Configuration factors between a small plane and a large sphere.
Diffuse configuration factors between small plane and large sphere by unit sphere method, presenting limiting cases
Heinisch, R. P.↗
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Optimum radars and filters for the passive sphere system
Studies have been conducted to determine the influence of the tracking radar and data reduction technique on the accuracy of the meteorological measurements made in the 30 to 100 kilometer altitude region by the ROBIN passive falling sphere. A survey of accuracy requirements was made of agencies interested in data from this region of the atmosphere. In light of these requirements, various types of radars were evaluated to determine the tracking system most applicable to the ROBIN, and methods were developed to compute the errors in wind and density that arise from noise errors in the radar supplied data. The effects of launch conditions on the measurements were also examined. Conclusions and recommendations have been made concerning the optimum tracking and data reduction techniques for the ROBIN falling sphere system.
Luers, J. K.↗
Sphere launcher
The sphere launcher was designed to eject a 200 lb, 15 in. diameter sphere from a space vehicle or missile, at a velocity of 58 ft/sec without imparting excessive lateral loads to the vehicle. This launching is accomplished with the vehicle operating in vacuum conditions and under a 9 g acceleration. Two principal elements are used: a high thrust, short burn time rocket motor and two snubbers for reducing the lateral loads to acceptable limits.
Reed, W. B.↗
Torque on a sphere inside a rotating cylinder.
A circular cylinder of finite dimensions is made to rotate around a sphere fixed in the center of the cylinder. The couple on the sphere is measured over a wide range of rotational speeds for both Newtonian and non-Newtonian fluids. For the Newtonian liquids a comparison of the experimental results is made with Collins' (1955) expansion of the couple as a series in even powers of the angular Reynolds number. For non-Newtonian liquids the apparatus proves to be extremely useful for an accurate determination of the zero shear rate viscosity using only a small amount of fluid.
Mena, B.↗
Hypersonic nonequilibrium flow past a sphere at low Reynolds numbers
Detailed flow field properties are computed in the nose region of a sphere from the Navier-Stokes equations for a range of Reynolds numbers. Comparisons are made of theoretical flow fields with those obtained in experiments and also with other analyses. In particular, the effects of various approximations on the flow field are investigated. It is shown that the Navier-Stokes model consistently predicts a smaller region of disturbance upstream of a sphere than that in experiments.
Li, C. P.↗
A similarity solution of the Navier-Stokes equations with wall catalysis and slip for hypersonic, low Reynolds number flow over spheres
The slip conditions for a multicomponent mixture with diffusion, wall-catalyzed atom recombination and thermal radiation are derived. The more realistic multicomponent species slip conditions are shown to be necessary for accurate merged shock layer solutions on a sphere. These slip conditions are used in a first-order similarity solution of the Navier-Stokes equations with nonequilibrium chemistry for the merged shock layer. Results of this quick numerical solution are compared with a time dependent solution around the sphere and with measured arc jet results at low Reynolds numbers. The similarity solution, unlike the time dependent solution, shows smooth radial profiles of the pressure and smooth variations of velocity slip, skin friction, temperature slip and heat transfer around the body. The present first-order similarity solution is valid up to 25 deg from the stagnation point and takes less than 1% of the computer time to run a time dependent scheme. The smaller stand-off distance obtained from the similarity solution is supported by experimental data. The measured heat flux is closer to the similarity solution than the time dependent method at the stagnation point and shows the proper variation with circumferential angle up to at least 40 deg.
Hendricks, W. L.↗
Isolated Stroemgren spheres as a source of galactic H alpha emission
The isolated H alpha emission features reported by Reynolds et al. are identified with Stroemgren spheres surrounding observed O stars; the root mean square electron densities and Stroemgren radii are calculated from the observed emission measure and stellar type. The density has an average value of 2 per cu cm but increases to 3.3 per cu cm for stars within 200 pc of the galactic plane. An analysis of the Catalogue of Galactic O Stars shows that enhanced H alpha emission is observed around all known O stars. The diffuse component of H alpha emission is what one would expect from the line-of-sight overlapping of isolated Stroemgren spheres surrounding B stars and appears to correlate with features on extinction maps, as derived. There is no compelling reason to suggest any large-scale intercloud ionization from H alpha data alone.
Elmergreen, B. G.↗
Scattering by spheres with nonisotropic refractive indices
Experimental scattering results using a microwave analog technique are described. Artificially constructed axially symmetric spheres with a graphite-like fine-layered composite structure and anisotropic refractive indices were employed to aid high-precision measurements of forward scattering under stable conditions (temperature, physical dimensions, electronic conditions) and to facilitate studies of the extinction and polarization of light by graphite particles in interstellar space. A theoretical approximation utilizing Mie theory for spheres with suitable orientation-dependent refractive indices is applied to account for changes in the complex forward-scattering amplitudes and phase in response to target orientation. The methods are extended to the full range of scattering angles, from the forward direction continuously to about 165 deg and at 180 deg. Agreement between experiment and prediction is close when the symmetry axis is parallel to the polarization.
Wang, R. T.↗
Absolute calibration of the RADSCAT scatterometer using precision spheres
Tests using precision sphere targets suspended from balloons were conducted to calibrate the received-power/transmitted-power tatio of the RADSCAT scatterometer. Comparisons were made of these measured results with theoretical return from spheres. The RADSCAT scatterometer measurements at 13.9 GHz should be corrected by -2.4 dB, and those at 9.3 GHz, by -4.3 dB. The techniques described should be generally applicable to calibration of scatterometers where measurement precision is of prime importance. Inferred from the magnitude of these RADSCAT corrections was the present state of technology in building precision scatterometers.
