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NASA NTRS1980

Design of a recursive vector processor using polynomial splines

The problem of obtaining smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements is considered. A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation. Here, piecewise bicubic Hermite polynomials are extensively used as approximating functions, and the smoothing integral is converted to a discrete quadratic form. This makes it possible to convert the problem of fitting an approximating function to one of estimating the function values and derivatives at the nodes.

Kim, C. S.↗

NASA NTRS1982

The relationship between wind vector and normalized radar cross section used to derive Seasat-A Satellite Scatterometer winds

The Seasat-A Satellite Scatterometer (SASS) ocean normalized radar cross section (NRCS) dependence on the 19.5-m neutral stability wind vector may be specified as a function of radar incidence angle, the angle between wind direction and radar azimuth, and the neutral stability wind speed expressed in m/sec at a height of 19.5 m. An account is given of the development of models both expressing this relationship and providing the basis of inversion of NRCS to SASS winds, from initially aircraft scatterometer measurement-based forms to three Seasat field-validation experiments which furnish model NRCS versus surface windspeed data for comparison with SASS data.

Schroeder, L. C.↗

NASA NTRS1982

Integrating matrix solution of the hybrid state vector equations for beam vibration

A simple, versatile, and efficient computational technique has been developed for dynamic analysis of linear elastic beam and rod type of structures. Moreover, the method provides a rather general solution approach for two-point boundary value problems that are described by a single independent spatial variable. For structural problems, the method is implemented by a mixed state vector formulation of the differential equations, combined with an integrating matrix solution procedure. Highly accurate solutions are easily achieved with this approach. Example solutions are given for beam vibration problems including discontinuous stiffness and mass parameters, elastic restraint boundary conditions, concentrated inertia loading, and rigid body modes

Lehman, L. L.↗

NASA NTRS1982

Initial vector magnetic anomaly map from Magsat

Global magnetic component anomaly field maps have been derived from the Magsat vector magnetometer data obtained from November 1979 through May 1980. The amplitude of variations of the components over the maps are between 10 and 15 nT, well above the noise in the data. Averaged data, in 2-by-2 deg blocks, exhibit standard errors of the mean of about 1 nT over most of the X and Z maps, and about 2 nT over most of the Y maps. Errors rise to about twice these amounts near the auroral belts. Most of the anomalies in the component data are consistent with a crustal magnetization model which incorporates dipoles aligned only in the direction of the main field. However, there appear to be some regions which require dipoles aligned in some other direction i.e., remanent magnetization.

Langel, R. A.↗

NASA NTRS1982

On the possibility of detecting large-scale crustal remanent magnetization with Magsat vector magnetic anomaly data

Magnetic anomaly component data measured by Magsat is compared with synthetic anomaly component fields arising from an equivalent source dipole array at the earth's surface generated from total field anomaly data alone. It is found that the synthetic components fit the component data regardless of the dipole orientation assigned to the equivalent sources and of the dipole spacing. Tentative conclusions are: (1) over the U.S., vector anomaly fields can be determined to the accuracy of the measurements from the total field anomaly data alone; and (2) the equivalent source technique is not useful for determining the direction of large-scale crustal magnetization.

Galliher, S. C.↗

NASA NTRS1982

A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

An adaptive grid, finite-volume method has been used to solve the Navier-Stokes equations for complete (forebody and afterbody) flowfields around blunt bodies. The code, which is applicable for axisymmetric or two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required computational points. The solution technique is explicit, utilizing a maximum time-step advancement at each grid point to accelerate convergence to the steady state. The code has been fully vectorized for efficient solution on the CYBER 203 computer. A very flexible rezoning routine is used to concentrate mesh points anywhere in the field, either by a user-defined weighting function or by allowing high gradient regions to adjust the grid. The grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost. Currently, the code runs in approximately 0.000016 seconds per grid point per iteration.

Gnoffo, P. A.↗

NASA NTRS1982

Solution of the two-dimensional Euler equations with generalized coordinate transformation using flux vector splitting

An implicit finite difference code using flux vector splitting has been developed for solving the two-dimensional inviscid gas dynamics equations. The method is spatially second-order acurate, fully conservative, and uses body-conforming generalized coordinates for treating complex geometries. Numerical results have been obtained for transonic flow over a circular cylinder and airfoils. Steady results for a half cylinder (top and bottom symmetry-imposed) range from critical flow to a strong shock case with rotationally induced flow separation. Full cylinder solutions at freestream Mach number values of 0.5, however, show unsteady oscillation. A perturbation form of the method has also been developed and used to compute both fore and aft inviscid flow separation about a cylinder for a nonuniform incoming stream.

Buning, P. G.↗

NASA NTRS1982

The digital autopilot for thrust vector control of the Shuttle Orbital maneuvering system

This paper describes the requirements for and the design, development and performance of the digital autopilots (DAPs) for thrust vector control, utilizing the orbital maneuvering system (OMS) of the Space Shuttle Orbiter. The hardware and software requirements which caused the design to assume its current form are described. Also, the design synthesis, which considered rigid body stability margins, bending and slosh stabilization, guidance loop compensation, off-nominal performance and hardware and software limitations is presented. The performance of the OMS control system is summarized utilizing flight data from the first three Space Transportation System (STS) flights.

Penchuk, A.↗

NASA NTRS1984

Hardware Fault Simulator Generates Test Vectors For Complex IC's

Report describes technique using fault simulator implemented entirely in hardware to generate and optimize test vectors for microprocessor. Hardware fault simulator approach reduces test time, while maintaining high reliability in detecting faults.

