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The differential maneuvering simulator for simulating two aircraft or spacecraft operating in a differential mode is described. Tests made to verify that the system could provide the required simulated aircraft motions are given. The mathematical model which converts computed aircraft motions into the required motions of the various projector gimbals is described.
A series of three computer programs for the mathematical analysis of navigation and guidance of lunar and interplanetary trajectories was developed. All three programs require the integration of n-body trajectories for both interplanetary and lunar missions. The virutal mass technique is used in all three programs. The user's manual contains the information necessary to operate the programs. The input and output quantities of the programs are described. Sample cases are given and discussed.
A mathematical model and digital computer simulation of the human cardiovascular system and its controls have been developed to simulate pulsatile dynamic responses to the cardiovascular experiments of the Skylab missions and to selected physiological stresses of manned space flight. Specific model simulations of the bicycle ergometry, lower body negative pressure, and tilt experiments have been developed and verified for 1-g response by comparison with available experimental data. The zero-g simulations of two Skylab experiments are discussed.
The statistical characteristics of the SKYLAB S-193 altimeter altitude noise are considered. These results are reported in a concise format for use and analysis by the scientific community. In most instances the results have been grouped according to satellite pointing so that the effects of pointing on the statistical characteristics can be readily seen. The altimeter measurements and the processing techniques are described. The mathematical descriptions of the computer programs used for these results are included.
In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.
A generalized, real time, piloted, visual simulation of a single rotor helicopter, suspension system, and external load is described and validated for the full flight envelope of the U.S. Army CH-54 helicopter and cargo container as an example. The mathematical model described uses modified nonlinear classical rotor theory for both the main rotor and tail rotor, nonlinear fuselage aerodynamics, an elastic suspension system, nonlinear load aerodynamics, and a loadground contact model. The implementation of the mathematical model on a large digital computing system is described, and validation of the simulation is discussed. The mathematical model is validated by comparing measured flight data with simulated data, by comparing linearized system matrices, eigenvalues, and eigenvectors with manufacturers' data, and by the subjective comparison of handling characteristics by experienced pilots. A visual landing display system for use in simulation which generates the pilot's forward looking real world display was examined and a special head up, down looking load/landing zone display is described.
A mathematical model and digital computer simulation of the human cardiovascular system and its controls were developed to simulate transient responses to bicycle ergometer exercise. The purpose of the model was to provide a method to analyze cardiovascular control hypotheses which cannot be easily tested in an animal or human or in a spaceflight environment.
The frequency spectra and corresponding beat frequencies created by the relative motions between multiple Solar Power Satellites due to solar wind, lunar gravity, etc. were analyzed. The results were derived mathematically and verified through computer simulation. Frequency spectra plots were computer generated. Detailed computations were made for the seven following locations in the continental US: Houston, Tx.; Seattle, Wa.; Miami, Fl.; Chicago, Il.; New York, NY; Los Angeles, Ca.; and Barberton, Oh.
A 150 mlb thrust level hybrid resistojet which may operate on either H2 or NH3 is described whose design technique allows temperature distribution forecasting by means of a microcomputer-implemented mathematical model. The longer computer run times that accompany the exclusive use of BASIC, relative to assembled languages, are offset by the flexibility offered and the reduction of reprogramming and debugging efforts. The integration of a compact first-stage coiled heater with a concentric tubular gas heater offers direct matching of the 28 V terminal of the spacecraft system, while keeping maximum heater wall temperatures to less than 60 K over that of the gas temperature at the throat. Among the novel materials employed are grain-stabilized rhenium for heating elements and high purity aluminas for insulators.
Investigations into the forces which govern the geometric configuration of the liquid vapor interface in Grumman's high capacity monogroove Heat Pipe are made. Two separate methods are used to determine the time to prime and computer programs using these mathematical techniques are developed and presented. A description of the two techniques along with a discussion of the variation of the results follows. In addition, experimental procedures for tests designed to verify modeling predictions are described.
