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At least 1,225 records · Page 68

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NASA NTRS1977

The angular dependence of partially redistributed resonance radiation

Explicit expressions for the angular distribution and frequency dependence of radiation scattered by a spatially degenerate atom undergoing collisions are derived using a previously developed formalism of the quantum theory of line broadening for an atom in its rest frame. Results valid in the impact regime for resonant scattering are presented for the cases of linear incident and scattered polarization circular incident and linear scattered polarization, and unpolarized incident radiation with no monitoring of the scattered polarization. These results relate to scattering involving a j - j + or - 1 - j atomic transition, with lower-state interactions neglected; the expressions obtained take a relatively simple form involving atomic multipolar relaxation rates of the order of k = 0 and k = 2. The angular distributions for each case are combined with the frequency dependences to yield a three-component frequency redistribution function for an s-p-s transition, the components being a coherent term, a frequency-redistributed term with the same angular dependence as the coherent term, and an isotropic frequency-redistributed term.

Ballagh, R. J.↗

NASA NTRS1977

Galatry profile convolved with the Fabry-Perot instrument function

The physical conditions in laboratory gases and in the upper atmosphere of the planets, including earth, can be deduced from a measurement of the intensity and line profile of different radiating molecules. Because of the low pressures in the upper atmospheres, many molecular lines with small pressure-broadening coefficients are collisionally narrowed. These lines are resolvable with a Fabry-Perot interferometer. Analytical expressions are given relating the measured line intensity and profile to the true line intensity and profile. A deconvolution of the measured profile gives the parameters A, beta, and K characterizing the collisionally narrowed Galatry profile. General expressions for the nonideal interferometer are discussed, and, specifically, mirror defects and a limited detector aperture are treated.

Goorvitch, D.↗

NASA NTRS1977

The effects of bandpass limiters on n-phase tracking systems

The combination of a bandpass limiter and an n-th power tracking loop is considered. Performance of the combination does not depend on the form of the nonlinear function used to create the n-th harmonic signal as long as some energy in that zone is produced. The order in which the limiter and n-th power nonlinearity occur is unimportant so that the results apply equally well to the n-phase Costas type of implementations of the n-th power loops. Closed form expressions for the signal suppression factors are obtained. Coherent and noncoherent SNR's out of the n-th power-limiter combination can be expressed in terms of two of these suppression factors. The loop SNR of an n-th power-limited phase locked loop is estimated by simply calculating the suppression factors for n-th and 2n-th power loops. Finally, n-th power phase locked loops without limiters are compared with similar loops with limiters; the limiter can actually enhance output SNR at moderate to large input SNR.

Butman, S. A.↗

NASA NTRS1977

Large-scale inhomogeneity of the Universe - Spherically symmetric models

Dust-filled Tolman-Bondi (1934, 1947) spherically symmetric cosmological models are studied with application to superclustering of galaxies. Asymptotic expressions are given for the density and curvature contrast, valid near the singularity and at long times. The density profile of infalling material is expressed in terms of a single arbitrary function (the distribution of total energy per unit mass). Measurement of the distribution of excess galaxy counts and deviations from the Hubble flow in the vicinity of a supercluster could provide a determination of the cosmological deceleration parameter.

Silk, J.↗

NASA NTRS1977

Photometry of the Gallilean satellites

The dependence of the magnitudes and colors on both solar and orbital phase angles is derived from photometric observations of the Gallilean satellites. The rotational variations are best defined by the most recent observations; as a consequence of the complex albedo distributions on the satellites, the light curves cannot be represented by simple analytic expressions. The recent data also establish the mean magnitudes on the V photometric system to within + or - 0.02 magnitude and permit accurate geometric albedos to be derived. The dependence of magnitude on solar phase angle, and particularly at very small phase angles, is best shown by the extensive observations from 1926 and 1927. The determined rotational curves are used to reduce these data and express the phase effect in terms of a linear curve for phase angles greater than 6 deg and a quadratic curve for smaller angles. The phase dependence of these satellites is compared with that observed for other small bodies in the solar system; particularly interesting are the anomalously large phase coefficient and opposition effect of Io.

