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Data are presented on the peak effect of a Nb-Ti alloy. The temperature dependence of the critical current at a field equal to or higher than the peak field is shown to agree with a model of a rigidly pinned vortex lattice.
Variational equations were applied to the case of a rapidly spinning triaxial body moving in an elliptic orbit, in which the orbital plane is regressing at a constant rate. The explicit differential equations obtained in this application were integrated by the method of averaging to develop secular analytical expressions, which, to first-order in a small parameter, describe the complete space motions of the rigid body under the influence of nonresonant gravity-gradient perturbations. The effects of aerodynamic torque on the rotational motion of an orbiting satellite are studied, as another example of the application of the variational equations derived and the method of averaging.
A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress intensity factor is presented graphically.
A brief description is presented of a canonical set of equations which governs the behavior of an n-body spacecraft. General results are given for the case in which the spacecraft is modeled in terms of n rigid bodies connected by dissipative elastic joints. The final equations are free from constraint torques and involve only r variables (r is the number of degrees of freedom of the system). An advantage which accompanies the elimination of the constraint torques is a decrease in the computer run time (especially when n is large).
We report a high-statistics magnetic spectrometer measurement of the geomagnetic cutoff rigidity and related effects at Palestine, Texas. The effective cutoffs we observe are in agreement with computer-calculated cutoffs. We also report measured spectra of albedo and atmospheric secondary particles that come below geomagnetic cutoff.
Materials and design technology of the all-silica LI-900 rigid surface insulation (RSI) thermal protection system (TPS) concept for the shuttle spacecraft is presented. All results of contract development efforts are documented. Engineering design and analysis of RSI strain arrestor plate material selections, sizing, and weight studies are reported. A shuttle prototype test panel was designed, analyzed, fabricated, and delivered. Thermophysical and mechanical properties of LI-900 were experimentally established and reported. Environmental tests, including simulations of shuttle loads represented by thermal response, turbulent duct, convective cycling, and chemical tolerance tests are described and results reported. Descriptions of material test samples and panels fabricated for testing are included. Descriptions of analytical sizing and design procedures are presented in a manner formulated to allow competent engineering organizations to perform rational design studies. Results of parametric studies involving material and system variables are reported. Material performance and design data are also delineated.
Several computer subroutines are designed to provide the solution to minimum-dimension sets of discrete-coordinate equations of motion for systems consisting of an arbitrary number of hinge-connected rigid bodies assembled in a tree topology. In particular, these routines may be applied to: (1) the case of completely unrestricted hinge rotations, (2) the totally linearized case (all system rotations are small), and (3) the mixed, or partially linearized, case. The use of the programs in each case is demonstrated using a five-body spacecraft and attitude control system configuration. The ability of the subroutines to accommodate prescribed motions of system bodies is also demonstrated. Complete listings and user instructions are included for these routines (written in FORTRAN V) which are intended as multi- and general-purpose tools in the simulation of spacecraft and other complex electromechanical systems.
Some methods of approaching a solution to the Hamilton-Jacobi equation are outlined and examples are given to illustrate particular methods. These methods may be used for cases where the Hamilton-Jacobi equation is not separable and have been particularly useful in solving the rigid body motion of an earth satellite subjected to gravity torques. These general applications may also have usefulness in studying the motion of satellites with aerodynamic torque and in studying space vehicle motion where thrusting is involved.
The formalism for studying perturbations of a triaxial rigid body within the Hamilton-Jacobi framework is developed. The motion of a triaxial artificial earth satellite about its center of mass is studied. Variables are found which permit separation, and the Euler angles and associated conjugate momenta are obtained as functions of canonical constants and time.
The equations of motion are derived, in vector-dyadic format, for a topological tree of coupled rigid bodies, point masses, and symmetrical momentum wheels. These equations were programmed, and form the basis for the general-purpose digital computer program N-BOD. A complete derivation of the equations of motion is included along with a description of the methods used for kinematics, constraint elimination, and for the inclusion of nongyroscope forces and torques acting external or internal to the system.
