Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Ellipsoids”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

A soft X-ray map of the Perseus cluster of galaxies

A 0.5-3-keV X-ray map of the Perseus cluster of galaxies is presented. The map shows a region of strong emission centered near NGC 1275 plus a highly elongated emission region which lies along the line of bright galaxies that dominates the core of the cluster. The data are compared with various models that include point and diffuse sources. One model which adequately represents the data is the superposition of a point source at NGC 1275 and an isothermal ellipsoid resulting from the bremsstrahlung emission of cluster gas. The ellipsoid has a major core radius of 20.5 arcmin and a minor core radius of 5.5 arcmin, consistent with the values obtained from galaxy counts. All acceptable models provide evidence for a compact source (less than 3 arcmin FWHM) at NGC 1275 containing about 25% of the total emission. Since the diffuse X-ray and radio components have radically different morphologies, it is unlikely that the emissions arise from a common source, as proposed in inverse-Compton models.

Cash, W.↗
NASA NTRS1977

An 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 (3) (SE 3), one referred to the ellipsoid of the SE 3 system, 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.

Ganeko, Y.↗
NASA NTRS1978

Fission origin of the moon - Cause and timing

A new scenario is offered for the origin of the moon. It is assumed that the earth formed initially with about the maximum amount of angular momentum consistent with dynamical stability. This state is approximated by the secularly unstable Maclaurin spheroids (highly flattened hamburger-shaped bodies). It is shown that the earth cannot depart from this state at a reasonable rate as long as its viscosity is in the range of liquid rock. Since core formation supplies about 1600 kJ/kg, the earth will not leave this state until core formation is complete. When cooling produces a rise in viscosity, the earth will necessarily evolve along a path which is approximated by the Riemann ellipsoids (which have rapid internal motion). The evolution is toward a Jacobi ellipsoid, but it is intercepted by the development of a third-harmonic (pear-shaped) instability, which is catastrophic and leads to fission. The process of fission itself may be fundamentally analogous to the breaking of a wave in water. We cannot exclude the possibility that some other planets evolved similarly.

Okeefe, J. A.↗
NASA NTRS1978

Anastigmatic three-mirror telescope

A three-mirror telescope for extraterrestrial observations is described. An ellipsoidal primary mirror, a hyperbolic secondary mirror, and an ellipsoidal tertiary mirror, produce an image in a conveniently located finite plane for viewing.

Korsch, D. G.↗
NASA NTRS1979

The Inertia Coefficients of an Airship in a Frictionless Fluid

The apparent inertia of an airship hull is examined. The exact solution of the aerodynamical problem is studied for hulls of various shapes with special attention given to the case of an ellipsoidal hull. So that the results for the ellipsoidal hull may be readily adapted to other cases, they are expressed in terms of the area and perimeter of the largest cross section perpendicular to the direction of motion by means of a formula involving a coefficient kappa which varies only slowly when the shape of the hull is changed, being 0.637 for a circular or elliptic disk, 0.5 for a sphere, and about 0.25 for a spheroid of fineness ratio. The case of rotation of an airship hull is investigated and a coefficient is defined with the same advantages as the corresponding coefficient for rectilinear motion.

Bateman, H.↗
NASA NTRS1979

Flow and Force Equations for a Body Revolving in a Fluid

A general method for finding the steady flow velocity relative to a body in plane curvilinear motion, whence the pressure is found by Bernoulli's energy principle is described. Integration of the pressure supplies basic formulas for the zonal forces and moments on the revolving body. The application of the steady flow method for calculating the velocity and pressure at all points of the flow inside and outside an ellipsoid and some of its limiting forms is presented and graphs those quantities for the latter forms. In some useful cases experimental pressures are plotted for comparison with theoretical. The pressure, and thence the zonal force and moment, on hulls in plane curvilinear flight are calculated. General equations for the resultant fluid forces and moments on trisymmetrical bodies moving through a perfect fluid are derived. Formulas for potential coefficients and inertia coefficients for an ellipsoid and its limiting forms are presented.

Zahm, A. F.↗
NASA NTRS1980

Life near the Roche limit - Behavior of ejecta from satellites close to planets

A study of the dynamics of nearby debris from impact craters was made to explain the distinctive features seen on Phobos, Deimis, and Amalthea. The planetary tides and satellite rotation were considered, and the usual pseudo-energy (Jacobi) integral was numerically calculated in the framework of a restricted body problem where satellites are modelled as triaxial ellipsoids rather than point masses. Iso-contours of this integral show that Deimos and Amalthea are entirely closed by Roche lobes, and the surfaces of their model ellipsoids lie nearly along equipotentials. Presently, the surface of Phobos overflows its Roche lobe, except for regions within a few km of the sub-Mars and anti-Mars points. The behavior of crater ejecta from the satellites of Mars were also examined by numerical integration of trajectories for particles leaving their surfaces in the equatorial plane.

