A method for determining an optimum shape of a class of thin shells of revolution
Optimum shape of convex thin shell of revolution with respect to volume, weight and length - mathematical function
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Optimum shape of convex thin shell of revolution with respect to volume, weight and length - mathematical function
Flammability testing of components in the design of Apollo spacecraft is discussed. The purpose of component flammability testing was to determine the flammability characteristics of a variety of different sizes, shapes, and configurations of nonmetallic materials of similar or different types that make up a functional assembly, subsystem, or system in a spacecraft. The test criteria and requirements for the nonmetallic materials are presented.
Modification of the rectangular bicubic spline fit interpolation scheme so as to make it suitable for use with a polar grid pattern. In the proposed modified scheme the interpolation function is expressed in terms of the radial length and the arc length, and the shape of the patch, which is a wedge or a truncated wedge, is taken into account implicitly. Examples are presented in which the proposed interpolation scheme was used to reproduce the equations of a hemisphere.
Substrates at the Apollo 15 and 16 sites were analyzed and showed essentially the same graphic mean, graphic standard deviation, and graphic skewness. The graphic kurtosis of Apollo 16 soils is slightly smaller than that of Apollo 15. In Apollo 15 soil samples, grain size and graphic standard deviation increase with depth, while the trend is reversed in Apollo 16 soil samples. Lower sphericity values for Apollo 15 samples coincide with concentrations of highly irregularly shaped glass particles. Two-dimensional sphericity of Apollo 15 samples is contoured as a function of particle size and depth below lunar surface. The results are consistent with an overall model for soil development in which samples closer to the surface are more mature in response to more prolonged reworking of meteorite impact.
In the present paper, the light scattering characteristics of spheroidal particles are evaluated within the framework of a scattering theory developed for a homogeneous isotropic spheroid. This approach is shown to be well suited for computing the scattering quantities of spheroidal particles of fairly large sizes (up to a size parameter of 30). The effects of particle size, shape, index of refraction, and orientation on the scattering efficiency factors and the scattering intensity functions are studied and interpreted physically. It is shown that, in the case of oblique incidence, the scattering properties of a long slender prolate spheroid resemble those of an infinitely long circular cylinder.
The use of a self pulsed laser system for accurately describing the surface shape of large space deployed antenna structures was evaluated. Tests with a breadboard system verified functional operation with short time resolution on the order of .2 mm, nonambiguous ranging, and a maximum range capability on the order of 150 m. The projected capability of the system is resolution of less than .1 mm over a reasonable time period and a range extension to over 300 m.
A general design method was developed for steady, three dimensional, potential, incompressible or subsonic-compressible flow. In this design method, the flow field, including the shape of its boundary, was determined for arbitrarily specified, continuous distributions of velocity as a function of arc length along the boundary streamlines. The method applied to the design of both internal and external flow fields, including, in both cases, fields with planar symmetry. The analytic problems associated with stagnation points, closure of bodies in external flow fields, and prediction of turning angles in three dimensional ducts were reviewed.
A Curtis matrix is used to compute cooling by the 15 micron and 10 micron bands of carbon dioxide. Escape of radiation to space and exchange the lower boundary are used for the 9.6 micron band of ozone. Voigt line shape, vibrational relaxation, line overlap, and the temperature dependence of line strength distributions and transmission functions are incorporated into the Curtis matrices. The distributions of the atmospheric constituents included in the algorithm, and the method used to compute the Curtis matrices are discussed as well as cooling or heating by the 9.6 micron band of ozone. The FORTRAN programs and subroutines that were developed are described and listed.
With over forty satellites in geostationary orbit, and many more planned, it is becoming increasingly difficult to find suitable orbit positions for new systems operating at 4 and 6 GHz. Efficient spectrum-orbit utilization can be achieved with frequency-reuse techniques - orthogonal polarization, earth-station antenna discrimination, and satellite antenna discrimination - provided that service-area geography is considered. Service arc - that portion of the orbit which affords useful service to all points in a given area - is a function of the area's climate, terrain, and location as well as its size and shape. Of the three techniques, satellite antenna discrimination is the most sensitive to these factors. According to the BSS (broadcasting-satellite service) antenna reference pattern, the maximum discrimination possible is the on-axis gain, which can be as high as 49 dB for a beamwidth of 0.6 degrees, or as low as 32 dB for a 3.5-degree beamwidth. Unlike the Fixed-Satellite Service (FSS), the BSS will normally have beams that cover no more than one or two time zones.
