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The derivation is presented of the differential stiffness for triangular solid of revolution elements. The derivation takes into account the element rigid body rotation only, the rotation being about the circumferential axis. Internal pressurization of a pneumatic tire is used to illustrate the application of this feature.
Twelve airline pilots were studied to determine the effects of whole-body rotation on choice-reaction time to the horizontal motion of a line on a cathode-ray tube. On each trial, one of five levels of visual acceleration and five corresponding proportions of rotary acceleration were presented simultaneously. Reaction time to the visual motion decreased with increasing levels of visual motion and increased with increasing proportions of rotary acceleration. The results conflict with general theories of facilitation during double stimulation but are consistent with neural-clock model of sensory interaction in choice-reaction time.
We define a class of detection-estimation problems on matrix Lie groups in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear, we are able to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite-dimensional optimal solution to a nonlinear estimation problem and consist of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid-body rotational control system.
A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.
The three dimensional unsteady flow field behind a transonic compressor rotor with a design pressure ratio of 1.6 at a tip Mach number of 1.2 has been resolved on the blade passing time scale. Quantities determined were total and static pressures, tangential flow angle, and radial flow angle. The spatial and temporal resolution achieved was sufficient to determine velocity components inside individual blade wakes and in the surrounding flow. From these measurements the flow structure is described at stations immediately behind the rotor and one chord downstream. Some dominant features of the flow just behind the rotor are large radial velocity components, large static pressure fluctuations near the blade wakes, and definite unsteadiness (in rotor coordinates) of the wakes. The wake behavior one chord downstream is described in terms of the effect of the strong mean swirl on the behavior of shear disturbances. In the outer portion of the annulus, where the mean flow approximates a solid body rotation, a strong, persistent oscillatory flow is found with 16 periods in the circumference as roughly predicted by theory. In the inner portion of the annulus the disturbances attenuate axially.
A vortex-lattice technique is developed to model unsteady, incompressible flow past thin wings. This technique predicts the shape of the wake as a function of time; thus, it is not restricted by planform, aspect ratio, or angle of attack as long as vortex bursting does not occur and the flow does not separate from the wing surface. Moreover, the technique can be applied to wings of arbitrary curvature undergoing general motion; thus, it can treat rigid-body motion, arbitrary wing deformation, gusts in the freestream, and periodic motions. Numerical results are presented for low-aspect rectangular wings undergoing a constant-rate, rigid-body rotation about the trailing edge. The results for the unsteady motion are compared with those predicted by assuming quasi-steady motion. The present results exhibit hysteretic behavior.
Preliminary estimates are presented of vibratory loads and stresses in hingeless and teetering rotors for the proposed NSF-NASA Mod-0 wind power system. Preliminary blade design utilizes a tapered tubular aluminum spar which supports nonstructural aluminum ribs and skin and is joined to the rotor hub by a steel shank tube. Stresses in the shank of the blade are calculated for static, rated, and overload operating conditions. Blade vibrations were limited to the fundamental flapping modes, which were elastic cantilever bending for hingeless rotor blades and rigid-body rotation for teetering rotor blades. The MOSTAB-C computer code was used to calculate aerodynamic and mechanical loads. The teetering rotor has substantial advantages over the hingeless rotor with respect to shank stresses, fatigue life, and tower loading. The hingeless rotor analyzed does not appear to be structurally stable during overloads.
The concept of rotary-wing aircraft in general is defined. The energy effectiveness of helicopters is compared with that of other static thrust generators in hover, as well as with various air and ground vehicles in forward translation. The most important aspects of rotor-blade dynamics and rotor control are reviewed. The simple physicomathematical model of the rotor offered by the momentum theory is introduced and its usefulness and limitations are assessed. The combined blade-element and momentum theory approach, which provides greater accuracy in performance predictions, is described as well as the vortex theory which models a rotor blade by means of a vortex filament or vorticity surface. The application of the velocity and acceleration potential theory to the determination of flow fields around three dimensional, non-rotating bodies as well as to rotor aerodynamic problems is described. Airfoil sections suitable for rotors are also considered.