A computer simulation of a mathematical circulation model is used to study the alterations of body fluids and their electrolyte composition that occur in weightlessness. The behavior of the renal-regulating hormones which control these alterations is compared in simulations of several one-g analogs of weightlessness and space flight. It is shown that the renal-regulating hormones represent a tightly coupled system that responds acutely to volume disturbances and chronically to electrolyte disturbances. During hypogravic conditions these responses lead to an initial suppression of hormone levels and a long-term effect which varies depending on metabolic factors that can alter the plasma electrolytes. In addition, it is found that if pressure effects normalize rapidly, a transition phase may exist which leads to a dynamic multiphasic endocrine response.
The role of the thundercloud in the global electric circuit has been considered by many researchers. Thus, Holzer and Saxon (1952) have constructed a simple model of a bipolar thunderstorm. The global models considered provide insight into the atmospheric electric circuit but are restricted, both by various analytical mathematical representations and by computer size, to a grid of about five degrees in latitude and longitude. A need exists, therefore, for the development of a numerical regional model capable of resolving small-scale phenomena so that their coupling into the global-scale circuit can be examined. The construction of a two-dimensional quasi-static numerical model of atmospheric electricity is discussed. The model provides a basis for the calculation of the global electric field and current distribution produced by a single thunderstorm generator. In connection with the calculations, the thunderstorm was defined by a quasi-static current source function which generates a dipole charge configuration.
Testing under variety of support conditions combined with computer analysis to update mathematical models to match test data. Report suggests dynamic characteristics of large space structures predicted, without full-scale testing, by method that combines experiment and analysis. Method, multiple-boundary-condition testing, developed for such large space structures as dish antennas, towers, and solar-cell arrays.
In this study a mathematical model and a computer code based on this model was developed to allow prediction of the product distribution in chemical reactors for converting gaseous silicon compounds to condensed-phase silicon. Specifically, the model formulated describes the silicon vapor separation/collection from the developing turbulent flow stream within reactors of the Westinghouse type. Migration of the silicon vapor to the reactor walls was described by the parametric solutions presented here, in order to reduce the experimentation necessary in the design of such reactors. Calculations relating to the collection efficiencies of such reactors are presented as a function of the reactor throughflow and distance along its length.
Mathematical models, diagrams, and computer programs involving an unmanned mission to the planet Venus are presented. This work was done in support of the proposed project called Ninevah. The specific subjects covered are trajectory analysis, propulsion analysis, and structural analysis.
The Institute conducts unclassified basic research in applied mathematics, numerical analysis, and computer science in order to extend and improve problem-solving capabilities in science and engineering, particularly in aeronautics and space. The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers. ICASE reports are considered to be primarily preprints of manuscripts that have been submitted to appropriate research journals or that are to appear in conference proceedings.
Slot timing recovery in a direct-detection optical PPM communication system can be achieved by processing the photodetector output waveform with a nonlinear device whose output forms the input to a phase-locked loop. The choice of a simple transition detector as the nonlinearity is shown to give satisfactory synchronization performance. The rms phase error of the recovered slot clock and the effect of slot timing jitter on the bit error probability were directly measured. The experimental system consisted of an AlGaAs laser diode (wavelength = 834 nm) and a silicon avalanche photodiode photodetector. The system used Q = 4 PPM signaling and operated at a source data rate of 25 Mbits/s. The mathematical model developed to compute the rms phase error of the recovered clock is shown to be in good agreement with results of actual measurements of phase errors. The use of the recovered slot clock in the receiver resulted in no significant degradation in receiver sensitivity compared to a system with perfect slot timing. The system achieved a bit error probability of 10 to the -6th at a received optical signal energy of 55 detected photons per information bit.
An effort is made to characterize the tradeoffs and overheads limiting the speedup potential theoretically projected for pipeline-incorporating computer architectures, using a mathematical model of the roles played by the various parameters. Pipeline optimization proceeds by a partitioning of the pipeline into an optimum number of segments so that maximization of throughput is obtained. Inferences are drawn from the model, and potential improvements to it are identified. Substantial agreement is obtained with Kunkel and Smith's (1986) CRAY-1S simulations of pipelining.