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Imaginary hyperbolic grid patterns formed by three local AM broadcasting stations were utilized in study. Each hyperbola is defined by constant phase difference between arbitrary signals integrally related to those coming from two stations. When three stations are used, grid is formed covering area with intersecting hyperbolas.
A comprehensive analytical model which considers time and space development of the flow field in solid propellant rocket motors with high volumetric loading density is described. The gas dynamics in the motor chamber is governed by a set of hyperbolic partial differential equations, that are coupled with the ignition and flame spreading events, and with the axial variation of mass addition. The flame spreading rate is calculated by successive heating-to-ignition along the propellant surface. Experimental diagnostic studies have been performed with a rectangular window motor (50 cm grain length, 5 cm burning perimeter and 1 cm hydraulic port diameter), using a controllable head-end gaseous igniter. Tests were conducted with AP composite propellant at port-to-throat area ratios of 2.0, 1.5, 1.2, and 1.06, and head-end pressures from 35 to 70 atm. Calculated pressure transients and flame spreading rates are in very good agreement with those measured in the experimental system.
The major goals in re-designing the Multispectral Scanner and Data System (MSDS) sky reference are: (1) to remove the sun-elevation angle and aircraft-attitude angle dependence from the solar-sky illumination measurement, and (2) to obtain data on the optical state of the atmosphere. The present sky reference is dependent on solar elevation and provides essentially no information on important atmospheric parameters. Two sky reference designs were tested. One system is built around a hyperbolic mirror and the reflection approach. A second approach to a sky reference utilizes a fish-eye lens to obtain a 180 deg field of view. A detailed re-design of the present sky reference around the fish-eye approach, even with its limitations, is recommended for the MSDS system. A preamplifier study was undertaken to find ways of improving the noise-equivalent reflectance by reducing the noise level for silicon detector channels on the MSDS.
A user's manual for the current CONIC computer program is presented. The program was written in FORTRAN for use on the TRW Time Share system. The CONIC program is used to calculate the relative motion of two bodies in any conic-section orbit (circular, elliptical, parabolic, or hyperbolic). This manual describes the basic equations used for trajectory propagation and defines the input and output parameters of the program. Sample runs with corresponding figures and a detailed flow chart of the program are included.
Hyperbolic systems of partial differential equations governing supersonic inviscid flows are discussed and analyzed. Finite-difference analogues for integrating these systems in the interior of fluid domains are described from two points of view: a differential form approach and an integral form approach. The algorithms presented are analyzed for stability and accuracy. The concept of time splitting is discussed and supplied to these methods to achieve increased numerical efficiency. Techniques for treating conditions at the boundaries of the fluid domain and shock-wave discontinuities at surfaces within the domain are described.
An analysis of the sputtering of metal surfaces and grids by ions of medium energies is given and it is shown that an exact, nonlinear, hyperbolic wave equation for the temperature field describes the transient transport of heat in metals. Quantum statistical and perturbation theoretical analysis of surface sputtering by low energy ions are used to develop the same expression for the sputtering rate. A transport model is formulated for the deposition of sputtered atoms on system components. Theoretical efforts in determining the potential distribution and the particle velocity distributions in low pressure discharges are briefly discussed.
The purpose of this paper is to develop a sufficiently accurate analysis, which is much simpler than exact three-dimensional analysis, for statics and dynamics of composite laminates. The governing differential equations and boundary conditions are derived by following a variational approach. The displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and rotary inertia are included. A procedure for obtaining the general solution of the above governing differential equations in the form of hyperbolic-trigonometric series is given. The accuracy of the present theory is assessed by obtaining results for free vibrations and flexure of simply supported rectangular laminates and comparing them with results from exact three-dimensional analysis.
The mixed elliptic-hyperbolic relaxation method for obtaining steady-state solutions to two-dimensional transonic potential equations is extended to the transonic small disturbance equation in three dimensions. In particular, transonic flow is considered both about nonlifting wing-cylinder combinations and over thin lifting wings with sweep and taper. The treatment is restricted to freestream Mach numbers less than one and to wings with subsonic trailing edges.
The reasons for and the results of laboratory simulation studies of space plasma flow over obstacles are discussed in the context of satellite-ionosphere interactions and of forthcoming Skylab experiments. So far, it appears that ions passing through the plasma sheath are focused onto the wake axis, thereby creating an enhanced ion current which peaks at approximately a 'Mach' number of radii downstream from floating spherical bodies. The location of the peak enhancement shows a hyperbolic dependence on body potential, while its structure depends on the body cross-sectional geometry rather than on the axial dimension. There is a corresponding enhancement of the electron current coexistent with the ion-current enhancement. An electron temperature enhancement can sometimes occur in the near-wake 'ion void' region with a magnitude inversely proportional to charged particle density. Some supplementary experiments are suggested to support the planned Skylab experiments.
