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At least 235 records · Page 13

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NASA NTRS1980

The primer vector in linear, relative-motion equations

Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.

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NASA NTRS1981

Three-axis attitude determination from vector observations

Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations. The first of these, the TRIAD algorithm, provides a deterministic (i.e., nonoptimal) solution for the attitude based on two vector observations. The second, the QUEST algorithm, is an optimal algorithm which determines the attitude that achieves the best weighted overlap of an arbitrary number of reference and observation vectors. Analytical expressions are given for the covariance matrices for the two algorithms using a fairly realistic model for the measurement errors. The mathematical relationship of the two algorithms and their relative merits are discussed and numerical examples are given. The advantage of computing the covariance matrix in the body frame rather than in the inertial frame (e.g., in terms of Euler angles) is emphasized. These results are valuable when a single-frame attitude must be computed frequently. They will also be useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.

Shuster, M. D.↗

NASA NTRS1981

Motion of the angular momentum vector in body coordinates for torque-free dual-spin spacecraft

The motion of the angular momentum vector in body coordinates for torque free, asymmetric dual spin spacecraft without and, for a special case, with energy dissipation on the main spacecraft is investigated. Without energy dissipation, two integrals can be obtained from the Euler equations of motion. Using the classical method of elimination of variable, the motion about the equilibrium points (six for the general case) are derived with these integrals. For small nutation angle, theta, the trajectories about the theta = 0 deg and theta = 180 deg points readily show the requirements for stable motion about these points. Also the conditions needed to eliminate stable motion about the theta = 180 deg point as well as the other undesireable equilibrium points follow directly from these equations. For the special case where the angular momentum vector moves about the principal axis which contains the momentum wheel, the notion of 'free variable' azimuth angle is used. Physically this angle must vary from 0 to 2 pi in a circular periodic fashion. Expressions are thus obtained for the nutation angle in terms of the free variable and other spacecraft parameters. Results show that in general there are two separate trajectory expressions that govern the motion of the angular momentum vector in body coordinates.

Fedor, J. V.↗

NASA NTRS1982

The Seasat-A satellite scatterometer - The geophysical evaluation of remotely sensed wind vectors over the ocean

A description is given of the algorithm used to convert Seasat-A satellite microwave scatterometer measurements of ocean normalized radar cross section to the neutral stability vector wind at 19.5 m height, as well as to compare these winds with high-quality surface observations. The wind vector algorithm used an empirical normalized radar cross section model function to describe the ocean normalized radar cross section's dependence on the 19.5-m neutral stability wind vector. In addition, two model functions were evaluated by means of an independent set of in situ surface wind observations from the Joint Air Sea Interaction experiment (JASIN). Better results were produced by these comparisons than the stipulated Seasat wind speed and direction accuracy specifications of + or - 2 m/sec and + or - 20 deg, respectively, over the 0-16 m/sec range of winds observed during JASIN.

Jones, W. L.↗

NASA NTRS1982

A parametric study of the behavior of the angular momentum vector during spin rate changes of rigid body spacecraft

During a spin-up or spin-down maneuver of a spinning spacecraft, it is usual to have not only a constant body-fixed torque about the desired spin axis, but also small undesired constant torques about the transverse axes. This causes the orientation of the angular momentum vector to change in inertial space. Since an analytic solution is available for the angular momentum vector as a function of time, this behavior can be studied for large variations of the dynamic parameters, such as the initial spin rate, the inertial properties and the torques. As an example, the spin-up and spin-down maneuvers of the Galileo spacecraft was studied and as a result, very simple heuristic solutions were discovered which provide very good approximations to the parametric behavior of the angular momentum vector orientation.

Longuski, J. M.↗

NASA NTRS1983

The use of laterally vectored thrust to counter thrust asymmetry in a tactical jet aircraft

A nonlinear, six degree-of-freedom flight simulator for a twin engine tactical jet was built on a hybrid computer to investigate lateral vectoring of the remaining thrust component for the case of a single engine failure at low dynamic pressures. Aircraft control was provided by an automatic controller rather than a pilot, and thrust vector control was provided by an open-loop controller that deflected a vane (located on the periphery of each exhaust jet and normally streamlined for noninterference with the flow). Lateral thrust vectoring decreased peak values of lateral control deflections, eliminated the requirement for steady-state lateral aerodynamic control deflections, and decreased the amount of altitude lost for a single engine failure.

