Model of human-operator response to step transitions in controlled element dynamics
Derivation of analytical model to predict operator transition response
MATHEMATICAL MODEL↗
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Comparison of analytical and physical modeling of planetesimal accumulation
Three cases for which the analytic solutions to the planetary embryo coagulation equation are known, namely those of constant coagulation rate, of rate proportional to the sum of the masses of the two colliding bodies, and of rate proportional to the product of their masses, are presently used to test the mathematical validity of the Wetherill and Stewart (1989) physical model for the evolution of planetary embryos' mass distribution. In all cases, excellent agreement is found between numerical physical modeling results and those of the analytic solutions. The treatment of the runaway case can proceed via extension of the efforts of Trubnikov (1971).
Wetherill, George W.↗
Helicopter mathematical models and control law development for handling qualities research
Progress made in joint NASA/Army research concerning rotorcraft flight-dynamics modeling, design methodologies for rotorcraft flight-control laws, and rotorcraft parameter identification is reviewed. Research into these interactive disciplines is needed to develop the analytical tools necessary to conduct flying qualities investigations using both the ground-based and in-flight simulators, and to permit an efficient means of performing flight test evaluation of rotorcraft flying qualities for specification compliance. The need for the research is particularly acute for rotorcraft because of their mathematical complexity, high order dynamic characteristics, and demanding mission requirements. The research in rotorcraft flight-dynamics modeling is pursued along two general directions: generic nonlinear models and nonlinear models for specific rotorcraft. In addition, linear models are generated that extend their utilization from 1-g flight to high-g maneuvers and expand their frequency range of validity for the design analysis of high-gain flight control systems. A variety of methods ranging from classical frequency-domain approaches to modern time-domain control methodology that are used in the design of rotorcraft flight control laws is reviewed. Also reviewed is a study conducted to investigate the design details associated with high-gain, digital flight control systems for combat rotorcraft. Parameter identification techniques developed for rotorcraft applications are reviewed.
Chen, Robert T. N.↗
Model Verification of Mixed Dynamic Systems
MOVER uses experimental data to verify mathematical models of "mixed" dynamic systems. The term "mixed" refers to interactive mechanical, hydraulic, electrical, and other components. Program compares analytical transfer functions with experiment.
Evensen, D. A.↗
Measurement of trace levels of chlorine in the stratosphere
Mathematical models of stratospheric ozone have predicted a reduction in the total ozone due to chlorofluoromethanes released into the atmosphere. Analytical procedures for the collection of air in the stratosphere and for analysis of these air samples for trace levels of chlorine, regardless of the state of chemical composition were developed. Calibration experiments are conducted in order to validate all methods and procedures. Results of neutron activation analysis calibration procedures using standard chlorine gases are included.
Warren, D. C.↗
Equilibrium and tearing stability of thin current layers in magnetic arcades
The MHD equilibrium of a thin, force-free current layer in a magnetic arcade is solved analytically. Various approximations are made in order to achieve a lowest order description that is physically relevant as well as mathematically tractable: The arcade is assumed to emanate from feet that are well localized, the current emanates from a localized sheet within the feet and is relatively weak. The resulting expressions for B (sup arrow) are relatively simple and natural flux coordinates are identifiable. The stability of such a current sheet to resistive filamentation is then investigated.
Hassam, A. B.↗
Shielding from space radiations
This Progress Report covering the period of 1 June 1993 to 1 Dec. 1993 presents the development of an analytical solution to the heavy ion transport equation in terms of a one-layer Green's function formalism. The mathematical developments are recasted into an efficient computer code for space applications. The efficiency of this algorithm is accomplished by a nonperturbative technique of extending the Green's function over the solution domain. The code may also be applied to accelerator boundary conditions to allow code validation in laboratory experiments. Results from the isotopic version of the code with 80 isotopes present for a single layer target material, for the case of an Iron beam projectile at 600 MeV/nucleon in water is presented.
Chang, C. Ken↗
Shielding from space radiations
This Progress Report covering the period of 1 June 1993 to 1 Dec. 1993 presents the development of an analytical solution to the heavy ion transport equation in terms of a one-layer Green's function formalism. The mathematical developments are recasted into an efficient computer code for space applications. The efficiency of this algorithm is accomplished by a nonperturbative technique of extending the Green's function over the solution domain. The code may also be applied to accelerator boundary conditions to allow code validation in laboratory experiments. Results from the isotopic version of the code with 80 isotopes present for a single layer target material, for the case of an iron beam projectile at 600 MeV/nucleon in water is presented.