Timoc, C. C.↗

NASA NTRS1983

Time-based self-spacing techniques using cockpit display of traffic information during approach to landing in a terminal area vectoring environment

A simulation study was undertaken to evaluate two time-based self-spacing techniques for in-trail following during terminal area approach. An electronic traffic display was provided in the weather radarscope location. The displayed self-spacing cues allowed the simulated aircraft to follow and to maintain spacing on another aircraft which was being vectored by air traffic control (ATC) for landing in a high-density terminal area. Separation performance data indicate the information provided on the traffic display was adequate for the test subjects to accurately follow the approach path of another aircraft without the assistance of ATC. The time-based technique with a constant-delay spacing criterion produced the most satisfactory spacing performance. Pilot comments indicate the workload associated with the self-separation task was very high and that additional spacing command information and/or aircraft autopilot functions would be desirable for operational implementational of the self-spacing task.

Williams, D. H.↗

NASA NTRS1982

Survey of new vector computers: The CRAY 1S from CRAY research; the CYBER 205 from CDC and the parallel computer from ICL - architecture and programming

Problems which can arise with vector and parallel computers are discussed in a user oriented context. Emphasis is placed on the algorithms used and the programming techniques adopted. Three recently developed supercomputers are examined and typical application examples are given in CRAY FORTRAN, CYBER 205 FORTRAN and DAP (distributed array processor) FORTRAN. The systems performance is compared. The addition of parts of two N x N arrays is considered. The influence of the architecture on the algorithms and programming language is demonstrated. Numerical analysis of magnetohydrodynamic differential equations by an explicit difference method is illustrated, showing very good results for all three systems. The prognosis for supercomputer development is assessed.

Gentzsch, W.↗

NASA NTRS1983

Vector-algebra approach to extract Denavit-Hartenberg parameters of assembled robot arms

The Denavit-Hartenberg parameters characterize the joint axis systems in a robot arm and, naturally, appear in the transformation matrices from one joint axis system to another. These parameters are needed in the control of robot arms and in the passage of sensor information along the arm. This paper presents a vector algebra method to determine these parameters for any assembled robot arm. The idea is to measure the location of the robot hand (or extension) for different joint angles and then use these measurements to calculate the parameters.

Barker, L. K.↗

NASA NTRS1982

Ion beamlet vectoring by grid translation

Ion beamlet vectoring is investigated by collecting deflection and divergence angle data for two-grid systems as a function of the relative displacement of these grids. Results show that at large displacements, accelerator grid impingement becomes a limiting factor and this determines the useful range of beamlet deflection. Beamlet deflection was shown to vary linearly with grid offset angle over this range. Values of deflection-to-offset angle ratio and useful range of deflection are presented as functions of grid-hole geometries, perveance levels, and accelerating voltages. It is found that the divergence of the beamlets is unaffected by deflection over the useful range of beamlet deflection. The grids of a typical dished-grid ion thruster are examined to determine where over the grid surface the grid offsets exceed the useful range, which indicates the regions on the surface where high accelerator grid impingment is probably occurring.

Homa, J. M.↗

NASA NTRS1983

State vector formulation of substructure coupling for damped systems

A generalized substructure coupling procedure in state vector form is derived for a complex system with general viscous damping. This first-order differential equation formulation is used in order to permit complex substructure modes to be employed easily. The free-interface normal (complex) modes and rigid-body modes of the substructure are defined. Complex residual attachment modes which result from static approximation of neglected higher modes are derived. The motion of each substructure is represented by a selected set of component modes. Equations of interface compatibility are employed to obtain an independent set of system equations of motion. A new method which employs incomplete complex normal modes in conjunction with the complex residual attachment modes to account for the contribution of neglected higher order modes is derived. Examples are employed to indicate how a damped structure may be analyzed by including the effect of residual attachment modes. Numerical results indicate that the new component mode synthesis method provides sytem equations of motion with reduced number of degrees of feedom leading to more accurate approximations to the system frequencies and damping factors than are obtained by pure mode truncation.

Chung, Y.-T.↗

NASA NTRS1982

Estimation of wave vector characteristics

A brief summary is presented of the techniques used to receive, transmit, and display frequency-time information. The mathematical basis for extracting wave vector information from the three electric and three magnetic wave fields is stated for the simple plane wave, single-source case. For the more realistic multiple-wave, multiple source case, basic correlation schemes and model-fitting techniques are described. Examples of results are given from various satellites for which two or more wave components could be treated. Finally, expectations for the upcoming OPEN mission are presented.

Shawhan, S. D.↗

NASA NTRS1983

Efficient solution of the Euler and Navier-Stokes equations with a vectorized multiple-grid algorithm

A multiple-grid algorithm for use in efficiently obtaining steady solutions to the Euler and Navier-Stokes equations is presented. The convergence of the explicit MacCormack algorithm on a fine grid is accelerated by propagating transients from the domain using a sequence of successively coarser grids. Both the fine and coarse grid schemes are readily vectorizable. The combination of multiple-gridding and vectorization results in substantially reduced computational times for the numerical solution of a wide range of flow problems. Results are presented for subsonic, transonic, and supersonic inviscid flows and for subsonic attached and separated laminar viscous flows. Work reduction factors over a scalar, single-grid algorithm range as high as 76.8. Previously announced in STAR as N83-24467

Chima, R. V.↗

NASA NTRS1983

Solid rocket booster thrust vector control subsystem description

Major Solid Rocket Booster-Thrust Vector Control (SRB-TVC) subsystem components and subcomponents used in the Space Transportation System (STS) are identified. Simplified schematics, detailed schematics, figures, photographs, and data are included to acquaint the reader with the operation, performance, and physical layout as well as the materials and instrumentation used.

Redmon, J., Jr.↗

NASA NTRS1983

A fully vectorized numerical solution of the incompressible Navier-Stokes equations

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Patel, N.↗