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NASA NTRS1983

Numerical computation of transonic flow about wing-fuselage configurations on a vector computer

The transonic wing analysis code TWING, which uses the AF2 relaxation algorithm, has been vectorized to run on the Cray-1S computer. Vectorization of this code improved computational efficiency over that of the CDC 7600 computer by factors of 11 to 13. The improvement compares favorably with the prediction of a theoretical performance model. A convenient generalization now permits the treatment of rudimentary wing-fuselage combinations. Flow predictions for a transport configuration in both isolated-wing and wing-fuselage modes show the expected trends in shock strength and position when compared with wind-tunnel results. An isolated fighter wing is examined in terms of execution time on three different computers and in comparison with experimental data. The computational fluid dynamics code produced during this study is a careful union of an efficient three-dimensional, transonic, numerical algorithm and the vector features presently available on modern computers.

Thomas, S. D.↗

NASA NTRS1983

Improved cloud motion wind vector and altitude assignment using VAS

A CO2 cloud tracking technique to determine simultaneous heights and velocities of cloud motion winds is presented. Using animated CO2 channel imagery from VAS (Visible Infrared Spin-Scan Radiometer Atmospheric Sounder), multi-level cloud situations are separated into high, middle and low level cloud motion wind vectors by the CO2 slicing method. The VAS CO2 channel radiometric values are used in the CO2 absorption method to assign quantitative heights to the cloud vectors; cloud top pressures are determined from the ratio of the deviations in cloud produced radiances and the corresponding clear air values for three CO2 channels in a radiative transfer equation formulation. Two case studies are presented that show CO2 cloud-motion wind vectors to be in good agreement with radiosonde wind observations and CO2 cloud heights to be within a 50 mb rms deviation of radiosonde, bispectral and stereo height determinations.

Menzel, W. P.↗

NASA NTRS1983

Flux vector splitting and approximate Newton methods

In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocity-sound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasi-one-dimensional flow in a nozzle. Results are given for steady flows with shocks.

Jespersen, D. C.↗

NASA NTRS1983

Effect of thrust vectoring and wing maneuver devices on transonic aeropropulsive characteristics of a supersonic fighter

The aeropropulsive characteristics of an advanced fighter designed for supersonic cruise were determined in the Langley 16-Foot Transonic Tunnel. The objectives of this investigation were to evaluate the interactive effects of thrust vectoring and wing maneuver devices on lift and drag and to determine trim characteristics. The wing maneuver devices consisted of a drooped leading edge and a trailing-edge flap. Thrust vectoring was accomplished with two dimensional (nonaxisymmetric) convergent-divergent nozzles located below the wing in two single-engine podded nacelles. A canard was utilized for trim. Thrust vector angles of 0 deg, 15 deg, and 30 deg were tested in combination with a drooped wing leading edge and with wing trailing-edge flap deflections up to 30 deg. This investigation was conducted at Mach numbers from 0.60 to 1.20, at angles of attack from 0 deg to 20 deg, and at nozzle pressure ratios from about 1 (jet off) to 10. Reynolds number based on mean aerodynamic chord varied from 9.24 x 10 to the 6th to 10.56 x 10 to the 6th.

Capone, F. J.↗

NASA NTRS1984

The vectorization of a ray tracing program for image generation

Ray tracing is a widely used method for producing realistic computer generated images. Ray tracing involves firing an imaginary ray from a view point, through a point on an image plane, into a three dimensional scene. The intersections of the ray with the objects in the scene determines what is visible at the point on the image plane. This process must be repeated many times, once for each point (commonly called a pixel) in the image plane. A typical image contains more than a million pixels making this process computationally expensive. A traditional ray tracing program processes one ray at a time. In such a serial approach, as much as ninety percent of the execution time is spent computing the intersection of a ray with the surface in the scene. With the CYBER 205, many rays can be intersected with all the bodies im the scene with a single series of vector operations. Vectorization of this intersection process results in large decreases in computation time. The CADLAB's interest in ray tracing stems from the need to produce realistic images of mechanical parts. A high quality image of a part during the design process can increase the productivity of the designer by helping him visualize the results of his work. To be useful in the design process, these images must be produced in a reasonable amount of time. This discussion will explain how the ray tracing process was vectorized and gives examples of the images obtained.

Plunkett, D. J.↗

NASA NTRS1985

Static internal performance of a two-dimensional convergent nozzle with thrust-vectoring capability up to 60 deg

An investigation was conducted at wind-off conditions in the static-test facility of the Langley 16-Foot Transonic Tunnel to determine the internal performance characteristics of a two-dimensional convergent nozzle with a thrust-vectoring capability up to 60 deg. Vectoring was accomplished by a downward rotation of a hinged upper convergent flap and a corresponding rotation of a center-pivoted lower convergent flap. The effects of geometric thrust-vector angle and upper-rotating-flap geometry on internal nozzle performance characteristics were investigated. Nozzle pressure ratio was varied from 1.0 (jet off) to approximately 5.0.