Chang, C. Ken↗
On the numerical computation of nonlinear force-free magnetic fields
An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from a source surface, given the proper boundary conditions. The results of this work; describing the mathematical formalism that was developed, the numerical techniques employed, and the stability criteria developed for these numerical schemes are presented. An analytical solution is used for a test case; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent ( 5%).
Wu, S. T.↗
Interactive aircraft flight control and aeroelastic stabilization
Aeroservoelastic optimization techniques were studied to determine a methodology for maximization of the stable flight envelope of an idealized, actively controlled, flexible airfoil. The equations of motion for the airfoil were developed in state-space form to include time-domain representations of aerodynamic forces and active control. The development of an optimization scheme to stabilize the aeroelastic system over a range of airspeeds, including the design airspeed is outlined. The solution approach was divided in two levels: (1) the airfoil structure, with a design variable represented by the shear center position; and (2) the control system. An objective was stated in mathematical form and a search was conducted with the restriction that each subsystem be constrained to be optimal in some sense. Analytical expressions are developed to compute the changes in the eigenvalues of the closed-loop, actively controlled system. A stability index is constructed to ensure that stability is present at the design speed and at other airspeeds away from the design speed.
Weisshaar, T. A.↗
Microdynamic modelling of joint-dominated truss-based structures
A methodology for the mathematical modeling of preloaded joint-dominated truss-based space structures applicable in the microdynamic regime is presented. First, various factors which could affect the microdynamic behavior of joint-dominated truss structures are examined. Then, mathematical models for various types of joints involving contact deformations are derived from Hertzian contact theory. Their dynamic behavior is studied analytically and numerically by means of computer simulation. It was found that both synchronous and asynchronous oscillations having the same orders of magnitude are excited by sinusoidal load perturbations in the microdynamic regime. These oscillations persist even in the presence of light linear damping. The integration of the derived joint models with those for the elastic links of preloaded planar truss structures is discussed.
Wang, P. K. C.↗
Investigation of Three Analytical Hypothesis for Determining Material Creep Behavior under Varied Loads, with an Application to 2024-T3 Aluminum-Alloy Sheet in Tension at 400 F
Three existing hypotheses are formulated mathematically to estimate tensile creep strain under varied loads and constant temperature from creep data obtained under constant load and constant temperature. hypotheses investigated include the time-hardening, strain-hardening, and life-fraction rules. Predicted creep behavior is compared with data obtained from tensile creep tests of 2024-T3 aluminum-alloy sheet at 400 F under cyclic-load conditions. creep strain under varied loads is presented on the basis of an equivalent stress, derived from the life-fraction rule, which reduces the varied-load case to a constant-load problem. Creep strain in the region of interest for structural design and rupture times, determined from the hypotheses investigated, are in fair agreement with data in most cases, although calculated values of creep strain are generally greater than the experimental values because creep recovery is neglected in the calculations.
Berkovits, Avraham↗
A Boltzmann machine for the organization of intelligent machines
In the present technological society, there is a major need to build machines that would execute intelligent tasks operating in uncertain environments with minimum interaction with a human operator. Although some designers have built smart robots, utilizing heuristic ideas, there is no systematic approach to design such machines in an engineering manner. Recently, cross-disciplinary research from the fields of computers, systems AI and information theory has served to set the foundations of the emerging area of the design of intelligent machines. Since 1977 Saridis has been developing an approach, defined as Hierarchical Intelligent Control, designed to organize, coordinate and execute anthropomorphic tasks by a machine with minimum interaction with a human operator. This approach utilizes analytical (probabilistic) models to describe and control the various functions of the intelligent machine structured by the intuitively defined principle of Increasing Precision with Decreasing Intelligence (IPDI) (Saridis 1979). This principle, even though resembles the managerial structure of organizational systems (Levis 1988), has been derived on an analytic basis by Saridis (1988). The purpose is to derive analytically a Boltzmann machine suitable for optimal connection of nodes in a neural net (Fahlman, Hinton, Sejnowski, 1985). Then this machine will serve to search for the optimal design of the organization level of an intelligent machine. In order to accomplish this, some mathematical theory of the intelligent machines will be first outlined. Then some definitions of the variables associated with the principle, like machine intelligence, machine knowledge, and precision will be made (Saridis, Valavanis 1988). Then a procedure to establish the Boltzmann machine on an analytic basis will be presented and illustrated by an example in designing the organization level of an Intelligent Machine. A new search technique, the Modified Genetic Algorithm, is presented and proved to converge to the minimum of a cost function. Finally, simulations will show the effectiveness of a variety of search techniques for the intelligent machine.
