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NASA NTRS1988

Acoustic propagation in a thermally stratified atmosphere

Acoustic propagation in an atmosphere with a specific form of a temperature profile has been investigated by analytical means. The temperature profile used is representative of an actual atmospheric profile and contains three free parameters. Both lapse and inversion cases have been considered. Although ray solutions have been considered, the primary emphasis has been on solutions of the acoustic wave equation with point source where the sound speed varies with height above the ground corresponding to the assumed temperature profile. The method used to obtain the solution of the wave equation is based on Hankel transformation of the wave equation, approximate solution of the transformed equation for wavelength small compared to the scale of the temperature (or sound speed) profile, and approximate or numerical inversion of the Hankel transformed solution. The solution displays the characteristics found in experimental data but extensive comparison between the models and experimental data has not been carried out.

Vanmoorhem, W. K.↗
NASA NTRS1988

Theoretical comparison of maser materials for a 32-GHz maser amplifier

The computational results of a comparison of maser materials for a 32 GHz maser amplifier are presented. The search for a better maser material is prompted by the relatively large amount of pump power required to sustain a population inversion in ruby at frequencies on the order of 30 GHz and above. The general requirements of a maser material and the specific problems with ruby are outlined. The spin Hamiltonian is used to calculate energy levels and transition probabilities for ruby and twelve other materials. A table is compiled of several attractive operating points for each of the materials analyzed. All the materials analyzed possess operating points that could be superior to ruby. To complete the evaluation of the materials, measurements of inversion ratio and pump power requirements must be made in the future.

Lyons, James R.↗
NASA NTRS1989

Analysis of modified SMI method for adaptive array weight control

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

Dilsavor, R. L.↗
NASA NTRS1989

A cloud model simulation of space shuttle exhaust clouds in different atmospheric conditions

A three-dimensional cloud model was used to characterize the dominant influence of the environment on the Space Shuttle exhaust cloud. The model was modified to accept the actual heat and moisture from rocket exhausts and deluge water as initial conditions. An upper-air sounding determined the ambient atmosphere in which the cloud could grow. The model was validated by comparing simulated clouds with observed clouds from four actual Shuttle launches. The model successfully produced clouds with dimensions, rise, decay, liquid water contents and vertical motion fields very similar to observed clouds whose dimensions were calculated from 16 mm film frames. Once validated, the model was used in a number of different atmospheric conditions ranging from very unstable to very stable. In moist, unstable atmospheres simulated clouds rose to about 3.5 km in the first 4 to 8 minutes then decayed. Liquid water contents ranged from 0.3 to 1.0 g kg-1 mixing ratios and vertical motions were from 2 to 10 ms-1. An inversion served both to reduce entrainment (and erosion) at the top and to prevent continued cloud rise. Even in the most unstable atmospheres, the ground cloud did not rise beyond 4 km and in stable atmospheres with strong low level inversions the cloud could be trapped below 500 m. Wind shear strongly affected the appearance of both the ground cloud and vertical column cloud. The ambient low-level atmospheric moisture governed the amount of cloud water in model clouds. Some dry atmospheres produced little or no cloud water. One case of a simulated TITAN rocket explosion is also discussed.

Chen, C.↗
NASA NTRS1987

Spatially random models, estimation theory, and robot arm dynamics

Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.

Rodriguez, G.↗
NASA NTRS1987

Kinematically redundant robot manipulators

Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques.

Baillieul, J.↗
NASA NTRS1988

Recursive dynamics of topological trees of rigid bodies via Kalman filtering and Bryson-Frazier smoothing

The inverse and forward dynamics problems for a set of rigid bodies connected by hinges to form a topological tree are solved by using recursive techniques from linear filtering and smoothing theory. An inward filtering sequence computes a set of constraint moments and forces. This is followed by an outward sequence to determine a corresponding set of angular and linear accelerations. An inward sequence begins at the tips of all of the terminal bodies of the tree and proceeds inwardly through all of the branches until it reaches the root. Similarly, an outward sequence begins at the root and propagates to all of the tree branches until it reaches the tips of the terminal bodies. The paper also provides an approach to evaluate recursively the composite multibody system inertia matrix and its inverse.

Rodriguez, G.↗
NASA NTRS1988

Recovery of excitation intensity dependence in pulsed, focused beams - Nonsaturated case

It is shown how the dependence of a nonsaturated excitation process on local, instantaneous intensity can be obtained from temporally and spatially unresolved data by inversion, even for a nonuniform intensity distribution in the probe volume. This treatment is in contrast with the usual approach in which effects of nonuniform excitation are either disregarded or simulated. For exponential intensity profiles, the solution is obtained in the form of an Abel inversion. The ill-conditioned nature of the problem is demonstrated, and extension to the study of intensity-dependent line shapes is made.

Ruyten, Wilhelmus M.↗
NASA NTRS1988

The surface morphology of crystals melting under solutions of different densities

Examples of solids melting beneath liquids are described for cases where the bulk liquid volume is stabilized against convection by a positive vertical temperature gradient, either with, or without local density inversion at the melting interface. The examples include ice melting beneath brine or methanol solutions and tin or lead melting under molten Sn-20 wt pct Pb or Pb-20 wt pct Sn, respectively. Without density inversion the melting is slow, purely diffusion controlled and the interfaces are smooth; with convection assisted melting the rate increases by some two orders of magnitude and the interfaces develop a rough profile - in the case of ice both irregular and quasi-steady state features are observed. The observations are discussed in terms of prevailing temperature and concentration gradients.