Grantham, W. L.↗
Measurement of Blast Waves from Bursting Pressureized Frangible Spheres
Small-scale experiments were conducted to obtain data on incident overpressure at various distances from bursting pressurized spheres. Complete time histories of blast overpressure generated by rupturing glass spheres under high internal pressure were obtained using eight side-on pressure transducers. A scaling law is presented, and its nondimensional parameters are used to compare peak overpressures, arrival times, impulses, and durations for different initial conditions and sizes of blast source. The nondimensional data are also compared, whenever possible, with results of theoretical calculations and compiled data for Pentolite high explosive. The scaled data are repeatable and show significant differences from blast waves generated by condensed high-explosives.
Esparza, E. D.↗
Measurements of blast waves from bursting frangible spheres pressurized with flash-evaporation vapor or liquid
Incident overpressure data from frangible spheres pressurized with a flash-evaporating fluid in liquid and vapor form were obtained in laboratory experiments. Glass spheres under higher than ambient internal pressure of Freon-12 were purposely burst to obtain time histories of overpressure. Nondimensional peak pressures, arrival and duration times, and impulses are presented, and whenever possible plotted and compared with compiled data for Pentolite high-explosive. The data are generally quite repeatable and show differences from blast data produced by condensed high-explosives.
Esparaza, E. D.↗
A split sphere 60,000 ton press
A split sphere press which can have a total force of 60,000 tons applied to its exterior by a 0.55 GPa hydrostatic pressure vessel is described. The inner anvils are made of tungsten carbide and show considerable plastic deformation under load. Much greater pressures, in the 100 GPa range, are possible if diamond tipped anvils are used. Because of the uniformly loaded multi-anvil arrangement, the diamond tips can be maintained under a high degree of compressive load and therefore prevent fracture which may occur in a conventional opposed anvil arrangement. Press operation on CdS, ZnSe, ZnS, GaP, and BP samples is described, and their resistance versus external pressure on the sphere are plotted.
Wanagel, J.↗
Analyzing and modeling gravity and magnetic anomalies using the SPHERE program and Magsat data
Computer codes were completed, tested, and documented for analyzing magnetic anomaly vector components by equivalent point dipole inversion. The codes are intended for use in inverting the magnetic anomaly due to a spherical prism in a horizontal geomagnetic field and for recomputing the anomaly in a vertical geomagnetic field. Modeling of potential fields at satellite elevations that are derived from three dimensional sources by program SPHERE was made significantly more efficient by improving the input routines. A preliminary model of the Andean subduction zone was used to compute the anomaly at satellite elevations using both actual geomagnetic parameters and vertical polarization. Program SPHERE is also being used to calculate satellite level magnetic and gravity anomalies from the Amazon River Aulacogen.
Braile, L. W.↗
C-1 surface interpolation for scattered data on a sphere
An algorithm is described for constructing a smooth computable function, f, defined over the surface of a sphere and interpolating a set of n data values, u sub i, associated with n locations, P sub i, on the surface of the sphere. The interpolation function, f, will be continuous and have continuous first partial derivatives. The locations, p sub i, are not required to lie on any type of regular grid.
Lawson, C. L.↗
Theoretical study of the freezing of polystyrene sphere suspensions
A theoretical study of melting in aqueous suspensions of polystyrene spheres is presented. The Helmholtz free energies of the liquid and solid phase of the suspensions are calculated as functions of sphere number density and electrolyte concentrations. The results tend to show that the freezing curve of such suspensions is that of a conventional classical liquid with repulsive short-range interactions. The interactions can be treated satisfactorily within a slightly modified Debye-Hueckel approximation. The modifications include size correction and a correction for nonlinear screening. The results are confirmed by analogous calculations for the solid phase, and for the line along which liquid and solid free energies are equal.
Shih, W.-H.↗
Surface characteristics of metallic glass spheres of Au(55)Pb(22.5)Sb(22.5)
It is pointed out that the production of metallic glasses of high atomic number is currently of considerable importance for inertial confinement fusion (ICF) target applications. In connection with the present investigation, spherules of the alloy Au(55)Pb(22.5)Sb(22.5) were produced. Metallic glass was formed on solidification. With the aid of X-ray diffraction studies, it was established that the spheres were completely amorphous. A near-surface phase separation on spheres of the metallic glass could be observed. Energy dispersive spectroscopy (EDS) measurements showed that the average composition of the surface differed from that of the bulk.
Lee, M. C.↗
Multiple Equilibria of the Barotropic Vorticity Equation on a Sphere
Multiple states of the barotropic vorticity equation in which the balance is between the first and third terms on the r.h.s. of (1) are given. Solutions of this type were also considered by Charney and Devore (1979) in their discussion of thermally, rather than topographically, forced waves. Whereas in the case of topographic forcing the multiplicity arises from what they called form-drag instability in the wave-zonal flow interaction, in the thermal forcing case the associated instability appears to be the Rossby-wave instability discussed by Lorenz (1972), and the multiple states of the highly truncated model proved to be unstable when more degrees of freedom were added. The multiple statistically steady solutions described are thus novel in that they do not involve form-drag instability, they have stable statistics in calculations with a large number of degrees of freedoms, and they occur on the sphere, with no artificial confinement in a resonant cavity. Furthermore, the solutions are obtained with no external forcing of the zonal flow. The full non-linear equations for two-dimensional non-divergent motion between smooth, rigid boundaries on a sphere were used.
Suarez, M. J.↗
The temperature distribution within a sphere placed in a directed uniform heat flux and allowed to radiatively cool
The temperature field within a sphere is found when the sphere is heated by a directed heat flux and cooled by blackbody radiation. For small heat fluxes, the analytic solution is obtained by transform methods. For large heat fluxes, the solution is computed numerically.
Duffy, D.↗