SEARCH · Engineering Papers

Results for “Mathematics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,603 records · Page 89

All sources NASA NTRS DOE OSTI

NASA NTRS1930

The Torsion of Members Having Sections Common in Aircraft Construction

Within recent years a great variety of approximate torsion formulas and drafting-room processes have been advocated. In some of these, especially where mathematical considerations are involved, the results are extremely complex and are not generally intelligible to engineers. The principal object of this investigation was to determine by experiment and theoretical investigation how accurate the more common of these formulas are and on what assumptions they are founded and, if none of the proposed methods proved to be reasonable accurate in practice, to produce simple, practical formulas from reasonably correct assumptions, backed by experiment. A second object was to collect in readily accessible form the most useful of known results for the more common sections. Formulas for all the important solid sections that have yielded to mathematical treatment are listed. Then follows a discussion of the torsion of tubular rods with formulas both rigorous and approximate.

Trayer, George W↗

NASA NTRS1955

The Theories of Turbulence

The theory of turbulence reached its full growth at the end of the 19th century as a result of the work by Boussinesq and Reynolds. It then underwent a long period of stagnation which ended under the impulse given to it by the development of wind tunnels caused by the needs of aviation. Numerous researchers, attempted to put Reynolds' elementary statistical theory into a more precise form. During the war, some isolated scientists - von Weizsacker and Heisenberg in Germany, Kolmogoroff in Russia, Onsager in the U.S.A. - started a program of research. By a system of assumptions which make it possible to approach the structure of turbulence in well-defined limiting conditions quantitatively, they obtained a certain number of laws on the correlations and the spectrum. Since the late reports have improved the mathematical language of turbulence, it was deemed advisable to start with a detailed account of the mathematical methods applicable to turbulence, inspired at first by the work of the French school, above all for the basic principles, then the work of the foreigners, above all for the theory of the spectrum.

MECHANICS, STATISTICAL↗

NASA NTRS1994

Anticipatory Neurofuzzy Control

Technique of feedback control, called "anticipatory neurofuzzy control," developed for use in controlling flexible structures and other dynamic systems for which mathematical models of dynamics poorly known or unknown. Superior ability to act during operation to compensate for, and adapt to, errors in mathematical model of dynamics, changes in dynamics, and noise. Also offers advantage of reduced computing time. Hybrid of two older fuzzy-logic control techniques: standard fuzzy control and predictive fuzzy control.

Mccullough, Claire L.↗

NASA NTRS1994

Computer Modeling Of Atomization

Improved mathematical models based on fundamental principles of conservation of mass, energy, and momentum developed for use in computer simulation of atomization of jets of liquid fuel in rocket engines. Models also used to study atomization in terrestrial applications; prove especially useful in designing improved industrial sprays - humidifier water sprays, chemical process sprays, and sprays of molten metal. Because present improved mathematical models based on first principles, they are minimally dependent on empirical correlations and better able to represent hot-flow conditions that prevail in rocket engines and are too severe to be accessible for detailed experimentation.

Giridharan, M.↗

NASA NTRS1990

An investigation of constraint-based component-modeling for knowledge representation in computer-aided conceptual design

Originally, computer programs for engineering design focused on detailed geometric design. Later, computer programs for algorithmically performing the preliminary design of specific well-defined classes of objects became commonplace. However, due to the need for extreme flexibility, it appears unlikely that conventional programming techniques will prove fruitful in developing computer aids for engineering conceptual design. The use of symbolic processing techniques, such as object-oriented programming and constraint propagation, facilitate such flexibility. Object-oriented programming allows programs to be organized around the objects and behavior to be simulated, rather than around fixed sequences of function- and subroutine-calls. Constraint propagation allows declarative statements to be understood as designating multi-directional mathematical relationships among all the variables of an equation, rather than as unidirectional assignments to the variable on the left-hand side of the equation, as in conventional computer programs. The research has concentrated on applying these two techniques to the development of a general-purpose computer aid for engineering conceptual design. Object-oriented programming techniques are utilized to implement a user-extensible database of design components. The mathematical relationships which model both geometry and physics of these components are managed via constraint propagation. In addition, to this component-based hierarchy, special-purpose data structures are provided for describing component interactions and supporting state-dependent parameters. In order to investigate the utility of this approach, a number of sample design problems from the field of aerospace engineering were implemented using the prototype design tool, Rubber Airplane. The additional level of organizational structure obtained by representing design knowledge in terms of components is observed to provide greater convenience to the program user, and to result in a database of engineering information which is easier both to maintain and to extend.

