector surfaces, and alternatively, to wavefronts, to obtain analytical caustics of two sheets or branches. Gauss/Seidel aberrations are introduced into the wavefront approach, forcing the retention of all three coefficients of both the first- and the second-fundamental forms of differential geometry. An existing method for obtaining caustic surfaces through exploitation of the singularities in flux density is examined, and several constant-intensity contour maps are developed using only the intrinsic Gaussian, mean, and normal curvatures of the reflector. Numerous references are provided for extending the material of the present document to the morphologies of caustics and their associated diffraction patterns.

Schmidt, R. F.↗

NASA NTRS1988

An analytical method for ditching analysis of an airborne vehicle

A simple analytical method has been introduced for aerohydrodynamic load analysis of an airborne configuration during water ditching. The method employs an aerodynamic panel code, based on linear potential flow theory, to simulate the flow of air and water around an aircraft configuration. The free surface separating the air and water region is represented by doublet sheet singularities. Although all the theoretical load distributions are computed for air, provisions are made to correct the pressure coefficients obtained on the configuration wetted surfaces to account for the water density. As an analytical tool, the Vortex Separation Aerodynamic (VSAERO) code is chosen to carry out the present investigation. After assessing the validity of the method, its first application is to analyze the water ditching of the Space Shuttle configuration at a 12 degree attitude.

Linear potential flow↗

NASA NTRS1987

Investigation of the feasibility of an analytical method of accounting for the effects of atmospheric drag on satellite motion

An analytic technique for accounting for the joint effects of Earth oblateness and atmospheric drag on close-Earth satellites is investigated. The technique is analytic in the sense that explicit solutions to the Lagrange planetary equations are given; consequently, no numerical integrations are required in the solution process. The atmospheric density in the technique described is represented by a rotating spherical exponential model with superposed effects of the oblate atmosphere and the diurnal variations. A computer program implementing the process is discussed and sample output is compared with output from program NSEP (Numerical Satellite Ephemeris Program). NSEP uses a numerical integration technique to account for atmospheric drag effects.

Bozeman, Robert E.↗

NASA NTRS1988

Analytical determination of critical crack size in solar cells

Although solar cells usually have chips and cracks, no material specifications concerning the allowable crack size on solar cells are available for quality assurance and engineering design usage. Any material specifications that the cell manufacturers use were developed for cosmetic reasons that have no technical basis. Therefore, the Applied Solar Energy Corporation (ASEC) has sponsored a continuing program for the fracture mechanics evaluation of GaAs. Fracture mechanics concepts were utilized to develop an analytical model that can predict the critical crack size of solar cells. This model indicates that the edge cracks of a solar cell are more critical than its surface cracks. In addition, the model suggests that the material specifications on the allowable crack size used for Si solar cells should not be applied to GaAs solar cells. The analytical model was applied to Si and GaAs solar cells, but it would also be applicable to the semiconductor wafers of other materials, such as a GaAs thin film on a Ge substrate, using appropriate input data.

Chen, C. P.↗

NASA NTRS1988

Analytical approximation of a distorted reflector surface defined by a discrete set of points

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Acosta, Roberto J.↗

NASA NTRS1987

An analytical solution to obtain the optimum source location using multiple direction finders on a spherical surface

An analytical solution is presented for determining the optimum location of a radiating source on the surface of a sphere, given multiple bearings. The bearings are assumed to have small errors of the order of 0-10 deg. The optimum location is found by minimizing the sum of the squares of the perpendicular great-circle distances from the source to the bearing lines. This is achieved analytically through an eigenvalue approach, rather than the usual iterative, numerical approach. Bearings of different weight are taken into account by approximating the distance from each direction finder to the source. The result is general and may have wide application. Since it is simple and nearly as fast as the triangulation technique for source location, it is now used in the SUNY-Albany East Coast Lightning Detection Network to compute the optimum location for lightning in real time.

Orville, Richard E., Jr.↗

NASA NTRS1986

Analytical and experimental studies of the surface flaw

This paper uses the Newman-Raju model, the Paris crack growth rate law, and a fixed R ratio to demonstrate the analytical considerations associated with predicting stress intensity distributions and fatigue crack growth of surface flaws under conditions of small-scale yielding. Problems which lie outside the realm of the model used in the analytical description are presented. It is concluded that, while the model employed provides remarkable predictive capability in a variety of surface flaw problems, many exceptional cases remain to be modeled.

