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At least 145 records · Page 8

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NASA NTRS1983

A mathematical characterization of vegetation effect on microwave remote sensing from the Earth

In passive microwave remote sensing of the earth, a theoretical model that utilizes the radiative transfer equations was developed to account for the volume scattering effects of the vegetation canopy. Vegetation canopies such as alfalfa, sorghum, and corn are simulated by a layer of ellipsoidal scatterers and cylindrical structures. The ellipsoidal scatterers represent the leaves of vegetation and are randomly positioned and oriented. The orientation of ellipsoids is characterized by a probability density function of Eulerian angles of rotation. The cylindrical structures represent the stalks of vegetation and their radii are assumed to be much smaller than their lengths. The underlying soil is represented by a half-space medium with a homogeneous permittivity and uniform temperature profile. The radiative transfer quations are solved by a numerical method using a Gaussian quadrature formula to compute both the vertical and horizontal polarized brightness temperature as a function of observation angle. The theory was applied to the interpretation of experimental data obtained from sorghum covered fields near College Station, Texas.

Choe, Y.↗

NASA NTRS1987

Transonic analysis and design of axisymmetric bodies in nonuniform flow

An inviscid nonuniform axisymmetric transonic code was developed for applications in analysis and design. Propfan slipstream effect on pressure distribution for a body with and without sting was investigated. Results show that nonuniformity causes pressure coefficient to be more negative and shock strength to be stronger and more rearward. Sting attached to a body reduced the pressure peak and moves the rear shock forward. Extent and Mach profile shapes of the nonuniformity region appeared to have little effect on the pressure distribution. Increasing nonuniformity magnitude made pressure coefficient more negative and moved the shock rearward. Design study was conducted with the CONMIN optimizer for an ellipsoid and a body with the NACA-0012 counter. For the ellipsoid, the general trend showed that to reduce the pressure drag, the front portion of the body should be thinner and the contour of the rear portion should be flatter than the ellipsoid. For the design of a body with a sharp trailing edge in transonic flow with an initial shape given by the NACA-0012 contour, the pressure drag was reduced by decreasing the nose radius and increasing the thickness in the aft portion. Drag reduction percentages are given.

Chang, Jen-Fu↗

NASA NTRS1988

Numerical investigation of three-dimensional flow separation using the boundary layer equations

The steady, incompressible, three-dimensional laminar and turbulent boundary-layer equations are solved in a streamline coordinate system and in a self-adaptive grid system using Matsuno's finite difference method. Techniques are described for calculating laminar and turbulent separation using the boundary-layer equations. Any type (bubble type or free vortex-layer type) of major separation line can be calculated at an angle of attack on ellipsoids of revolution by this boundary layer code. Results are presented for ellipsoids of revolution at angles of attack up to 45 degrees. Agreements with other numerical and experimental results are very good for laminar flows. Turbulent flows are also investigated with algebraic turbulence models proposed by Rotta and Cebeci and Smith. Good agreement with experimental results was obtained at a small angle of attack (10 degrees) but only qualitative agreement was obtained at a high angle of attack (30 degrees) for turbulent flow on a 6:1 ellipsoid of revolution.

Wie, Yong-Sun↗

NASA NTRS1989

The shapes of small satellites

Limb coordinates from spacecraft images have been used to measure the shapes of the small satellites of Mars, Jupiter, Saturn, and Uranus, with a view to the quantitative testing of those shapes' physical significance. A comparison of eight small satellites' ellipsoidal models with equilibrium ellipsoids indicates that the shapes of even moderately irregular satellites are poor predictors of mean densities; icy satellites smaller than about 150 km in mean radius are irregularly shaped, and exhibit no trend in roughness. Larger icy satellites are ellipsoidal, and rocky satellites with mean radius in the 6-110 km range are also irregularly shaped.

Thomas, Peter C.↗

NASA NTRS1989

On the manipulability of dual cooperative robots

The definition of manipulability ellipsoids for dual robot systems is given. A suitable kineto-static formulation for dual cooperative robots is adopted which allows for a global task space description of external and internal forces, and relative velocities. The well known concepts of force and velocity manipulability ellipsoids for a single robot are formally extended and the contributions of the two single robots to the cooperative system ellipsoids are illustrated. Duality properties are discussed. A practical case study is developed.