Leavitt, L. D.↗

NASA NTRS1985

Diagnostics of vector magnetic fields

It is shown that the vector magnetic fields derived from observations with a filter magnetograph will be severely distorted if the spatially unresolved magnetic structure is not properly accounted for. Thus the apparent vector field will appear much more horizontal than it really is, but this distortion is strongly dependent on the area factor and the temperature line weakenings. As the available fluxtube models are not sufficiently well determined, it is not possible to correct the filter magnetograph observations for these effects in a reliable way, although a crude correction is of course much better than no correction at all. The solution to this diagnostic problem is to observe simultaneously in suitable combinations of spectral lines, and/or use Stokes line profiles recorded with very high spectral resolution. The diagnostic power of using a Fourier transform spectrometer for polarimetry is shown and some results from I and V spectra are illustrated. The line asymmetries caused by mass motions inside the fluxtubes adds an extra complication to the diagnostic problem, in particular as there are indications that the motions are nonstationary in nature. The temperature structure appears to be a function of fluxtube diameter, as a clear difference between plage and network fluxtubes was revealed. The divergence of the magnetic field with height plays an essential role in the explanation of the Stokes V asymmetries (in combination with the mass motions). A self consistent treatment of the subarcsec field geometry may be required to allow an accurate derivation of the spatially averaged vector magnetic field from spectrally resolved data.

Stenflo, J. O.↗

NASA NTRS1985

Application of Ritz vectors for dynamic analysis of large structures

The use of an orthogonal set of specially selected Ritz vectors is shown to be very effective in reducing the cost of dynamic analysis by modal superposition. Several mechanical structures are examined, and the Ritz vector approach is compared to the classical eigenvector approach on the basis of cost, accuracy and elapsed analysis (throughput) time. Mathematical proof of the completeness of orthogonal Ritz vectors is provided for the case of a positive definite mass matrix and a symmetric stiffness matrix.

Arnold, R. R.↗

NASA NTRS1986

The construction and use of divergence free vector expansions for incompressible fluid flow calculations

For incompressible fluids the law of mass conservation reduces to a constraint on the velocity vector, namely that it be divergence free. This constraint has long been a source of great difficulty to the numericist seeking to discretize the Navier-Stokes and Euler equations. A spectral method is discussed which overcomes this difficulty. Its efficacy is demonstrated on some simple problems. The velocity is approximated by a finite sum of divergence free vectors, each of which satisfies the same boundary conditions as the velocity. Projecting the governing equation onto the space of inviscid vector fields eliminates the pressure term and produces a set of ordinary differential equations that must be solved for the coefficents in the velocity. The pressure can then be recovered if it is needed.

Mhuiris, N. M. G.↗

NASA NTRS1986

Application of a VLSI vector quantization processor to real-time speech coding

Attention is given to a working vector quantization processor for speech coding that is based on a first-generation VLSI chip which efficiently performs the pattern-matching operation needed for the codebook search process (CPS). Using this chip, the CPS architecture has been successfully incorporated into a compact, single-board Vector PCM implementation operating at 7-18 kbits/sec. A real time Adaptive Vector Predictive Coder system using the CPS has also been implemented.

Davidson, G.↗

NASA NTRS1986

Magnetic field vector and electron density diagnostics from linear polarization measurements in 14 solar prominences

The Hanle effect is the modification of the linear polarization parameters of a spectral line due to the effect of the magnetic field. It has been successfully applied to the magnetic field vector diagnostic in solar prominences. The magnetic field vector is determined by comparing the measured polarization to the polarization computed, taking into account all the polarizing and depolarizing processes in line formation and the depolarizing effect of the magnetic field. The method was applied to simultaneous polarization measurements in the Helium D3 line and in the hydrogen beta line in 14 prominences. Four polarization parameters are measured, which lead to the determination of the three coordinates of the magnetic field vector and the electron density, owing to the sensitivity of the hydrogen beta line to the non-negligible effect of depolarizing collisions with electrons and protons of the medium. A mean value of 1.3 x 10 to the 10th power cu. cm. is derived in 14 prominences.

Bommier, V.↗

NASA NTRS1987

Extrapolation methods for vector sequences

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Smith, David A.↗