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Computer program can be used to analyze any disk or shell of revolution of arbitrary cross section under inertial loads caused by rotation about shell axis and under various static loads, including thermal gradients. Geometric shapes incorporated in program are ellipsoidal, spherical, ogival, toroidal, conical, circular plate, cylindrical, and parabolic.
An interesting variation on the familiar method of determining the earth's equatorial radius a sub e, from a knowledge of the earth's equatorial gravity is suggested. The value of equatorial radius thus found is 6378,142 + or - 5 meters. The associated parameters are GM = 3,986008 + or - 4 X 1014 cu cm/sec/sec which includes the relative mass of atmosphere approximately 0.000001 x GM, the equatorial gravity gamma sub e = 978,030.9 milligals (constrained in this solution by the Potsdam Correction of 13.67 milligals as the Potsdam Correction is more directly, or less indirectly, measurable than the equatorial gravity) and an ellipsoidal flattening of f = 1/298.255.
A solution is obtained for the geodetic boundary value problem which defines height anomalies to + or - 5 cm, if the earth were rigid. The solution takes into account the existence of the earth's topography, together with its ellipsoidal shape and atmosphere. A relation is also established between the commonly used solution of Stokes and a development correct to order e cubed. The data requirements call for a complete definition of gravity anomalies at the surface of the earth and a knowledge of elevation characteristics at all points exterior to the geoid. In addition, spherical harmonic representations must be based on geocentric rather than geodetic latitudes.
Preliminary Mariner 9 map products were based on computed aerocentric coordinates at the point where the optic path intercepts a spherical reference figure for Mars. The intercept point on a reference ellipsoid would in general have slightly different values of radius, latitude, and longitude. For near-vertical viewing used for mapping, these differences are on the order of 0.1 in latitude and longitude, which is negligible compared to the uncertainties of the initial uncontrolled mosaics and maps.
The objectives of the Mars surface properties working group are described. The objectives were: (1) determine a simple reference surface that would adequately represent the shape of the planet for cartographic purposes; (2) monitor the topographic results and to assess the relative calibration and accuracies of these techniques, thereby leading to a composite topographic map of the planet; and (3) facilitate the exchange of data in closely connected disciplines. The shape, topography, and isobaric surface are discussed along with the gravity field, and crustal density model. It was found that there is no simple reference figure for the planetary surface, although an offset, triaxial ellipsoid is adequate for most purposes.
Demonstration that the output from a ring core sensor is directly proportional to the first time derivative of the product of dynamic permeability and magnetic intensity perturbation within the core caused by an external, uniform magnetic field. (Dynamic permeability is defined to be the slope of the hysteresis loop at a given point in time). Assuming that ellipsoidal shells can approximate the core, the demagnetization factor can be 'estimated' in the first order to be proportional to the first power of the quantity tape thickness (or number of wraps) divided by the core diameter. The constant of proportionality is determined from laboratory data. When an additional scale adjustment is applied to the resulting sensor output formula, the computed output tracks laboratory data for a range of sensor geometries.
A finite-difference relaxation method is presented for numerical solution of the full potential equation and exact boundary conditions for general axisymmetric bodies is inviscid, steady transonic flow. Body-normal coordinates are used in the nose region and sheared cylindrical coordinates are used on the afterbody to accommodate corners such as boattails and flares. An improved difference scheme is used which does not require that the flow be nearly alined with a coordinate direction in supersonic regions, and which treats either subsonic or supersonic free streams. Numerical results are illustrated for some simple classical shapes such as spheres and ellipsoids, and for more practical shapes like tangent-ogives with boattails. Special attention is given to bodies which have been studied for area-rule applications. Agreement with available experimental results is good in cases where viscous effects and wind-tunnel wall interference are not important.
Tungsten halogen projection lamps have integral ellipsoidal reflector, and hexagonal shaped plastic Fresnel lenses. Reflector is dichroic coated to reduce infrared content of reflected radiation. Array of lamps and lenses produces uniform collimated beam having near AM2 spectrum and intensity that can be used for testing flat plate solar collectors.
A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.
Diversity data obtained using the ATS-5 satellite and available BTL data were compared with optimum diversity gain predictions. This comparison indicates that terminal spacings exceeding 8 km result in values of diversity gain within 1.5 dB of the optimum. The thunderstorm cell modeling technique for predicting attenuation and diversity gain statistics was extended to include ellipsoidal cell models. A three rain gage method for the measurement of cell size, ellipticity, and orientation was developed.