Morrison, D.↗

NASA NTRS1977

Determination of longitudinal aerodynamic derivatives from steady-state measurement of an aircraft

A method for the estimation of aerodynamic derivatives from steady-state symmetric flight data is developed. The derivatives considered are the longitudinal static stability and control derivatives, damping derivatives due to tail, and the derivatives expressing the speed effect on the lift and pitching moment coefficients. The method is an extension of the well known theory of longitudinal static stability and control, and corresponding flight data interpretation. Measured data is assumed in the form of trim curves and lift vs angle of attack. The expressions for the derivative estimates are in the form of algebraic relationships containing known constants, and directly or indirectly measured quantities.

Klein, V.↗

NASA NTRS1977

Modal characteristics of crossed rectangular waveguides

An integral-eigenvalue problem is formulated for a crossed rectangular waveguide and solved numerically by applying the Ritz-Galerkin method. Theoretical formulas for determining cutoff frequencies and modal-field expressions are obtained for the specific case of a symmetrical rectangular waveguide, cutoff frequencies are calculated numerically, and the results are verified by comparison with available experimental data. The modal fields are expressed in terms of Fourier series for both TE and TM modes. It is found that the bandwidth can be increased to a maximum of 38% when the waveguide dimensions are properly selected and that the numerical results are in agreement with those computed by the method of partial regions. Some practical applications of the modal-field equations are briefly noted.

Lin, F.-L. C.↗

NASA NTRS1977

Statistical principles of inversion theory

Statistical methods are used to deal with the inverse problem of radiative transfer. All the available information about an unknown profile can be expressed in the form of values of functions of that profile and error estimates of these values. Estimation theory shows how these values are combined to give an estimate of the unknown profile and its error covariance. Many inversion methods are expressed in this form, although the error estimate is not usually carried out. Practical applications are described, both for inversion of individual profiles, and the global analysis of satellite data.

Rodgers, C. D.↗

NASA NTRS1978

Propagation of sound waves through a linear shear layer: A closed form solution

Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis was exact for all frequencies and was developed assuming a linear velocity profile in the shear layer. This assumption allowed the solution to be expressed in terms of parabolic cyclinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number gave expressions which correspond to solutions previously obtained for these limiting cases.

Scott, J. N.↗

NASA NTRS1978

An approach to the determination of aircraft handling qualities using pilot transfer functions

It was shown that a correlation exists between pilot-aircraft system closed-loop characteristics, determined by using analytical expressions for pilot response along with the analytical expression for the aircraft response, and pilot ratings obtained in many previous flight and simulation studies. Two different levels of preferred pilot response were used. These levels were: (1) a static gain and a second-order lag function with a lag time constant of 0.2 second; and (2) a static gain, a lead time constant of 1 second, and a 0.2-second lag time constant. If a system response with a pitch-angle time constant of 2.6 seconds and a stable oscillatory mode of motion with a period of 2.5 seconds could be achieved with the first-level pilot model, it was shown that the pilot rating will be satisfactory for that vehicle.

Adams, J. J.↗

NASA NTRS1976

Analytical modeling of under-the-wing externally blown flap powered-lift noise

The sound field produced by the interaction of a subsonic jet with a large-scale model of the under the wing externally blown flap in an approach attitude was analyzed. The analysis was performed to obtain a better understanding of the dominant noise sources and the mechanisms governing the peak sound pressure level frequencies of the broadband spectra. An analytical expression is derived which incorporates two available theories and experimental data; the expression predicts the sound field along a circular arc of approximately 120 deg measured from the upstream jet axis in the fly-over plane. The analysis compares favorably with test results obtained from two large-scale models, one using cold air from a conical nozzle and the other using hot gas from a TF-34 turbofan engine having a conical exhaust nozzle with a 12 lobe internal forced mixer. The frequency at which the peak sound pressure level occurs appears to be governed by a phenomenon which produces periodic formation and shedding of large-scale turbulence structures from the nozzle lip.