Moed, Michael C.↗
Frost formation on an airfoil: A mathematical model 1
A computer model to predict the frost formation process on a flat plate was developed for application to most environmental conditions under which frost occurs. The model was analytically based on a generalized frost thermal conductivity expression, on frost density and thickness rate equations, and on modified heat and mass transfer coefficients designed to fit the available experimental data. The broad experimental ranges reflected by the extremes in ambient humidities, wall temperatures, and convective flow properties in the various publications which were examined served to severely test the flexibility of the model. An efficient numerical integration scheme was developed to solve for the frost surface temperature, density, and thickness under the changing environmental conditions. The comparison of results with experimental data was very encouraging.
Dietenberger, M.↗
Analysis of the injection of a heated turbulent jet into a cross flow
The development of a theoretical model is investigated of the incompressible jet injection process. The discharge of a turbulent jet into a cross flow was mathematically modeled by using an integral method which accounts for natural fluid mechanisms such as turbulence, entrainment, buoyancy, and heat transfer. The analytical results are supported by experimental data and demonstrate the usefulness of the theory for estimating the trajectory and flow properties of the jet for a variety of injection conditions. The capability of predicting jet flow properties, as well as two- and three-dimensional jet paths, was enhanced by obtaining the jet cross-sectional area during the solution of the conservation equations. Realistic estimates of temperature in the jet fluid were acquired by accounting for heat losses in the jet flow due to forced convection and to entrainment of free-stream fluid into the jet.
Campbell, J. F.↗
An efficient code for the simulation of nonhydrostatic stratified flow over obstacles
The physical model and computational procedure of the code is described in detail. The code is validated in tests against a variety of known analytical solutions from the literature and is also compared against actual mountain wave observations. The code will receive as initial input either mathematically idealized or discrete observational data. The form of the obstacle or mountain is arbitrary.
Pihos, G. G.↗
Three-axis attitude determination from vector observations
Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations. The first of these, the TRIAD algorithm, provides a deterministic (i.e., nonoptimal) solution for the attitude based on two vector observations. The second, the QUEST algorithm, is an optimal algorithm which determines the attitude that achieves the best weighted overlap of an arbitrary number of reference and observation vectors. Analytical expressions are given for the covariance matrices for the two algorithms using a fairly realistic model for the measurement errors. The mathematical relationship of the two algorithms and their relative merits are discussed and numerical examples are given. The advantage of computing the covariance matrix in the body frame rather than in the inertial frame (e.g., in terms of Euler angles) is emphasized. These results are valuable when a single-frame attitude must be computed frequently. They will also be useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.
Shuster, M. D.↗
Analytical techniques for the analysis of stall/spin flight test data
Analytical techniques for the analysis of stall/spin flight test data are reviewed by discussing (1) certain special flight instrumentation issues, (2) the mathematical modeling techniques, and (3) the analysis of post stall and spinning flight of general aviation airplanes. The angles of attack, sideslip, roll, pitch, and yaw are derived from measurements of angular velocity and linear acceleration. The key to the success of this approach is to simultaneously estimate both the biases in the instrumentation and the initial conditions. Techniques for determining stability derivatives from flight data are applied to angles of attack too high for stabilized flight. This practice greatly expands the range over which aerodynamic characteristics can be determined from flight test. Nonlinear terms in certain aerodynamic functions are shown to be valid by comparing them with the trends of results at different angles of attack. A very old technique of studying spins is extended and applied to some modern light airplanes. Airplanes for which the wing provides the dominant moments during spins, offer the possibility of linking spin characteristics to longitudinal data.
Taylor, L. W., Jr.↗