Kolb, Mark A.↗

NASA NTRS1990

Shape design sensitivities using fully automatic 3-D mesh generation

Previous work in three dimensional shape optimization involved specifying design variables by associating parameters directly with mesh points. More recent work has shown the use of fully-automatic mesh generation based upon a parameterized geometric representation. Design variables have been associated with a mathematical model of the part rather than the discretized representation. The mesh generation procedure uses a nonuniform grid intersection technique to place nodal points directly on the surface geometry. Although there exists an associativity between the mesh and the geometrical/topological entities, there is no mathematical functional relationship. This poses a problem during certain steps in the optimization process in which geometry modification is required. For the large geometrical changes which occur at the beginning of each optimization step, a completely new mesh is created. However, for gradient calculations many small changes must be made and it would be too costly to regenerate the mesh for each design variable perturbation. For that reason, a local remeshing procedure has been implemented which operates only on the specific edges and faces associated with the design variable being perturbed. Two realistic design problems are presented which show the efficiency of this process and test the accuracy of the gradient computations.

Botkin, M. E.↗

NASA NTRS1993

The development and potential of inverse simulation for the quantitative assessment of helicopter handling qualities

In this paper it is proposed that inverse simulation can make a positive contribution to the study of handling qualities. It is shown that mathematical descriptions of the MTEs (Mission Task Elements) defined in ADS-33C may be used to drive an inverse simulation thereby generating, from an appropriate mathematical model, the controls and states of a subject helicopter flying it. By presenting the results of such simulations it is shown that, in the context of inverse simulation, the attitude quickness parameters given in ADS-33C are independent of vehicle configuration. An alternative quickness parameter, associated with the control displacements required to fly the MTE is proposed, and some preliminary results are presented.

Bradley, Roy↗

NASA NTRS1993

Teaching planetary sciences to elementary school teachers: Programs that work

Planetary sciences can be used to introduce students to the natural world which is a part of their lives. Even children in an urban environment are aware of such phenomena as day and night, shadows, and the seasons. It is a science that transcends cultures, has been prominent in the news in recent years, and can generate excitement in young minds as no other science can. Planetary sciences also provides a useful tool for understanding other sciences and mathematics, and for developing problem solving skills which are important in our technological world. However, only 15 percent of elementary school teachers feel very well qualified to teach earth/space science, while better than 80 percent feel well qualified to teach reading; many teachers avoid teaching science; very little time is actually spent teaching science in the elementary school: 19 minutes per day in K-3 and 38 minutes per day in 4-6. While very little science is taught in elementary and middle school, earth/space science is taught at the elementary level in less than half of the states. It was pointed out that science is not generally given high priority by either teachers or school districts, and is certainly not considered on a par with language arts and mathematics. Therefore, in order to teach science to our youth, we must empower our teachers, making them familiar and comfortable with existing materials. In our earlier workshops, several of our teachers taught in classrooms where the majority of the students were Hispanic (over 90 percent). However, few space sciences materials existed in Spanish. Therefore, most of our materials could not be used effectively in the classroom. To address this issue, NASA materials were translated into Spanish and a series of workshops for bilingual classroom teachers from Tucson and surrounding cities was conducted. Our space sciences workshops and our bilingual classroom workshops and how they address the needs of elementary school teachers in Arizona are addressed in detail.

Lebofsky, Larry A.↗

NASA NTRS1993

Mars 1994/1996: The French navigation tasks

In the fall of 1994, Russia will launch a spacecraft to Mars. France is involved in many scientific experiments which are onboard the spacecraft, as PI or CI. Some days before the Mars orbit insertion maneuver, two small stations and two penetrators will be injected into an entry trajectory. They will carry out for at least six months in situ analysis on the Martian surface. Two years later, a second spacecraft will be launched. It will carry the French balloon and a small rover. The scientific data of these landers will be relayed to earth via the spacecraft. However, during the first 20 days of their mission, Mars Observer will be used. To this end, a Mars balloon relay will be used, which will receive the data from the landers and store them into the memory of the Mars Observer camera. The spacecraft will also be used to localize the landers with the help of relative one-way Doppler measurements. An international cooperative is set up for this process, including JPS, Russian ballistic centers (Babakine, Institute of Applied Mathematics, Moscow Flight Control Center), and CNES Toulouse. Another task dedicated to the space mathematics division of CNES is to support the French scientists to prepare their telecommands and to analyze their telemetry. This second part is integrated into the French ground segment created for the Mars 94/96 mission. This paper describes the method used in CNES for the localization process, the support provided to the scientists, and the links for the data exchange.