Chiacchio, P.↗

NASA NTRS1991

Metal thin-film optical polarizers for space applications, phase 2

A light polarizing material was developed for wavelengths in the visible and near infrared spectral band (400 to 3,000 nm). The material is comprised of ellipsoidal silver particles uniformly distributed and aligned on the surface of an optical material. A method is set forth for making polarizing material by evaporatively coating a smooth glass surface with ellipsoidal silver particles. The wavelength of peak absorption is chosen by selecting the aspect ratio of the ellipsoidal metal particles and the refractive index of the material surrounding the metal particles. The wavelength of peak absorption can be selected to fall at a desired wavelength in the range from 400 to 3,000 nm by control of the deposition process. This method is demonstrated by evaporative deposition of silver particles directly on to a smooth optical surface. By applying a multilayer silver coating of a glass disc, a contrast of greater than 40,000 was achieved at 590 nm. A polarizing filter was designed, fabricated, and assembled which achieved contrast of 100,00 at 59 nm and can serve as a replacement for crystal polarizers.

Slocum, Robert E.↗

NASA NTRS1994

Signatures of bulge triaxiality from kinematics in Baade's window

We study a sample of 62 Baade's Window, (l,b) = (1, -4)deg, K giants that have published proper motions, radial velocity, and metallicity. Using R(sub 0) = 8 kpc, we construct the velocity ellipsoids, namely the 3x3 velocity dispersion tensors, for the metal rich stars ((Fe/H) greater than or equal to 0) and metal poor stars ((Fe/H) less than or equal to -0.2). After diagonalizing the tensor, we find a vertex deviation characteristic of a nonaxisymmetric system. Eigenvalues for the two velocity ellipsoids (sigma(sub 1), sigma(sub 2), sigma(sub 3)) are (126, 89, 65) +/- 13 km/s for the metal rich sample and (154, 77, 83) +/- 25 km/s for the metal poor sample with their long axes pointing to two nearly perpendicular directions (l(sub v), b(sub v)) = (-65 +/- 9 deg, +14 +/- 9 deg) and (l(sub v), b(sub v)) = (25 +/- 14 deg, -11 +/- 14 deg), respectively. The vertex deviations of the velocity ellipsoids cannot be consistently explained by any oblate model. We are able to reject the hypothesis that the metal poor and metal rich populations are drawn from the same distribution at better than the 97% confidence level. We populate orbits in a realistic bar potential with a Gaussian velocity distribution, allowing us to simulate and interpret observations. We conclude that the data are consistent with a triaxial bulge pointing towards (l,b) with l less than 0 deg and b = 0 deg as suggested by earlier work on gas dynamics and the observed light distribution. We also predict that low latitude (absolute value of b less than or equal to 4 deg) bulge fields should show the vertex deviation more strongly and would therefore be the best locations for future proper motion studies. In the classification scheme of Athanassoula et al. (1983) the metal rich stars appear to occupy the B-family orbits which rotate in the prograde sense in the rest frame and have boxy shapes that are aligned with and supporting the bar. The metal poor stars in the sample lag behind the metal rich bulge and appear to occupy R-family orbits which rotate in the retrograde sense in the rest frame. They have nearly round loop shapes and are aligned perpendicularly to the bar, hence limit the triaxiality of the bar potential. The correlations between the metallicity and the orbit families can develop if the bulge forms dissipatively on a sufficiently long time scale. However, it is difficult to explain such correlations if most stars in the inner Galaxy form during the violent relaxation phase.

Zhao, Hongsheng↗

NASA NTRS1999

Method of Conjugate Radii for Solving Linear and Nonlinear Systems

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

Nachtsheim, Philip R.↗

NASA NTRS2004

Discovering Planetary Nebula Geometries: Explorations with a Hierarchy of Models

Astronomical objects known as planetary nebulae (PNe) consist of a shell of gas expelled by an aging medium-sized star as it makes its transition from a red giant to a white dwarf. In many cases this gas shell can be approximately described as a prolate ellipsoid. Knowledge of the physics of ionization processes in this gaseous shell enables us to construct a model in three dimensions (3D) called the Ionization-Bounded Prolate Ellipsoidal Shell model (IBPES model). Using this model we can generate synthetic nebular images, which can be used in conjunction with Hubble Space Telescope (HST) images of actual PNe to perform Bayesian model estimation. Since the IBPES model is characterized by thirteen parameters, model estimation requires the search of a 13-dimensional parameter space. The 'curse of dimensionality,' compounded by a computationally intense forward problem, makes forward searches extremely time-consuming and frequently causes them to become trapped in local solutions. We find that both the speed and of the search can be improved by judiciously reducing the dimensionality of the search space. Our basic approach employs a hierarchy of models of increasing complexity that converges to the IBPES model. Earlier studies establish that a hierarchical sequence converges more quickly, and to a better solution, than a search relying only on the most complex model. Here we report results for a hierarchy of five models. The first three models treat the nebula as a 2D image, while the last two models explore its characteristics as a 3D object and enable us to characterize the physics of the nebula. This five-model hierarchy is applied to HST images of ellipsoidal PNe to estimate their geometric properties and gas density profiles.