Mckinzie, D. J., Jr.↗

NASA NTRS1978

Stress intensity factors of composite orthotropic plates containing periodic buffer strips

The fracture problem of laminated plates which consist of bonded orthotropic layers is studied. The fields equations for an elastic orthotropic body are transformed to give the displacement and stress expressions for each layer or strip. The unknown functions in these expressions are found by satisfying the remaining boundary and continuity conditions. A system of singular integral equations is obtained from the mixed boundary conditions. The singular behavior around the crack tip and at the bimaterial interface is studied. The stress intensity factors are computed for various material combinations and various crack geometries. The results are discussed and are compared with those for isotropic materials.

Delale, F.↗

NASA NTRS1978

Determination of some dominant parameters of the global dynamic sea surface topography from GEOS-3 altimetry

The 1977 altimetry data bank is analyzed for the geometrical shape of the sea surface expressed as surface spherical harmonics after referral to the higher reference model defined by GEM 9. The resulting determination is expressed as quasi-stationary dynamic SST. Solutions are obtained from different sets of long arcs in the GEOS-3 altimeter data bank as well as from sub-sets related to the September 1975 and March 1976 equinoxes assembled with a view to minimizing seasonal effects. The results are compared with equivalent parameters obtained from the hydrostatic analysis of sporadic temperature, pressure and salinity measurements of the oceans and the known major steady state current systems with comparable wavelengths. The most clearly defined parameter (the zonal harmonic of degree 2) is obtained with an uncertainty of + or - 6 cm. The preferred numerical value is smaller than the oceanographic value due to the effect of the correction for the permanent earth tide. Similar precision is achieved for the zonal harmonic of degree 3. The precision obtained for the fourth degree zonal harmonic reflects more closely the accuracy expected from the level of noise in the orbital solutions.

Mather, R. S.↗

NASA NTRS1973

An approximate solution for the free vibrations of rotating uniform cantilever beams

Approximate solutions are obtained for the uncoupled frequencies and modes of rotating uniform cantilever beams. The frequency approximations for flab bending, lead-lag bending, and torsion are simple expressions having errors of less than a few percent over the entire frequency range. These expressions provide a simple way of determining the relations between mass and stiffness parameters and the resultant frequencies and mode shapes of rotating uniform beams.

Peters, D. A.↗

NASA NTRS1977

On the radiative damping of atmospheric waves

General expressions for computing time constants for radiative decay of harmonic temperature perturbations in planetary atmospheres are developed. Four spatial scales are shown to be generally important: the scale height of the atmospheric absorber, the absorption mean free path for thermal radiation, the altitude above the planetary surface, and the wavelength of the temperature perturbation. Atmospheric inhomogeneity is particularly important when the radiation mean free path and the vertical wavelength divided by 2 pi both exceed the absorber scale height. The surface is very important for wave decay at altitudes less than a few radiation mean free paths, and its effect depends on a comparison of the surface response time and the lifetime of the atmospheric perturbation. The surface response time depends on the conducting and emitting properties of the surface material and on the strength of turbulence in the planetary boundary layer. The additional influence of chemical reactions and phase changes on radiative damping is discussed, and several assumptions inherent in the development of the general expressions for time constants are evaluated. Terrestrial examples are used for purposes of illustration, but the development is kept sufficiently general so that the results remain applicable to most situations on other planets.

Prinn, R. G.↗

NASA NTRS1977

Perturbations of a close-earth satellite due to sunlight diffusely reflected from the earth. I - Uniform albedo

A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-earth satellite due to sunlight reflected from the earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomaly. The perturbations within a given revolution can be obtained analytically by integrating with respect to v while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution.

Lautman, D. A.↗

NASA NTRS1977

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗

NASA NTRS1978

Propagation of sound waves through a linear shear layer - A closed form solution

Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis is exact for all frequencies and is developed assuming a linear velocity profile in the shear layer. This assumption allows the solution to be expressed in terms of parabolic cylinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number give expressions which correspond to solutions previously obtained for these limiting cases.

Scott, J. N.↗