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At least 1,261 records · Page 70

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NASA NTRS1979

On nuclear spin statistics in rotational transition intensities in tetrahedral AB4 molecules

A general expression is derived for the integrated intensity of rotational transitions in the vibronic ground state of tetrahedral molecules, taking into account the nuclear spin statistics. It is shown that the ratio of this expression to previously published spin-free integrated intensities depends only on the tensor character N of the operator driving the transition, the appropriate rotational quantum numbers J and J', and the nuclear spin of the identical nuclei. Tables are given for N = 3, 4 and J no more than 50, which enable the calculation of integrated intensities for octopole and hexadecapole collision-induced dipole-moment transitions, centrifugal-distortion-induced dipole-moment transitions, and centrifugal-distortion-induced anisotropic-polarizability-tensor Raman transitions.

Rosenberg, A.↗

NASA NTRS1979

Surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface

The diffraction of a TM sub 0 surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained via a combination of the generalized scattering matrix technique and the Wiener-Hopf procedure. Expressions for the reflection and diffraction coefficients contain integrals which can be evaluated numerically.

Pathak, P. H.↗

NASA NTRS1979

Electromagnetic multipole fields of neutron stars

A formalism is developed for treating general multipole electromagnetic fields of neutron stars. The electric multipoles induced in a neutron star by its rotation with an arbitrary magnetic multipole at its center are presented. It is shown how to express a family of off-centered multipoles having the same l weight as an infinite array of centered multipoles of increasing l weight referred to the rotational axis. General expressions are given for the linear momentum present in the superposition of arbitrary multipole fields, and the results are combined to compute the radiation rate of linear momentum by an off-centered dipole to zeroth order in the parameter Omega x R/c. The general Deutsch (1955) solution is then rederived in a clear consistent manner, and some minor additions and corrections are provided.

Roberts, W. J.↗

NASA NTRS1980

An approximation to student's t-distribution

Three equations relate Student's t-distribution to standard normal distribution with maximum error of less than 0.8 percent. First equation, used for degrees of freedom (v) greater than 2, expresses t variable in terms of standard normal variable z. For v=1 and 2, second and third equations express t exactly in terms of probability P.

Rummler, D. R.↗

NASA NTRS1979

Care 3, Phase 1, volume 1

A computer program to aid in accessing the reliability of fault tolerant avionics systems was developed. A simple mathematical expression was used to evaluate the reliability of any redundant configuration over any interval during which the failure rates and coverage parameters remained unaffected by configuration changes. Provision was made for convolving such expressions in order to evaluate the reliability of a dual mode system. A coverage model was also developed to determine the various relevant coverage coefficients as a function of the available hardware and software fault detector characteristics, and subsequent isolation and recovery delay statistics.

Stiffler, J. J.↗

NASA NTRS1980

Effect of geometry and operating conditions on spur gear system power loss

The results of an analysis of the effects of spur gear size, pitch, width, and ratio on total mesh power loss for a wide range of speeds, torques, and oil viscosities are presented. The analysis uses simple algebraic expressions to determine gear sliding, rolling, and windage losses and also incorporates an approximate ball bearing power loss expression. The analysis shows good agreement with published data. Large diameter and fine pitched gears had higher peak efficiencies but low part load efficiency. Gear efficiencies were generally greater than 98 percent except at very low torque levels. Tare (no-load) losses are generally a significant percentage of the full load loss except at low speeds.

Anderson, N. E.↗

NASA NTRS1980

Radar altimeter mean return wave forms from near-normal-incidence ocean surface scattering

For a nearly Gaussian transmitted pulse shape scattered from a nearly Gaussian distributed sea surface, a small argument series expansion of one term lead to a several term power series expression for the mean return waveform. Specific expressions are given for the first four terms. These results, which require less computer time than numerical convolution, are useful for data analysis from current or past radar altimeters and for design studies of future systems. Several representative results are presented for an idealized Seasat-1 radar altimeter.

Hayne, G. S.↗

NASA NTRS1980

Two-photon excitation cross-section in light and intermediate atoms

The method of explicit summation over the intermediate states is used along with LS coupling to derive an expression for two-photon absorption cross section in light and intermediate atoms in terms of integrals over radial wave functions. Two selection rules, one exact and one approximate, are also derived. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum defect method are used. A relationship between the cross section and the oscillator strengths is derived. Cross sections due to selected transitions in nitrogen, oxygen, and chlorine are given. The expression for the cross section is useful in calculating the two-photon absorption in light and intermediate atoms.

Omidvar, K.↗

NASA NTRS1980

Second moments of optical degradation due to a thin turbulent layer

The effect of thin turbulent layers, including boundary layers and shear layers, on light propagation is examined from a theoretical point of view. In particular, a mathematical model is developed to describe the interaction between the aerodynamic or, more precisely, the density fluctuations and the electromagnetic field. It is assumed that the turbulence induces a normally distributed phase aberration which is a homogeneous random function in the plane of the aperture. Hypotheses concerning the density fluctuations in the layer sufficient to guarantee such a phase aberration are exhibited. The optical degradation is described in terms of the optical transfer function (OTF) and the Strehl ratio (I/I O ) which are random. Expressions for the first and second moments of these two parameters are developed from the definitions. Asymptotic ("large" aperture) approximations to these expressions are derived and discussed. Finally, the exact and approximate results are compared for several "typical" values of the ratios of aperture diameter to scale of density fluctuations and rms phase aberration to wave length respectively.