The far-field sound produced by a rigid body in arbitrary motion, with shock discontinuities close to the body, is studied. The analysis is based on the work of Ffowcs Williams and Hawkings (1969). An expression for the far-field sound pressure is obtained in the form of surface and line integrals carried out over a contracting sphere and its intersection with the body and shock surfaces. It is also found that in addition to the quadrupole distribution, the discontinuities in Lighthill stress at the shock, the fluid stresses at the body surface, and the curvatures (principal and mean) of the body and shock surfaces contribute to the sound field. Two examples are worked out.
The extent of plastic flow in a spherical solid (assumed to be homogeneous and elastically and plastically isotropic), surrounding a concentric rigid sphere was calculated as a function of applied external pressure. The applied pressure necessary to cause plastic deformation throughout the solid was obtained.
The computer program NASTRAN is used to solve electromagnetic field problems. The diffusion equation and the boundary conditions valid for problems of these kinds together with a replacing potential energy function are given. The extent to which an analogy with finite element displacement and temperature approaches holds is indicated. The outputting of complex quantities is made possible after adjustment of standard rigid format 1 input data blocks to module SDR2. The applications made involve the study of the proximity effect in a system of three parallel conductors and the analysis of the magnetic field in the vicinity of the points of contact in circuit breakers.
The acoustic slot elements, CSLOTi, are applied to analyze two-dimensional enclosures with fixed or moving boundaries. The capability utilized to compute (a) the acoustic natural modes and frequencies of a rigid walled enclosure and (b) the sound pressure at any point inside an enclosure when the surrounding walls are forced to vibrate. Applications to an automobile passenger compartment illustrate the technique. The axisymmetric fluid elements, CFLUIDi, are used in conjunction with a suitable choice of symmetry planes and a model of the surrounding structure to approximate a two-dimensional enclosure with flexible walls. The enclosure walls are modeled using finite elements or structural modes. Illustrative examples include a comparison of rectangular cavity modes with those calculated using the acoustic slot element and the free vibration modes of two enclosures coupled through a flexible rectangular panel.
The solar flare proton rigidity spectra for several flares occurring between 1967 and 1972 have been deduced from the ground level cosmic ray neutron monitor observations. To obtain consistent agreement for all the ground level events (GLEs) analyzed, the specific yield functions of Lockwood and Webber (1967) must be reduced slightly below P = 1.6 GV. The typical spectral indices of solar cosmic rays deduced for GLEs vary from 4 to 6 if the differential spectrum is represented by KP to the minus gamma power. Only occasionally is the spectrum as steep as 8 or 9. The observed spectral index is independent of the magnitude of the integral solar proton flux above 1 GV.
An analytical solution is provided of a simple control problem. A rigid symmetric spinning satellite is considered and the optimal control torque vector is obtained. It is pointed out that optimal control can be obtained even with unequal torque magnitudes.
A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress-intensity factor is presented graphically.
An experimental study was made to measure the mean flow field and acoustic power of a subsonic jet impinging normal to a large rigid surface. A 6.25 cm diameter, circular cool air jet was used at heights of 20, 10, and 5 jet diameters above the surface. The jet exit Mach number was varied from 0.28 to 0.93. Impact and static pressure surveys were made in directions both axial and lateral to the jet axis and also parallel and perpendicular to the surface. Acoustic power was calculated from microphone measurements made during each test run using a diffuse field calibration for the test facility. Results indicate that the flow field for jet impingement is characterized mainly by a strong rise in static pressure in the impingement region near the surface and by boundary layer development in the wall jet region. Acoustic power measurements generally followed a U(8) law for both the free jet and jet impingement although there was some variation especially at high Mach number and for close impingement distances. Overall noise levels increased with decreasing jet-to-surface height. Normalized power spectra correlated well for all cases when the Strouhal number was greater than 0.2; the correlation was poor when the Strouhal number was low.