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At least 1,297 records · Page 72

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NASA NTRS1973

Modeling a particular class of multiple-input/multiple-output black boxes with stochastic integral equations and identifying the required parameters

A method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenological in that it is desired that calculations made using the mathematical model should be close to what is actually observed at the output of the black box. How close is defined in the problem statement.

Eyman, E. D.↗

NASA NTRS1974

A comparison of two types of structural optimization procedures for satisfying flutter requirements

A comparison is made of results obtained from mathematical programming and optimality criteria procedures for the minimum-mass design of typical aircraft wing structures to satisfy prescribed flutter requirements. The mathematical programming method is based on an interior penalty function approach. A rigorous optimality criterion and an intuitive optimality criterion based on uniform strain energy density are considered. An intuitive resizing procedure is used for both optimality criterion solutions. All results are calculated using the same computer program, changing only the optimization procedure. Both high- and low-aspect-ratio wings are examined. Finite elements are used for structural modeling, and the generalized coordinates for the flutter solution are based on the natural vibration modes of the structure.

Haftka, R. T.↗

NASA NTRS1974

Parameter estimation for terrain modeling from gradient data

This paper developes a method for mathematically modeling terrain surfaces for use on an unmanned Martian vehicle. The data collected by the vehicle consists of terrain height and two directional slopes at each data point. The parameters for the mathematical terrain model are stochastically determined by using least square approximations.-

Shen, C. N.↗

NASA NTRS1974

External field effects on solidification - Macroscopic and microscopic models

Comparison of theoretical effects of magnetic and gravitational fields on melts of metals and semiconductors provides two kinds of insight into space processing materials problems. First, the task of comparing effects of the two fields yields mathematical models which may be used to estimate material properties and responses to processing under various field conditions. Then, by using these models, microgravity effects can be inferred from magnetic field data already obtained in laboratories on earth. Magnetohydrodynamics (static and oscillating fields) and the Free Volume Model are used to study macroscopic effects, and Sekerka's interface stability theory is used to show how external fields can affect microsegregation. It is demonstrated that the mathematical formalism is essentially the same for describing macroscopic effects of both microgravity and magnetic fields.

Miller, R. I.↗

NASA NTRS1975

Power spectrum analysis of staggered quadriphase-shift-keyed signals

Mathematical analysis of power spectrum of outputs from high-reliability communication system is used to determine system bandwidth. Analysis provides mathematical relationships of signal power spectrum at output of hard limiter for any type of baseband pulse input subjected only to output parameter constraints.

Mcwhorter, F. L.↗

NASA NTRS1975

Certain aspects of the psychological analysis of programmer activity

The psychological analysis of programmer activity showed that one of its basic characteristics is the need to employ formal languages. In determining ways of effectively mastering the capacity to write algorithms in the algorithmic language, it is expedient to proceed from its similarity to the living languages and the language of mathematical formulas, and to choose certain psychological principles of mastering foreign languages and mathematical symbols in teaching the algorithmic language. General models of the input language significantly increase the effectiveness of its mastery and permit the development of thinking on the part of the students.

Bondarovskaya, V. M.↗

NASA NTRS1975

Analysis of ground reflection of jet noise obtained with various microphone arrays over an asphalt surface

Ground reflection effects on the propagation of jet noise over an asphalt surface are discussed for data obtained using a 33.02-cm diameter nozzle with microphones at several heights and distances from the nozzle axis. Ground reflection effects are analyzed using the concept of a reflected signal transfer function which represents the influence of both the reflecting surface and the atmosphere on the propagation of the reflected signal in a mathematical model. The mathematical model used as a basis for the computer program was successful in significantly reducing the ground reflection effects. The range of values of the single complex number used to define the reflected signal transfer function was larger than expected when determined only by the asphalt surface. This may indicate that the atmosphere is affecting the propagation of the reflected signal more than the asphalt surface. The selective placement of the reinforcements and cancellations in the design of an experiment to minimize ground reflection effects is also discussed.

Miles, J. H.↗

NASA NTRS1975

System analysis of a piston steam engine employing the uniflow principle, a study in optimized performance

Results are reported which were obtained from a mathematical model of a generalized piston steam engine configuration employing the uniflow principal. The model accounted for the effects of clearance volume, compression work, and release volume. A simple solution is presented which characterizes optimum performance of the steam engine, based on miles per gallon. Development of the mathematical model is presented. The relationship between efficiency and miles per gallon is developed. An approach to steam car analysis and design is presented which has purpose rather than lucky hopefulness. A practical engine design is proposed which correlates to the definition of the type engine used. This engine integrates several system components into the engine structure. All conclusions relate to the classical Rankine Cycle.

Peoples, J. A.↗

NASA NTRS1975

The finite element method in low speed aerodynamics

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.

Baker, A. J.↗

NASA NTRS1972

Thermal Network Modelling Handbook

Thermal mathematical modelling is discussed in detail. A three-fold purpose was established: (1) to acquaint the new user with the terminology and concepts used in thermal mathematical modelling, (2) to present the more experienced and occasional user with quick formulas and methods for solving everyday problems, coupled with study cases which lend insight into the relationships that exist among the various solution techniques and parameters, and (3) to begin to catalog in an orderly fashion the common formulas which may be applied to automated conversational language techniques.

Source record↗

NASA NTRS1975

An adaptive maneuvering logic computer program for the simulation of one-to-one air-to-air combat. Volume 2: Program description

A detailed description is presented of the computer programs in order to provide an understanding of the mathematical and geometrical relationships as implemented in the programs. The individual sbbroutines and their underlying mathematical relationships are described, and the required input data and the output provided by the program are explained. The relationship of the adaptive maneuvering logic program with the program to drive the differential maneuvering simulator is discussed.

