SEARCH · Engineering Papers
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.
The pressure distribution over ellipsoids when in translatory motion through a perfect fluid is calculated. A method to determine the magnitude of the velocity and of the pressure at each point of the surface of an ellipsoid of rotation is described.
The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.
Trajectories of water droplets about an ellipsoid of revolution with a fineness ratio of 5 (which often approximates the shape of an aircraft fuselage or missile) were computed with the aid of a differential analyzer. Analyses of these trajectories indicate that the local concentration of liquid water at various points about an ellipsoid in flight through a droplet field varies considerably and under some conditions may be several times the free-stream concentration. Curves of the local concentration factor as a function of spatial position were obtained and are presented in terms of dimensionless parameters Re(sub 0) (free-stream Reynolds number) and K (inertia), which contain flight and atmospheric conditions. These curves show that the local concentration factor at any point is very sensitive to change in the dimensionless parameters Re(sub 0) and K. These data indicate that the expected local concentration factors should be considered when choosing the location of, or when determining antiicing heat requirements for, water- or ice-sensitive devices that protrude into the stream from an aircraft fuselage or missile. Similarly, the concentration factor should be considered when choosing the location on an aircraft of instruments that measure liquid-water content or droplet-size distribution in the atmosphere.
Trajectories of water droplets about an ellipsoid of revolution with a fineness ratio of 10 (10 percent thick) in flight through a droplet field were computed with the aid of a differential analyzer. Analyses of these trajectories indicate that the local concentration of liquid water at various points about an ellipsoid varies considerably and under some conditions may be several times the free-stream concentration. Curves of the local concentration factor as a function of spatial position were obtained and are presented in terms of dimensionless parameters that describe flight and atmospheric conditions. The data indicate that the expected local concentration factors should be considered when choosing the location of devices that protrude into the stream from aircraft fuselages or missiles, or when determining antiicing heat requirements for the protection of these devices.
Ellipsoidal correction terms have been derived for geoid undulation computations when the Stokes equation using gravity anomalies in a cap is combined with potential coefficient information. The correction terms are long wavelength and depend on the cap size in which its gravity anomalies are given. Using the regular Stokes equation, the maximum correction for a cap size of 20 deg is -33 cm, which reduces to -27 cm when the Stokes function is modified by subtracting the value of the Stokes function at the cap radius. Ellipsoidal correction terms were also derived for the well-known Marsh/Chang geoids. When no gravity was used, the correction could reach 101 cm, while for a cap size of 20 deg the maximum correction was -45 cm. Global correction maps are given for a number of different cases. For work requiring accurate geoid computations these correction terms should be applied.
The scattering of a single ellipsoidal inhomogeneity is studied via an eigenstrain approach. The displacement field is given in terms of volume integrals that involve eigenstrains that are related to mismatch in mass density and that in elastic moduli. The governing equations for these unknown eigenstrains are derived. Agreement with other approaches for the scattering problem is shown. The formulation is general and both the inhomogeneity and the host medium can be anisotrophic. The axisymmetric scattering of an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the scattered displacement field, the differential and total cross sections are formally given in series expansions for the case of uniformly distributed eigenstrains.
Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.
The determination of the elastodynamic fields of an ellipsoidal inhomogeneity is studied in detail via the eigenstrain approach. A complete formulation and a treatment of both types of eigenstrains for equivalence between the inhomogeneity problem and the inclusion problem are given. This approach is shown to be mathematically identical to other approaches such as the direct volume integral formulation. Expanding the eigenstrains and applied strains in the polynomial form in the position vector and satisfying the equivalence conditions at every point, the governing simultaneous algebraic equations for the unknown coefficients in the eigenstrain expansion are derived. The elastodynamic field outside an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the induced displacement field, as well as the differential and total cross sections are formally given in series expansion form for the case of uniformly distributed eigenstrains.
Spherical reflector around heat source increases efficiency and minimizes power requirements. Furnace consists of ellipsoid with point heat source, at one focus and sample heated at other focus. Spherical reflector with circular slit surrounds heat source. All radiation not passing through circular slit in spherical reflector reflected back to lamp. Radiation passing through spherical slit focused by ellipsoid surface onto sample. Arrangement uses heat efficiently, reduces waste heat generation and permits full view of specimen.
Direct-broadcast ellipsoidal antenna 40 percent smaller than spherical reflector. Balloon antenna has feedpoint on surface of ellipsoid outside balloon, simplifying balloon deployment and feed support. Dielectric shrouds used locally to adjust shape of balloon and maintain feed distance at its optimum value.
The major consequences of ellipsoidal geometry in an othewise standard radiometric model for asteroids are explored. It is shown that for small deviations from spherical shape a spherical model of the same projected area gives a reasonable aproximation to the thermal flux from an ellipsoidal body. It is suggested that large departures from spherical shape require that some correction be made for geometry. Systematic differences in the radii of asteroids derived radiometrically at 10 and 20 microns may result partly from nonspherical geometry. It is also suggested that extrapolations of the rotational variation of thermal flux from a nonspherical body based solely on the change in cross-sectional area are in error.
This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.
The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere-at least to the ellipsoid. The goal is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (the g sub 1 term). The terrain correction was also computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. The fast Fourier transformation was applied to the computations.
The preliminary results of a scheme currently being developed to fit a composite ellipsoid to the fuselage of a helicopter in the vicinity of the antenna location are discussed under the assumption that the antenna is mounted on the fuselage. The parameters of the close-fit composite ellipsoid would then be utilized as inputs into NEWAIR3, a code programmed in FORTRAN 77 for high frequency Geometrical Theory of Diffraction (GTD) Analysis of the radiation of airborne antennas.
Analytic formulas are developed for the semiaxes and for the deformation coefficients of a deformed ellipsoidal grating that minimize aberrations over a given spectral range. These include the Rowland circle mount and quasi-Rowland circle mounts, as required for systems that combine spectra from multiple gratings on a common detector. It is also shown that the necessary condition for a holographic grating to give a better performance over a conventional grating is the use of a convergent beam and a divergent beam for the recording. Examples applicable to the Far-Ultraviolet Spectroscopic Explorer are given. The light-path function for a deformed ellipsoidal holographic grating is also presented.
This note, prepared for the National Advisory Committee for Aeronautics, contains a discussion of the pressure distribution over ellipsoids when in translatory motion through a perfect fluid. An easy and convenient way to determine the magnitude of the velocity and of the pressure at each point of the surface of an ellipsoid of rotation is described. The knowledge of such pressure distribution is of great practical value for the airship designer. The pressure distribution over the nose of an airship hull is known to be in such good agreement with the theoretical distribution as to permit basing the computation of the nose stiffening structure on the theoretical distribution of pressure.
By using the Prandtl-Glauert method that is valid for three-dimensional flow problems, the value of the maximum incremental velocity for compressible flow about thin ellipsoids at zero angle of attack is calculated as a function of the Mach number for various aspect ratios and thickness ratios. The critical Mach numbers of the various ellipsoids are also determined. The results indicate an increase in critical Mach number with decrease in aspect ratio which is large enough to explain experimental results on low-aspect-ratio wings at zero lift.
We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamics equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters, and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction. In cases where the neutron stars have spins which are not aligned with the orbital angular momentum, the spin-induced quadrupole moment can lead to precession of the orbital plane and therefore modulation of the gravitational wave amplitude even at large orbital radius. However, the amplitude of the modulation is small for typical neutron star binaries with spins much smaller than the orbital angular momentum.