Dobrovolskis, A. R.↗
NASA NTRS1980

Influence of nonequilibrium radiation and shape change on aerothermal environment of Jovian entry body

Radiative transfer equations are derived under nonequilibrium conditions which include multilevel energy transitions. The nonequalibrium results, obtained with and without ablation injection in the shock layer, are found to be greatly influenced by the temperature distribution in the shock layer. In the absence of ablative products, the convective and radiative heating to the entry body are reduced significantly under nonequilibrium conditions. The influence of nonequilibrium is found to be greater at higher entry altitudes. With coupled ablation and carbon phenolic injection, 16 chemical species are used in the ablation layer for radiation absorption. Equilibrium and nonequilibrium results are compared under peak heating conditions. A 45 degree sphere cone, a 35 degree hyperboloid, and a 45 degree ellipsoid were used to study probe shape change. Results indicate that the shock layer flow field and heat transfer to the body are influenced significantly by the probe shape change. The effect of shape change on radiative heating of the afterbodies is found to be considerably larger for the sphere cone and ellipsoid than for the hyperboloid.

Tiwari, S. N.↗
NASA NTRS1981

Low thrust chemical orbit to orbit propulsion system propellant management study

Low thrust chemical propulsion systems were sized for transfer of large space systems from LEO to GEO. The influence of propellant combination, tankage and insulation requirements, and propellant management techniques on the LTPS mass and volume were studied. Liquid oxygen combined with hydrogen, methane or kerosene were the propellant combinations. Thrust levels of 445, 2230, and 4450 N were combined with 1, 4 and 8 perigee burn strategies. This matrix of systems was evaluated using multilayer insulation and spray-on-foam insulation systems. Various combinations of toroidal, cylindrical with ellipsoidal domes, and ellipsoidal tank shapes were investigated. Results indicate that low thrust (445 N) and single perigee burn approaches are considerably less efficient than the higher thrust level and multiple burn strategies. A modified propellant settling approach minimized propellant residuals and decreased system complexity, in addition, the toroid/ellipsoidal tank combination was predicted to be shortest.

Dergance, R. H.↗
NASA NTRS1980

Collapse, equilibrium, and fragmentation of rotating, adiabatic clouds

Numerical calculations of the collapse of adiabatic clouds from uniform density and rotation initial conditions show that when restricted to axisymmetry, the clouds form either near-equilibrium spheroids or rings. Rings form in the collapse of low thermal energy clouds and have a ratio of rotational kinetic energy to the absolute value of gravitational potential energy greater than approximately 0.43. When the axisymmetric constraint is removed and an initial m = 2 density variation is introduced, clouds either collapse to form near-equilibrium ellipsoids or else fragment into binary systems through a bar phase. Ellipsoids form in the collapse of high thermal energy clouds and have a rotational kinetic energy/absolute value of gravitational potential energy ratio less than approximately 0.27. The results are consistent with the critical values of the rotational kinetic energy/absolute value of gravitational potential energy ratio for instabilities in Maclaurin spheroids, and suggest that protostellar clouds may undergo a dynamic fragmentation in the nonisothermal collapse regime.

Boss, A. P.↗
NASA NTRS1980

Baffle design for earth radiation rejection in the Cryogenic Limb-Scanning Interferometer/Radiometer

The Cryogenic Limb-Scanning Interferometer/Radiometer (CLIR) is being developed to observe infrared emissions of the earth's upper atmosphere from space. The earth's surface is an extended source of intense background radiation with a small angular separation from the desired scene. The CLIR employs an off-axis Gregorian Telescope whose primary mirror and baffles are cooled by an open-cycle cryogen system. A system of specular annular baffles has been developed to minimize both stray light problems and cryogen consumption by retro-mapping the aperture into itself. Each off-axis ray which enters the aperture and strikes the specular baffle surface is reflected so that it passes out of the aperture and is not absorbed on a cryogenic surface. The specular baffle which lies closest to the aperture is an ellipsoid whose foci trace out the circular aperture on revolution about the axis. Its theoretical 'ray trace' efficiency is 100 percent. A subsequent baffle has an elliptical cross section whose near focus traces out the central hole in the ellipsoidal baffle and whose far focus traces out the aperture. Its theoretical efficiency is about 90 percent. These baffles reduce the earth radiation heat load on the cryogenic cooler by an order of magnitude, changing it from the dominant cause of cryogen consumption to a relatively small effect. An aperture shield is also desirable to reduce cryogen consumption, stray light, and contamination.

Bremer, J. C.↗
NASA NTRS1982

Extended range X-ray telescope: X-ray microscope design

A glancing incidence X-ray microscope using a confocal hyperboloid ellipsoid mirror was designed to couple optically a Wolter 1 telescope to a CCD focal plane detector. Both the RMS spot size and the point spread function calculations were used to evaluate the resolution, defocusing, and vignetting effects of the system for microscope focal lengths of 1, 1.5, and 2 meters and for magnifications varying from 2 to 10x. For the specific application with the S-056 telescope, a 2 meter, 8x microscope with a fabrication ratio of the microscope mirror length to the inner diameter at hyperboloid ellipsoid intersection of 2.5 was designed to be used with a thinned, back illuminated CCD detector array with 320 by 512, 30 micron pixels.