Burgin, G. H.↗

NASA NTRS1975

Weight minimization of structures for fixed flutter speed via an optimality criterion

A rigorous optimality criterion is derived and a hybrid weight-reduction algorithm developed for the weight minimization of lifting surfaces with a constraint on flutter speed. The weight-reduction algorithm incorporates a simple recursion formula derived from the optimality criterion. Monotonic weight reduction is accomplished by dynamically adjusting a parameter in the recursion formula so as to achieve a predetermined weight decrease. The algorithm thus combines the simplicity of optimality-criterion methods with the convergence characteristics of mathematical-programming methods. The imposition of the flutter constraint is simplified by forcing to zero the imaginary part of the flutter eigenvalue, with the airspeed fixed. Four examples are discussed. The results suggest that significant improvements in efficiency are possible, in comparison with techniques based purely on mathematical programming.

Segenreich, S. A.↗

NASA NTRS1975

A new structural analysis/synthesis capability - ACCESS

The creation of an efficient automated capability for minimum weight design of structures is reported. The ACCESS 1 computer program combines finite element analysis techniques and mathematical programming algorithms using an innovative collection of approximation concepts. Design variable linking, constraint deletion techniques and approximate analysis methods are used to generate a sequence of small explicit mathematical programming problems which retain the essential features of the design problem. Organization of the finite element analysis is carefully matched to the design optimization task. The efficiency of the ACCESS 1 program is demonstrated by giving results for several example problems.

Schmit, L. A.↗

NASA NTRS1975

Analysis of ground reflection of jet noise obtained with various microphone arrays over an asphalt surface

Ground reflection effects on the propagation of jet noise over an asphalt surface are discussed for data obtained using a 33.02 cm (13-in.) diameter nozzle with microphones at several heights and distances from the nozzle axis. Analysis of ground reflection effects is accomplished using the concept of a reflected signal transfer function which represents the influence of both the reflecting surface and the atmosphere on the propagation of the reflected signal in a mathematical model. The mathematical model used as a basis for the computer program was successful in significantly reducing the ground reflection effects. The range of values of the single complex number used to define the reflected signal transfer function was larger than expected when determined only by the asphalt surface. This may indicate that the atmosphere is affecting the propagation of the reflected signal more than the asphalt surface. Also discussed is the selective placement of the reinforcements and cancellations in the design of an experiment to minimize ground reflection effects.

Miles, J. H.↗

NASA NTRS1975

Electrophoretic separator for purifying biologicals

Mathematical expressions were developed to describe the interrelationships between operating requirements (capabilities), cell parameters, and system constraints in terms of design criteria definition. The mathematical model was programmed for computer solution. The model was exercised to identify performance-limiting characteristics, and analyses were conducted to predict operation in space of an experiment involving separation of four components. An engineering model of a flowing electrophoretic separator was constructed. The design is directed toward verifying improvements in resolution and throughput of a thicker cell than can be used on earth.

Source record↗

NASA NTRS1975

NASA/MSFC multilayer diffusion models and computer programs, version 5

The transport and diffusion models and algorithms developed for use by NASA in predicting concentrations and dosages downwind from normal and abnormal launches of rocket vehicles are described along with the associated computer programs for use in performing the calculations. Topics discussed include: the mathematical specifications and procedures used in the Preprocessor Program to calculate rocket exhaust cloud rise, cloud dimensions, and other input parameters to the transport and diffusion models; the revised mathematical specifications for the Multilayer Diffusion Models; users' instructions for implementing the Preprocessor and Multilayer Diffusion Models Programs; and worked example problems illustrating the use of the models and computer programs.

Dumbauld, R. K.↗

NASA NTRS1976

The passage of a distorted velocity field through a cascade of airfoils

An analysis has been developed to predict the unsteady force and moment generated by the passage of a timewise periodic total pressure distortion through an arbitrary cascade of airfoils. The mathematical formulation of this analysis is based on the assumption that the magnitudes of the timewise fluctuations of the variables which describe the flow field are small compared to their time average values. This assumption permits the development of a linear unsteady perturbation analysis about a steady flow field. In addition to this linearization assumption the fluid medium is assumed to be incompressible and inviscid. The mathematical development begins by decomposing the velocity field surrounding an infinite cascade of airfoils into its irrotational and rotational components. The rotational component is associated with an upstream unsteady total pressure distortion and is defined in terms of the vorticity field associated with the distortion pattern. The irrotational component is further decomposed into a steady and unsteady part. A combined analytical and numerical procedure has been developed to solve the field equations which govern the rotational and irrotational velocity fields. Results of this analysis show a strong influence of mean loading on the unsteady force generated by the passage of a one dimensional gust through a cascade of compressor blades.

Adamczyk, J. J.↗

NASA NTRS1976

Unsteady aerodynamic flow field analysis of the space shuttle configuration. Part 3: Unsteady aerodynamics of bodies with concave nose geometries

An analysis of the unsteady aerodynamics of bodies with concave nose geometries was performed. The results show that the experimentally observed pulsating flow on spiked bodies and in forward facing cavities can be described by the developed simple mathematical model of the phenomenon. Static experimental data is used as a basis for determination of the oscillatory frequency of spike-induced flow pulsations. The agreement between predicted and measured reduced frequencies is generally very good. The spiked-body mathematical model is extended to describe the pulsations observed in forward facing cavities and it is shown that not only the frequency but also the pressure time history can be described with the accuracy needed to predict the experimentally observed time average effects. This implies that it should be possible to determine analytically the impact of the flow pulsation on the structural integrity of the nozzles for the jettisoned empty SRM-shells.

Ericsson, L. E.↗