Huyser, Karen A.↗

NASA NTRS2009

Diamond Machining of an Off-Axis Biconic Aspherical Mirror

Two diamond-machining methods have been developed as part of an effort to design and fabricate an off-axis, biconic ellipsoidal, concave aluminum mirror for an infrared spectrometer at the Kitt Peak National Observatory. Beyond this initial application, the methods can be expected to enable satisfaction of requirements for future instrument mirrors having increasingly complex (including asymmetrical), precise shapes that, heretofore, could not readily be fabricated by diamond machining or, in some cases, could not be fabricated at all. In the initial application, the mirror is prescribed, in terms of Cartesian coordinates x and y, by aperture dimensions of 94 by 76 mm, placements of -2 mm off axis in x and 227 mm off axis in y, an x radius of curvature of 377 mm, a y radius of curvature of 407 mm, an x conic constant of 0.078, and a y conic constant of 0.127. The aspect ratio of the mirror blank is about 6. One common, "diamond machining" process uses single-point diamond turning (SPDT). However, it is impossible to generate the required off-axis, biconic ellipsoidal shape by conventional SPDT because (1) rotational symmetry is an essential element of conventional SPDT and (2) the present off-axis biconic mirror shape lacks rotational symmetry. Following conventional practice, it would be necessary to make this mirror from a glass blank by computer-controlled polishing, which costs more than diamond machining and yields a mirror that is more difficult to mount to a metal bench. One of the two present diamond machining methods involves the use of an SPDT machine equipped with a fast tool servo (FTS). The SPDT machine is programmed to follow the rotationally symmetric asphere that best fits the desired off-axis, biconic ellipsoidal surface. The FTS is actuated in synchronism with the rotation of the SPDT machine to generate the difference between the desired surface and the best-fit rotationally symmetric asphere. In order to minimize the required stroke of the FTS, the blanks were positioned at a large off-axis distance and angle, and the axis of the FTS was not parallel to the axis of the spindle of the SPDT machine. The spindle was rotated at a speed of 120 rpm, and the maximum FTS speed was 8.2 mm/s.

Ohl, Raymond G.↗

NASA NTRS2015

The Dependence of Cirrus Gamma Size Distributions Expressed as Volumes in N(sub 0)-Lambda-Mu Phase Space and Bulk Cloud Properties on Environmental Conditions: Results from the Small Ice Particles in Cirrus Experiment (SPARTICUS)

The variability of cirrus ice microphysical properties is investigated using observations obtained during the Small Particles in Cirrus (SPARTICUS) campaign. An existing approach that represents a size distribution (SD) as a single gamma function using an ellipsoid of equally realizable solutions in (N(sub 0), lambda, mu) phase space is modified to automatically identify multiple modes in SDs and characterize each mode by such an ellipsoid. The modified approach is applied to ice crystals with maximum dimension D greater than15 micrometers collected by the 2-D stereo and 2-D precipitation probes on the Stratton Park Engineering Company Learjet. The dependencies of N(sub 0), mu, and lambda from each mode, total number concentration, bulk extinction, ice water content (IWC), and mass median maximum dimension D(sub mm) as a function of temperature T and cirrus type are then analyzed. The changes in the observed codependencies between N(sub 0), mu, and lambda, bulk extinction, IWC, and D(sub mm) with environmental conditions indicate that particles were larger at higher T during SPARTICUS. At most two modes were observed in any SD during SPARTICUS, with the average boundary between them at 115 micrometers, similar to past studies not using probes with shatter mitigating tips and artifact removal algorithms. The bimodality of the SDs increased with T. This and the differences in N(sub 0), mu, and lambda between the modes suggest that particles with smaller D nucleated more recently than particles with larger D, which grew via vapor deposition and aggregation. Because smaller crystals, whose concentrations are uncertain, make marginal contributions to higher order moments, the use of higher moments for evaluating model fields is suggested.

Ellipsoids↗

NASA NTRS1964

Fresnel cup reflector directs maximum energy from light source

To minimize shielding and overheating, a composite Fresnel cup reflector design directs the maximum energy from a light source. It consists of a uniformly ellipsoidal end surface and an extension comprising a series of confocal ellipsoidal and concentric spherical surfaces.