The present work describes a mathematical model and numerical scheme for the computer-aided calculation of two- and three-dimensional transonic flow over an isolated yawed wing with oblique shock waves and a trailing vortex sheet. The flow is modeled by the potential equation for irrotational flow which is hyperbolic at supersonic points and elliptic at subsonic points. A coordinate-invariant difference scheme is used in which retarded difference formulas are constructed to conform with the local flow direction. The resulting 'rotated' difference scheme allows complete flexibility in the choice of a coordinate system. Shock waves are located automatically in the form of compression bands spread over a few mesh widths. The scheme has proven to be stable and convergent throughout the transonic range. Calculations have been performed for Mach number up to 1.2 and yaw angles up to 60 deg, the likely operating range of a yawed-wing transport designed to fly at supersonic speeds. Calculations becomes less accurate towards upper end of range, because the difference scheme is first-order accurate in the supersonic range.
A description of the joint design, materials, equipment, qualification testing, inspection methods, and applications involved in performing induction brazing on hyperbolic propellants tubing at Kennedy Space Center. Induction brazing is a form of brazing in which the energy is transmitted to the workpiece by electrical induction; the eddy currents generated in the metal produce heat by resistance losses. Since induction heating is fast and highly localized, undesirable heat effects are minimized and the resulting braze is of high quality.
An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.
A ray-trace analysis is described of aberrations and extreme rays of a Cassegrain-type telescope with a tilted secondary mirror. The work was motivated by the need to understand the factors limiting image quality and to assist in the design of secondary mirrors for three telescopes with oscillating secondary mirrors (OSM) used at Ames Research Center for high altitude infrared astronomy. The telescopes are a 31-cm-diameter Dall-Kirkham (elliptical primary, spherical secondary) flown aboard a Lear jet, a 71-cm balloon-borne Dall-Kirkham flown on the AIROscope gondola, and a 91-cm true Cassegrain (parabolic primary, hyperbolic secondary) flown aboard a C-141 jet transport. The optics for these telescopes were not designed specifically for OSM operation, but all have OSM's and all must be used with various detector configurations; therefore, a facility that evaluates the performance of a telescope for a given configuration is useful. The analytical expressions are summarized and results for the above systems are discussed. Details of the calculation and a discussion of the computer program are given in the appendices.
Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.
On 16 May 1974, it was announced that Loran-C was chosen as the navigation system to serve the U. S. Coastal Confluence Zone. At the present time, reliable CONUS Loran-C groundwave timing coverage extends westward only about as far as Boulder, CO. The groundwave hyperbolic and timing coverage which will result from the planned CONUS expansion are illustrated. Time frames are provided. A status report on the planned reduction in Loran-C PTTI tolerances is presented.
For various applications in fluid dynamics, it is assumed that the total temperature is constant. Therefore, the energy equation can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed. It is shown that the system is strictly hyperbolic and well posed for the initial value problems. Boundary conditions are described such that the linearized system is well posed. The Hopscotch method is investigated and numerical results are presented.
Analytical methods developed for consolidation of fatigue and fatigue-crack-propagation data for use in design of metallic aerospace structural components are evaluated. A comprehensive file of data on 2024 and 7075 aluminums, Ti-6Al-4V alloy, and 300M steel was established by obtaining information from both published literature and reports furnished by aerospace companies. Analyses are restricted to information obtained from constant-amplitude load or strain cycling of specimens in air at room temperature. Both fatigue and fatigue-crack-propagation data are analyzed on a statistical basis using a least-squares regression approach. For fatigue, an equivalent strain parameter is used to account for mean stress or stress ratio effects and is treated as the independent variable; cyclic fatigue life is considered to be the dependent variable. An effective stress-intensity factor is used to account for the effect of load ratio on fatigue-crack-propagation and treated as the independent variable. In this latter case, crack-growth rate is considered to be the dependent variable. A two term power function is used to relate equivalent strain to fatigue life, and an arc-hyperbolic-tangent function is used to relate effective stress intensity to crack-growth rate.
Research in the area of split and hyperbolic comets, orbital calculations, and interstellar comets is discussed. Other topics discussed include the role of comets in galactic chemistry, gamma ray bursts, and predicted favorable visibility conditions for anomalous tails of comets.