Asymptotic solutions of Novozhilov's equations of shells of revolution are derived for axisymmetric and first harmonic loadings. The solutions obtained are valid throughout the shallow and nonshallow regions. Stresses in dome shaped shells of revolution with a discontinuity in the form of a circular hole, a circular rigid insert, or a nozzle at the apex have been investigated. Numerical results are obtained for spheres, ellipsoids, and paraboloids, containing a discontinuity under a internal pressure and moment. Curves depicting stress distributions are given. The influence of three types of discontinuity on the stresses of the shells is also given.
The elastic deformation of two ellipsoidal solids in contact and subjected to Hertzian stress distribution was evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone was divided into equal rectangular areas, and it was assumed that a uniform pressure is applied over each rectangular area. The influence of the size of the rectangular area upon accuracy was also studied. The results indicate the distance from the center of the contact at which elastic deformation becomes insignificant.
The sizes, shapes, and complex refractive indices of particles are calculated in a study of the IR spectral reflectance of a semiinfinite medium composed of irregular particles of different materials. Geometric optics techniques with corrections for additional absorption due to particle edges and asperities is used in scattering and absorption calculations for particles larger than the wavelength. A Lorentz-Lorenz model is used to derive the averaged complex index of the medium, assuming that its individual particles are ellipsoids. Experimental results obtained on a Michelson interferometer for the spectral emittance of particulate mineral materials are compared with theoretical results. Good agreement between the experimental and theoretical results suggests the applicability, in remote IR spectroscopy, of the theoretical concepts applied in this study.
We consider analytically the use of existing instrumentation in determining asteroid gravity fields from orbiting spacecraft. Asteroids (Eros as an example) are modeled as homogeneous triaxial ellipsoids, with gravitational potential given by a sperical-harmonic expansion. Mass concentrations are modeled as point masses. The character of spacecraft orbits about asteroids is discussed, along with detectibility of gravitational coefficients and of mass concentrations. A Kalman-filtering treatment of the observation process, for Eros as example, shows that using DSN tracking and onboard gravity gradiometry, radar altimetry, and celestial angle measurements, a single orbit yields asteroid mass to 0.03% and coefficients C20 to C44 to 1% accuracies.
The observed nonspherical structure of the material ejected during a nova outburst is explained by considering a component of the cataclysmic binaries ignored in previous theories - the ring of material which lies in the equatorial plane and surrounds the white dwarf. When the expanding shell collides with the ring, a shock is formed which heats the material in the ring and in the portion of the shell striking the ring. There is enough energy and density in the expanding shell for it to sweep the ring along, but with a final velocity somewhat lower than the shell moving perpendicular to the ring. The result is a prolate ellipsoid with the long axis perpendicular to the plane of the binary orbit. As the nebulosity evolves, the density remains greater in the equatorial plane than at the polar axis. This hypothesis is supported by calculations of the forbidden emission line ratios which also imply a higher equatorial density.
The types of Doppler gravity data available for local as opposed to planetwide geophysical modeling are reviewed. Those gravity fields that are determined dynamically in orbit determination programs yield a smoothed representation of the local gravity field that may be used for quantitative modeling. An estimate of the difference between smoothed and true fields can be considered as a noise limitation in generating local gravity models. A nonlinear inversion for the geometry, depth, and density of the Mare Serenitatis mascon using an ellipsoidal model yielded a global least squares minimum in horizontal dimensions, depth, and thickness-density contrast product. It was subsequently found, by using a linear model, that there were an infinite number of solutions corresponding to various combinations of depth and lateral inhomogeneity. Linear modeling was performed by means of generalized inverse theory.
Methods are described for calculating left ventricular (LV) dimensions and chamber volumes from radiographic films. The use of biplane films for the calculation of LV volume and volume change is based on the assumption of an ellipsoidal geometry. Calculation of LV volumes from biplane films usually overestimated known volumes in postmortem hearts regardless of the methods used for volume calculation. The reasons for this are probably best explained by the fact that a smooth-surface ellipse is used to represent the irregular cavity of the LV chamber. LV volume calculated from data in a single plane compared favorably and closely with volumes calculated from biplane films. A table of normal values of ventricular volume established by angiographic studies is presented.
The elastic deformation of two ellipsoidal solids in contact and subjected to a Hertzian stress distribution was evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each rectangular area. A study was made of the influence on the size of the rectangular area upon accuracy. The results also indicate how far from the center of the contact one needs to go before elastic deformation becomes insignificant.