Three-dimensional fully self-consistent computer models were used to determine the evolution of galaxies consisting of 100 000 simulation stars. Comparison of two-dimensional simulations with three-dimensional simulations showed only a very slight stabilizing effect due to the additional degree of freedom. The addition of a fully self-consistent, nonrotating, exponential core/halo component resulted in considerable stabilization. A second series of computer experiments was performed to determine the collapse and relaxation of initially spherical, uniform density and uniform velocity dispersion stellar systems. The evolution of the system was followed for various amounts of angular momentum in solid body rotation. For initally low values of the angular momentum satisfying the Ostriker-Peebles stability criterion, the systems quickly relax to an axisymmetric shape and resemble elliptical galaxies in appearance. For larger values of the initial angular momentum bars develop and the systems undergo a much more drastic evolution.
Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.
The level C requirements for the shuttle orbiter terminal area energy management (TAEM) guidance and flight control functions to be incorporated into the Mission Control Center entry profile planning processor are described. This processor is used for preentry evaluation of the entry through landing maneuvers, and includes a simplified three degree-of-freedom model of the body rotational dynamics that is necessary to account for the effects of attitude response on the trajectory dynamics. This simulation terminates at TAEM-autoland interface.
The Level C requirements for the shuttle orbiter terminal area energy management (TAEM) guidance and flight control functions to be incorporated into the Mission Control Center entry profile planning processor are defined. This processor will be used for preentry evaluation of the entry through landing maneuvers, and will include a simplified three degree-of-freedom model of the body rotational dynamics that is necessary to account for the effects of attitude response on the trajectory dynamics. This simulation terminates at TAEM-autoland interface.
Interference fringes from superimposed beams move across a photodetector, creating electrical pulses. Frequency of pulses is direct measure of angular velocity of rotating body. If separation of the sources changes, it affects separation of all fringes equally and does not affect angular velocity measurement.
Spinning flywheels within rotor can null imbalance forces in rotor. Flywheels axes are perpendicular to each other and to rotor axis. Feedback signals from accelerometers or strain gages in platform control flywheel speeds and rotation directions. Concept should be useful for compensating rotating bodies on Earth. For example, may be applied to large industrial centrifuge, particularly if balance changes during operation.
The horizontal and vertical cloud structures, atmospheric waves, and wind velocities at the cloud top level were determined by the Pioneer Venus photopolarimeter images in the UV from January through March 1979. The images indicate long-term evolution of cloud characteristics, the atmospheric dynamics, and rapid small changes in cloud morphology. The clouds show a globally coordinated oscillation relative to latitude circles; retrograde zonal winds of 100 m/s near the equator are determined from the tracking of small-scale cloud properties, but two hemispheres show important variations. The zonal wind velocity in the southern hemisphere is reduced toward the poles at a rate similar to solid body rotation; the midlatitude jet stream noted by Mariner 10 is not observed.
The Pioneer 11 and the Voyager 1 encounters with Saturn have revealed a remarkable richness and diversity of physical phenomena. As a result of these discoveries and of continued earth-based studies, major changes have been made in the observations planned for Voyager 2. A description is presented of some of the opportunities for new observations to be made by Voyager 2, taking into account four major areas of investigation, including the atmosphere, rings, satellites, and magnetosphere. The study of the dynamics of Saturn's atmosphere is of interest because Saturn, like Jupiter, is a giant rapidly-rotating body composed mainly of hydrogen and helium, encircled by bands of clouds of frozen ammonia. More information is to be obtained concerning the B-ring and the F-ring, and images with better resolution of Hyperion and Iapetus are to be returned.
Stationary linear perturbation responses to Northern Hemisphere orography are calculated in a quasi-geostrophic barotropic model in solid-body rotation. The stationary mountain torque induced by these perturbations is then used to construct graphical solutions to the steady-state wave, mean-flow interaction problem. It is shown that multiple solutions exist in the system and are near either the forcing equilibrium of the zonal forcing or near the resonance points in the system. Some of these near-resonance solutions have block-like configurations with a confluence zone upstream from a large-amplitude structure consisting of a high at high latitudes and a low at low latitudes. These block-like configurations are shown to be near stable solutions of the system. Time-dependent calculations show that the initial state and the zonal forcing equilibrium are important in determining the long-term time evolution of the system.
A theoretical model of thermocapillary bubble motion inside a drop, located in a space laboratory, due to an arbitrary axisymmetric temperature distribution on the drop surface was constructed. Typical results for the stream function and temperature fields as well as the migration velocity of the bubble were obtained in the quasistatic limit. The motion of bubbles in a rotating body of liquid was studied experimentally, and an approximate theoretical model was developed. Comparison of the experimental observations of the bubble trajectories and centering times with theoretical predictions lends qualified support to the theory.