Smith, C. W.↗

NASA NTRS1988

Analytical and experimental validation of the Oblique Detonation Wave Engine concept

The Oblique Detonation Wave Engine (ODWE) for hypersonic flight has been analytically studied by NASA using the CFD codes which fully couple finite rate chemistry with fluid dynamics. Fuel injector designs investigated included wall and strut injectors, and the in-stream strut injectors were chosen to provide good mixing with minimal stagnation pressure losses. Plans for experimentally validating the ODWE concept in an arc-jet hypersonic wind tunnel are discussed. Measurements of the flow field properties behind the oblique wave will be compared to analytical predictions.

Adelman, Henry G.↗

NASA NTRS1988

An analytical method for the ditching analysis of an airborne vehicle

Pressure coefficient↗

NASA NTRS1988

An analytic-geometric model of the effect of spherically distributed injection errors for Galileo and Ulysses spacecraft - The multi-stage problem

In previous work the problem of injecting the Galileo and Ulysses spacecraft from low earth orbit into their respective interplanetary trajectories has been discussed for the single stage (Centaur) vehicle. The central issue, in the event of spherically distributed injection errors, is what happens to the vehicle? The difficulties addressed in this paper involve the multi-stage problem since both Galileo and Ulysses will be utilizing the two-stage IUS system. Ulysses will also include a third stage: the PAM-S. The solution is expressed in terms of probabilities for total percentage of escape, orbit decay and reentry trajectories. Analytic solutions are found for Hill's Equations of Relative Motion (more recently called Clohessy-Wiltshire Equations) for multi-stage injections. These solutions are interpreted geometrically on the injection sphere. The analytic-geometric models compare well with numerical solutions, provide insight into the behavior of trajectories mapped on the injection sphere and simplify the numerical two-dimensional search for trajectory families.

Longuski, James M.↗

NASA NTRS1988

Sampling Mars: Analytical requirements and work to do in advance

Sending a mission to Mars to collect samples and return them to the Earth for analysis is without doubt one of the most exciting and important tasks for planetary science in the near future. Many scientifically important questions are associated with the knowledge of the composition and structure of Martian samples. Amongst the most exciting questions is the clarification of the SNC problem- to prove or disprove a possible Martian origin of these meteorites. Since SNC meteorites have been used to infer the chemistry of the planet Mars, and its evolution (including the accretion history), it would be important to know if the whole story is true. But before addressing possible scientific results, we have to deal with the analytical requirements, and with possible pre-return work. It is unlikely to expect that a possible Mars sample return mission will bring back anything close to the amount returned by the Apollo missions. It will be more like the amount returned by the Luna missions, or at least in that order of magnitude. This requires very careful sample selection, and very precise analytical techniques. These techniques should be able to use minimal sample sizes and on the other hand optimize the scientific output. The possibility to work with extremely small samples should not obstruct another problem: possible sampling errors. As we know from terrestrial geochemical studies, sampling procedures are quite complicated and elaborate to ensure avoiding sampling errors. The significance of analyzing a milligram or submilligram sized sample and putting that in relationship with the genesis of whole planetary crusts has to be viewed with care. This leaves a dilemma on one hand, to minimize the sample size as far as possible in order to have the possibility of returning as many different samples as possible, and on the other hand to take a sample large enough to be representative. Whole rock samples are very useful, but should not exceed the 20 to 50 g range, except in cases of extreme inhomogeneity, because for larger samples the information tends to become redundant. Soil samples should be in the 2 to 10 g range, permitting the splitting of the returned samples for studies in different laboratories with variety of techniques.

Koeberl, Christian↗

NASA NTRS1989

Analytical model of a five degree of freedom magnetic suspension and positioning system

An analytical model of a five degree of freedom magnetic suspension and positioning system is presented. The suspended element is a cylinder which is composed of permanent magnet material and the magnetic actuators are air core electromagnets mounted in a planar array. The analytical model consists of an open loop representation of the suspension and positioning system with electromagnet currents as inputs and displacements and rates in inertial coordinates as outputs. The uncontrolled degree of freedom is rotation about the long axis of the suspended cylinder.

Groom, Nelson J.↗

NASA NTRS1988

A second-order analytic analysis for frozen orbits

An analytical method for studying characteristics of frozen orbits using mean orbital elements is presented. By removing some of the approximations of Brouwer and Kosai (1959) and using the method of integration by parts, an analytic solution is obtained accurate to the second order in the sense of expansion of the perturbing potential of an aspherical approximation. The solution applies to orbits at and near the critical inclination as well as to frozen orbits and, of course, to unfrozen orbits. The analysis reveals that a frozen orbit can be interpreted as an orbit in which movements of the long-periodic part of the rate of change of periapsis cancels the secular part exactly at any time.

Tang, Charles C. H.↗