Fang, Dacheng↗
NASA NTRS1989

A multigrid and upwind viscous flow solver on 3-D embedded and overlapped grids

A numerically efficient method is presented for solving the three-dimensional governing equations of the viscous compressible flow about complex configurations with topologically different components. The physical domain is decomposed into regions for which the grid generation is relatively simple and virtually with no significant restrictions. The Navier-Stokes equations are solved by an implicit, approximately factored, upwind, finite-volume scheme. The block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the holes created in the computational domain by the embedded and overlapped grids. The convergence is accelerated by a multigrid algorithm despite the existence of such holes. The solution for s supersonic flow past a blunt-nose-cylinder at high angle-of-attack is obtained using a C-O grid embedded in a global Cartesian grid.

Baysal, Oktay↗
NASA NTRS1988

An improved method for determining the vertical ozone distribution using satellite measurements

A procedure was developed for determining vertical ozone distributions from spectral measurements of UV radiances diffusely reflected from the terrestrial atmosphere. In this procedure, the inversion method of Aruga and Igarashi (1976) is improved by incorporating the effects of multiple scattering and the lower boundary of the atmosphere. The improved inversion algorithm was tested using data of NIMBUS-4 backscattered UV experiments. The results indicate that by using this method, the vertical distributions of atmospheric ozone can be obtained with high accuracy over a wide range of altitude.

Aruga, Tadashi↗
NASA NTRS1989

Digital restoration of multichannel images

The Wiener solution of a multichannel restoration scheme is presented. Using matrix diagonalization and block-Toeplitz to block-circulant approximation, the inversion of the multichannel, linear space-invariant imaging system becomes feasible by utilizing a fast iterative matrix inversion procedure. The restoration uses both the within-channel (spatial) and between-channel (spectral) correlation; hence, the restored result is a better estimate than that produced by independent channel restoration. Simulations are also presented.

Galatsanos, Nikolas P.↗
NASA NTRS1989

Combining electric field and aurora observations from DE 1 and 2 with ground magnetometer records to estimate ionospheric electromagnetic quantities

Global distribution of electric fields and currents in the high-latitude ionosphere was estimated using data from the ground-based network of magnetometers and from nearly simultaneous observations with DE 1 and DE 2 satellites. The electric field and current distributions at high altitudes were calculated from instantaneous ionospheric conductivity (estimated from the DE 1 auroral data), using the Kamide et al. (1981) magnetogram inversion technique; an optimum conductivity was then chosen iteratively so that the resultant electric fields would become consistent with electric field deduced from ion drifts measured along the DE-2 orbit. It is demonstrated that, when analyzing the large-scale electrodynamics of individual substorms, statistical conductivity models are not fully adequate for use with the magnetogram inversion technique.

Kamide, Y.↗
NASA NTRS1989

A physical model for predicting bidirectional reflectances over bare soil

While most previous attempts to retrieve soil surface optical property characteristics have proceeded through a fitting of empirical functions to the data, an optimization technique is presently applied to a physically-based surface reflectance model developed for the study of planetary surfaces. This inversion procedure is shown to allow the direct estimation of the single-scattering coefficient, two parameters describing the 'hot spot' phenomenon, and two parameters describing the scattering phase function. A comparison of inversion technique results with both synthetic data and actual observations shows the model to be capable of predicting the observed bidirectional reflectances as well as directional-hemispherical reflectances; it can also build the complete radiance field over the upward hemisphere.

Pinty, Bernard↗
NASA NTRS1989

Neural learning of constrained nonlinear transformations

Two issues that are fundamental to developing autonomous intelligent robots, namely, rudimentary learning capability and dexterous manipulation, are examined. A powerful neural learning formalism is introduced for addressing a large class of nonlinear mapping problems, including redundant manipulator inverse kinematics, commonly encountered during the design of real-time adaptive control mechanisms. Artificial neural networks with terminal attractor dynamics are used. The rapid network convergence resulting from the infinite local stability of these attractors allows the development of fast neural learning algorithms. Approaches to manipulator inverse kinematics are reviewed, the neurodynamics model is discussed, and the neural learning algorithm is presented.

Barhen, Jacob↗
NASA NTRS1990

Random-Field Estimation For Dynamics Of Robots

Report discusses use of random-field mathematical models as alternatives to deterministic models of classical mechanics to describe dynamics of robot arms. These alternative models used to establish relationship between methods of estimation theory and robot dynamics. Approach yields new class of algorithms performing computations typical of estimation theory to solve such fundamental problems in robotics as forward and inverse dynamics and inverse kinematics.

Rodriguez, Guillermo↗
NASA NTRS1987

Design and test of a natural laminar flow/large Reynolds number airfoil with a high design cruise lift coefficient

Research activity on an airfoil designed for a large airplane capable of very long endurance times at a low Mach number of 0.22 is examined. Airplane mission objectives and design optimization resulted in requirements for a very high design lift coefficient and a large amount of laminar flow at high Reynolds number to increase the lift/drag ratio and reduce the loiter lift coefficient. Natural laminar flow was selected instead of distributed mechanical suction for the measurement technique. A design lift coefficient of 1.5 was identified as the highest which could be achieved with a large extent of laminar flow. A single element airfoil was designed using an inverse boundary layer solution and inverse airfoil design computer codes to create an airfoil section that would achieve performance goals. The design process and results, including airfoil shape, pressure distributions, and aerodynamic characteristics are presented. A two dimensional wind tunnel model was constructed and tested in a NASA Low Turbulence Pressure Tunnel which enabled testing at full scale design Reynolds number. A comparison is made between theoretical and measured results to establish accuracy and quality of the airfoil design technique.

Kolesar, C. E.↗
NASA NTRS1989

Spin-lattice relaxation and the calculation of gain, pump power, and noise temperature in ruby

The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.

Lyons, J. R.↗