Laue, E. G.↗

NASA NTRS1971

Evaluation of two statistical models using the shock structure problem.

The accuracy of two statistical models for the collision integral of the Boltzmann equation has been evaluated by applying the models to the solution of the problem of shock structure in a monatomic gas and then comparing the theoretical results with available ex perimental data. The two models considered here are the Bhatnagar-Gross-Krook and ellipsoidal statistical models. The Mach number range covered is 1.59-10.7 and profiles for density and, where available, temperature are compared. The method of numerical solution is the discrete ordinate technique which looks quite promising for application to more complicated models. The results indicate that the ellipsoidal statistical model, which gives a correct value for the Prandtl number, gives accurate results for a low Mach number shock. However, the accuracy degenerates as the Mach number increases. The Bhatnagar-Gross-Krook model gives poorer agreement with experimental data in all cases examined.

Giddens, D. P.↗

NASA NTRS1973

Approximations to the mean surface of Mars and Mars atmosphere using Mariner 9 occultations

When the Mariner 9 spacecraft passed behind Mars in its orbiting phase, the radio beam was cut off by some physical feature. These occultations occurred during the months of November and December 1971 and again in April and May 1972. The fairly good global spread of these data was used to estimate the shape of the Martian globe, as definable by mathematical shapes (ellipsoidal and spherical harmonic). The refraction profiles allowed the estimation of pressure near the occultation point; these, corrected back to an arbitrary fixed value of pressure, chosen to be 6.1 mb, were used as radii to an isobaric surface. Preliminary results showed a figure displacement from the mass center with a best fit southeast by 2.85 km. There was also an equatorial displacement in the direction of about 100 deg W. Atmospheric approximations for the mass center to 6.1-mb pressure distances were fit to an ellipsoid.

Cain, D. L.↗

NASA NTRS1973

The figure of Mars and its effect on radar-ranging.

Formulae are given which indicate the errors made in computing the radar-range to a planet when one assumes the planet to have a spherical surface, centered at the center of mass. These formulae are evaluated for Mars, using an ellipsoidal fit of the martian surface obtained from the occultation measurements of the Mariner 9 spacecraft. The secularlike part of the errors amounts to about 4 km in range over the past 3 oppositions, due mainly to the flattening of 0.006 and to a 3 km southerly displacement of the center of figure from the center of mass. The method of solution is given in the appendix along with a method for applying the ellipsoidal model to the reduction of radar-range data.

Standish, E. M., Jr.↗

NASA NTRS1974

Spectral and textural processing of ERTS imagery

A procedure is developed to simultaneously extract textural features from all bands of ERTS multispectral scanner imagery for automatic analysis. Multi-images lead to excessively large grey tone N-tuple co-occurrence matrices; therefore, neighboring grey N-tuple differences are measured and an ellipsoidally symmetric functional form is assumed for the co-occurrence distribution of multiimage greytone N-tuple differences. On the basis of past data the ellipsoidally symmetric approximation is shown to be reasonable. Initial evaluation of the procedure is encouraging.

Haralick, R. M.↗

NASA NTRS1975

Dish antenna having switchable beamwidth

A switchable beamwidth antenna includes a concave parabolic main reflecting dish which has a central circular region and a surrounding coaxial annular region. A feed means selectively excites only the central region of the main dish via a truncated subreflector for wide beamwidth or substantially the entire main dish for narrow beamwidth. In one embodiment, the feed means comprises a truncated concave ellipsoid subreflector and separate feed terminations located at two foci of the ellipsoid. One feed termination directly views all of the main dish while the other feed termination, exciting the main dish via the subreflector, excites only the central region because of the subreflector truncation. In the another embodiment, the feed means comprises one feed termination and a convex hyperboloid subreflector via which the feed excites the main dish.

Schmidt, R. F.↗

NASA NTRS1976

Astrogeodetic geoid of Japan

Three kinds of astrogeodetic geoid maps for Japan are presented: one referred to the global (18, 18) geoid of the 1973 Smithsonian Standard Earth (III) (SE III), referred to the best-fitting ellipsoid of SE III, and one referred to the reference ellipsoid of the Tokyo datum. Interpolations of the deflection of the vertical are carried out by a least squares estimation method. The geoid height differences obtained are compared with solutions of satellite-derived station positions. Good agreement is found in a comparison with Doppler tracking stations.

Ganeko, Y.↗