W J Steinmetz↗

NASA NTRS1980

Effects of various assumptions on the calculated liquid fraction in isentropic saturated equilibrium expansions

The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.

Bursik, J. W.↗

NASA NTRS1980

A microprocessor based high speed packet switch for satellite communications

The architectures of a single processor, a three processor, and a multiple processor system are described. The hardware circuits, and software routines required for implementing the three and multiple processor designs are presented. A bit-slice microprocessor was designed and microprogrammed. Maximum throughput was calculated for all three designs. Queue theoretic models for these three designs were developed and utilized to obtain analytical expressions for the average waiting times, overall average response times and average queue sizes. From these expressions, graphs were obtained showing the effect on the system performance of a number of design parameters.

Arozullah, M.↗

NASA NTRS1980

Dynamic analysis of noncontacting face seals

The dynamic behavior of a noncontacting coned face seal is analyzed taking into account various design parameters and operating conditions. The primary seal ring motion is expressed by a set of nonlinear equations for three degrees of freedom. These equations, which are solved numerically, allow identification of two dimensionless groups of parameters that affect the seal dynamic behavior. Stability maps for various seals are presented. These maps contain a stable-to-unstable transition region in which the ring wobbles at half the shaft frequency. The effect of various parameters on seal stability is discussed and an empirical expression for critical stability is offered.

Etsion, I.↗

NASA NTRS1980

Evaluation of instability forces of labyrinth seals in turbines or compressors

The effects of a force induced by the labyrinth seal on the stability of rotor systems and the factors of the seal which affect the stability are investigated. In the analysis, it is assumed that the fluid in the seal is steady and that the rotor is set vertically in order to avoid the effects of gravity force. The force induced by the seal is expressed in terms proportional to the velocity and displacement of the rotor and is deduced to that expression for the oil film force in journal bearings. That force is taken into account in the equations of motion; then the stability of the system is discussed by energy concept. The force induced by the labyrinth seal always makes the rotor system unstable, and the tendency is marked when seal leakages are small. The resonance point of the rotor system is also affected by the labyrinth seal (the resonance point of the rotor system is removed by the seal leakages). The force induced by the labyrinth seal was measured by using a water-tunnel experimental system which was designed to measure the labyrinth seal force by using the similarity between gas and liquid flow theory.

Iwatsubo, T.↗

NASA NTRS1980

DIAL with heterodyne detection including speckle noise: Aircraft/shuttle measurements of O3, H2O, and NH3 with pulsed tunable CO2 lasers

Atmospheric trace constituent measurements with higher vertical resolution than attainable with passive radiometers are discussed. Infrared differential absorption lidar (DIAL), which depends on Mie scattering from aerosols, has special advantages for tropospheric and lower stratospheric applications and has great potential importance for measurements from shuttle and aircraft. Differential absorption lidar data reduction involves comparing large amplitude signals which have small differences. The accuracy of the trace constituent concentration inferred from DIAL measurements depends strongly on the errors in determining the amplitude of the signals. Thus, the commonly used SNR expression (signal divided by noise in the absence of signal) is not adequate to describe DIAL measurement accuracy and must be replaced by an expression which includes the random coherent (speckle) noise within the signal. A comprehensive DIAL computer algorithm is modified to include heterodyne detection and speckle noise. Examples for monitoring vertical distributions of O3, H2O, and NH3 using a ground-, aircraft-, or shuttle-based pulsed tunable CO2 laser DIAL system are given.

Brockman, P.↗

NASA NTRS1980

A study of the processes in the RF hydrogen gas dissociator

The role of the RF gas dissociator in the hydrogen maser is examined. Based on collisional and plasma transport processes, the performance of the source is investigated. It is found that while the complexity of the collisional processes in the RF dissociator prohibits an easily obtained quantitative expression for the performance of the source, it is nevertheless possible to make general inferences concerning the qualitative performance based on collisional effects. An analytical expression for the efficiency of the source in atom production is obtained based on plasma transport processes. On the basis of this study some recommendations are made for the development of more efficient RF hydrogen gas dissociators for use in masers.

Maleki, L.↗

NASA NTRS1979

A form-factor method for determining the structure of distorted stars

The equilibrium equations of a uniformly rotating and tidally distorted star are reduced to the same form as for a spherical star except for the inclusion of two form factors. One factor, expressing the buoyancy effects of centrifugal force, is determined directly from the integrated structure variables. The other factor, expressing the deviation from spherical shape, is shown to be relatively insensitive to errors in the assumed shape, so that accurate solutions are obtained in spite of the use of an a priori shape. The method is employed by adding computations for the factors to an existing spherical model program. Upper Main Sequence models determined by this method compare closely with results from the double approximation method even for critical rotation and tidal distortion.

Wolfe, R. H., Jr.↗

NASA NTRS1979

Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

Fymat, A. L.↗

NASA NTRS1979

Methodology for error analysis and simulation of lidar aerosol measurements

A methodology is presented for objective and automated determination of the uncertainty in lidar aerosol measurements. This methodology is based on standard error-propagation procedures, a large data base on atmospheric behavior, and long experience in lidar data processing. Algebraic expressions for probable error are derived as a function of the relevant parameters. The validity of these expressions is then tested by making simulated measurements and analyses in which random errors of appropriate size are injected at proper steps of the measurement and analysis process. An illustrative example is given where the methodology is applied to a new lidar system now being used for airborne measurements of the stratospheric aerosol.

Russell, P. B.↗