Shealy, D. L.↗
NASA NTRS1981

The influence of the interplanetary magnetic field and thermal pressure on the position and shape of the magnetopause

An ellipsoidal model, in which the size of an ellipsoid of revolution with a constant eccentricity is inversely proportional to the sixth root of the stream pressure of the solar wind, is used to represent the location of the dayside magnetopause and to study the influences of the interplanetary magnetic field and thermal pressure on its location. The effects of the IMF and thermal pressure on the location of the magnetopause are calculated analytically by using the Chapman-Ferraro theory. The changes in magnetopause size, shape and orientation caused by including the thermal pressure are inversely proportional to the square of the sonic Mach number of the solar wind and are sufficient to explain the observed slight departure of the magnetotail from the expected aberration due to the earth's orbital motion. The results suggest that little angular momentum is being carried away from the sun by the solar wind.

Zhuang, H. C.↗
NASA NTRS1982

On the distribution of orbits among long-period comets

The distribution of the axes defining the planes and orientations of the orbits of 542 long-period comets are analyzed. The directions of the perihelia and of the oriented plane normals show significant nonuniformity in their distributions. The preferred direction of perihelia near the apex of solar motion is refined to an (1 sigma) error circle of 20.6 deg, and possible concentrations of the plane normals and the directions of perihelion velocity along roughly orthogonal directions are noted, although the error circles extend to nearly full hemispheres. Planes of preference (and avoidance) are found from the distribution ellipsoids of the three orbital axes, with the perihelion directions lying preferentially along the galactic plane. The distribution ellipsoids of all three sets of orbital axes exhibit anisotropies roughly twice those expected for random distributions.

Bogart, R. S.↗
NASA NTRS1983

Composites with periodic microstructure

For an elastic body containing periodically distributed inhomogeneities, a general procedure is developed for estimating the overall properties of the composite in terms of several infinite series which, for the isotropic matrix (but anisotropic inclusions), depend only on the geometry of the inhomogeneities and hence can be calculated once and for all for each geometry. These infinite series are obtained and tabulated for ellipsoidal inhomogeneities, and the results are used to estimate the overall elastic moduli of composites which contain spherical or ellipsoidal voids or elastic inclusions.

Iwakuma, T.↗
NASA NTRS1984

Analysis of axisymmetric body effects on rotor aerodynamics using modified slender body theory

A modified slender body theory was used in modelling the flowfield around an axisymmetric body at zero angle of attack. The model was defined in an attempt to characterize body-induced effects on helicopter rotor performance and loading using efficient computation methods. The streamfunction for an axial source distribution was applied in the body model, which was then adapted to the helicopter analysis code (CAMRAD). The body-induced velocities were calculated for separate locations on the rotor disk. Three different rotor models in nonuniform inflow with a free wake geometry were considered. Comparison of predictions with data on ellipsoidal and axisymmetric bodies showed good agreement for moderately thick ellipsoidal bodies. Oscillatory blade bending moments were increased by the presence of the body, but overall performance impact was negligible. Computational efficiency was 10-20 percent better than with a potential flow panel code.

Yamauchi, G. K.↗
NASA NTRS1984

The precise computation of geoid undulation differences with comparison to results obtained from the global positioning system

Ellipsoidal height differences have been determined for 13 station pairs in the central Ohio region using measurements made with the Global Positioning System. This information was used to compute geoid undulation differences based on known orthometric heights. These differences were compared to gravimetrically-computed undulations (using a Stokes integration procedure, and least squares collocation having an internal r.m.s. agreement of plus or minus 1 cm in undulation differences). The two sets of undulation differences have an r.m.s. discrepancy of plus or minus 5 cm while the average station separation is of the order of 14 km. This good agreement suggests that gravimetric data can be used to compute accurate geoid undulation differences that can be used to convert ellipsoidal height differences obtained from GPS to orthometric height differences.

Engelis, T.↗
NASA NTRS1986

Speckle interferometry applied to asteroids and other solar system objects

Speckle interferometry is a high angular resolution technique that allows study of resolved asteroids. By following the changing size, shape, and orientation of minor planets, and with a few general assumptions (e.g., geometric scattering, triaxial ellipsoid figures, no albedo features), it is possible to directly measure an asteroid's true dimensions and the direction of its spin axis in one or two nights. A particular subset of triaxial ellipsoid figures are equilibrium shapes, and would imply that some asteroids are thoroughly fractured. Such shapes if they exist among the asteroids would allow a determination of bulk density since there is a unique relation among spin period, size, shape, and density. The discovery of even a single rubble pile, (just as the finding of even one binary asteroid by speckle interferometric techniques) would drastically alter the notion of asteroids as small solid planets. The Pluto/Charon system was studied to aid in improving the orbital elements necessary to predict the eclipse/occultation season currently in progress. Four asteroids were reduced to their size, shape, and pole direction: 433 Eros, 532 Herculina, 511 Davida, and 2 Pallas.

Drummond, J. D.↗