Measurements of the hydrodynamic pressure fluctuation levels showed that, for circular obstructions with a flow passage diameter less than one-half of the pipe diameter, hydrodynamic pressure fluctuations were small compared with the acoustic pressure, at locations greater than ten pipe diameters downstream of the restrictions. Thus, in the study currently reported, which was concentrated on measurement of the modal characteristics of the sound field downstream of the restrictions, special techniques to avoid contamination by hydrodynamic 'noise' were not necessary. The major results obtained in the study are scaling laws for the shape of the modal pressure spectrum and for the overall efficiency of noise generation. The characteristics of the modal pressure spectra are discussed. It is shown that the primary parameter controlling the spectrum shape is the frequency ratio (Helmholtz number/Strouhal number). The efficiency levels when plotted as a function of Mach number show a strong dependence on restriction size
Design requirements for photovoltaic modules and arrays used in commercial and industrial applications were identified. Building codes and referenced standards were reviewed for their applicability to commercial and industrial photovoltaic array installation. Four general installation types were identified - integral (replaces roofing), direct (mounted on top of roofing), stand-off (mounted away from roofing), and rack (for flat or low slope roofs, or ground mounted). Each of the generic mounting types can be used in vertical wall mounting systems. This implies eight mounting types exist in the commercial/industrial sector. Installation costs were developed for these mounting types as a function of panel/module size. Cost drivers were identified. Studies were performed to identify optimum module shapes and sizes and operating voltage cost drivers. The general conclusion is that there are no perceived major obstacles to the use of photovoltaic modules in commercial/industrial arrays.
The coupled differential equations of motion of the blades of a horizontal axis wind turbine are solved numerically, permitting the optimization of the design at relatively low cost. The equation of motion is transformed into a set of first order equations and solved with fourth order Runge-Kutta integrators. This technique is applied to a twisted, tapered blade of variable cross section and stiffness including discontinuities. The first six natural frequencies and mode shapes are obtained. The polar moment of inertia of the blades is obtained as a function of frequency and rotational speed.
A tetrahedral beam that can be compactly stowed, sequentially deployed, and widely manipulated to provide a structurally sound yet highly maneuverable truss structure is comprised of a number of repeating units of tandem tetralhedral sharing common sides. Fixed length battens are jointed into equilateral triangles called batten frames. Apexes of adjacent triangles are interconnected by longerons having a mid-point folding hinge. Joints, comprised of gussets pivotabley connected by links, permit two independent degrees of rotational freedom between joined adjacent batten frames, and provide a stable structure from packaged configuration to complete deployment. The longerons and joints can be actuated in any sequence, independently of one another. The beam is suited to remote actuation. Longerons may be provided with powered mid-point hinges enabling beam erection and packaging under remote control. Providing one or more longerons with powered telescoping segments permits the shape of the beam central axis to be remotely manipulated so that the beam may function as a remote manipulator arm.
A versatile multifunction package, POLYSITE, developed for Goddard's Land Analysis System, is described which simplifies the process of interactively selecting and correcting the sites used to study Landsat TM and MSS images. Image switching between the zoomed and nonzoomed image, color and shape cursor change and location display, and bit plane erase or color change, are global functions which are active at all times. Local functions possibly include manipulation of intensive study areas, new site definition, mensuration, and new image copying. The program is illustrated with the example of a full TM maser scene of metropolitan Washington, DC.
A comparison between Voyager 2 UV spectrometer data for stellar occultations of the Uranian ring system obtained at 0.11 microns and 2.2-micron earth-based occultation data reveals the anticipated factor-of-two reduction in observed optical depths relative to those observed from earth. This is due to Voyager's proximity to the rings, which allows light diffracted out of the direct beam by ring particles to be replaced by light diffracted into the direct beam light from other particles, and further permits the placing of firm lower limits on typical particle sizes of 0.3 and 1 cm for the epsilon and delta rings, respectively. As a function of true anomaly, the epsilon ring profile is noted to remain very similar in shape and essentially constant in equivalent depth, even very near periapse.
An interactive procedure to construct grids about fighter aircraft configurations using a 'state-of-the-art' workstation is described. A multiple-block grid topology is used to minimize grid skewness. Grid points on the surface of a configuration are precomputed and stored on the faces of appropriate blocks. Grid points at intermediate and far field boundary surfaces are computed with analytical functions and stored on appropriate faces. Grid points in the interior of blocks are computed using transfinite interpolation with Lagrangian and exponential blending functions. Interactive software has been written for the IRIS 3030 graphics workstation to control the shape and spacing of grid points on intermediate and far field boundaries, and to control the interior interpolation.
Adhesive energies are computed for flat and atomically sharp tips as a function of the normal distance to the substrate. The dependence of binding energies on tip shape is investigated. The magnitudes of the binding energies for the atomic force microscope are found to depend sensitively on tip material, tip shape and the sample site being probed. The form of the energy-distance curve, however, is universal and independent of these variables, including tip shape.
Doubly excited 3P(e) resonant states in Ps(-) are calculated using a method of complex-coordinate rotation. Resonance parameters (both resonance positions and widths) for doubly excited states associated with the n = 2, 3, 4, 5, and 6 thresholds of positronium atoms are evaluated using elaborate Hylleraas-type functions. In addition to ten Feshbach-type resonances lying below various Ps thresholds, three shape resonances were identified, one each lying above the n = 2, 4, and 6 Ps thresholds. It is further noted that the energy levels for the present 3P(e) states are nearly degenerate with respect to the previously calculated 1P(0) states. Such a symmetric character suggests that the highly and doubly excited Ps(-), similar to its counterpart in H(-), would exhibit rovibrational behaviors analogous to those of XYX triatomic molecules.