Bonneau, Frederic↗

NASA NTRS1993

Research in progress and other activities of the Institute for Computer Applications in Science and Engineering

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics and computer science during the period April 1, 1993 through September 30, 1993. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustic and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science.

Source record↗

NASA NTRS1994

High performance real-time flight simulation at NASA Langley

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations must be deterministic and be completed in as short a time as possible. This includes simulation mathematical model computational and data input/output to the simulators. In 1986, in response to increased demands for flight simulation performance, personnel at NASA's Langley Research Center (LaRC), working with the contractor, developed extensions to a standard input/output system to provide for high bandwidth, low latency data acquisition and distribution. The Computer Automated Measurement and Control technology (IEEE standard 595) was extended to meet the performance requirements for real-time simulation. This technology extension increased the effective bandwidth by a factor of ten and increased the performance of modules necessary for simulator communications. This technology is being used by more than 80 leading technological developers in the United States, Canada, and Europe. Included among the commercial applications of this technology are nuclear process control, power grid analysis, process monitoring, real-time simulation, and radar data acquisition. Personnel at LaRC have completed the development of the use of supercomputers for simulation mathematical model computational to support real-time flight simulation. This includes the development of a real-time operating system and the development of specialized software and hardware for the CAMAC simulator network. This work, coupled with the use of an open systems software architecture, has advanced the state of the art in real time flight simulation. The data acquisition technology innovation and experience with recent developments in this technology are described.

Cleveland, Jeff I., II↗

NASA NTRS1994

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Bey, Kim S.↗

NASA NTRS1994

Time-delay control of a magnetic levitated linear positioning system

In this paper, a high accuracy linear positioning system with a linear force actuator and magnetic levitation is proposed. By locating a permanently magnetized rod inside a current-carrying solenoid, the axial force is achieved by the boundary effect of magnet poles and utilized to power the linear motion, while the force for levitation is governed by Ampere's Law supplied with the same solenoid. With the levitation in a radial direction, there is hardly any friction between the rod and the solenoid. The high speed motion can hence be achieved. Besides, the axial force acting on the rod is a smooth function of rod position, so the system can provide nanometer resolution linear positioning to the molecule size. Since the force-position relation is highly nonlinear, and the mathematical model is derived according to some assumptions, such as the equivalent solenoid of the permanently magnetized rod, so there exists unknown dynamics in practical application. Thus 'robustness' is an important issue in controller design. Meanwhile the load effect reacts directly on the servo system without transmission elements, so the capability of 'disturbance rejection; is also required. With the above consideration, a time-delay control scheme is chosen and applied. By comparing the input-output relation and the mathematical model, the time-delay controller calculates an estimation of unmodeled dynamics and disturbances and then composes the desired compensation into the system. Effectiveness of the linear positioning system and control scheme are illustrated with simulation results.

Tarn, J. H.↗

NASA NTRS1994

Building on the foundation for an engineering career

A predictable and preventable hurdle stops a majority of young women from entering the scientific and technical fields. This cuts down the individual's career possibilities and cuts in half the pool of potential U.S. engineers later available to industry. The waste of talent does not advance our country's competitive position. The typical American adolescent girl has acquired all the basic mathematical skills needed to pursue science and math, but, from adolescence on, she does not build the foundation of science and math courses that she would need later in life to work in engineering. Several questions are addressed: Why are some young women stopped cold in their mathematical tracks during adolescence? What is the influence of psychology, including discussion of the personality traits quantifiably shared by women in technical fields? and How should the school system adapt to keep their female charges learning math and science?

White, Susan↗

NASA NTRS1994

A rapid radiative transfer model for reflection of solar radiation

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

Xiang, X.↗

NASA NTRS1994

The updated statistical inversion technique to the evaluation of Umkehr observations

In the present study the standard retrieval Umkehr method to estimate the vertical distribution of ozone was updated using a statistical approach to the mathematical inversion scheme. The vertical ozone profile covariance matrix was used as a priori information for the inverse problem. A new method of the ozonesonde data organization according to air mass types helped to improve the covariance matrix quality. A retrieval method was developed using eigenvector technique. An optimal vertical ozone profile resolution was determined from the mathematical inversion scheme analysis based on the same technique. The sun radiation transfer was accounted for multiple scattering and atmospheric sphericity in this calculation. The retrievals using actual Umkehr Dobson spectrophotometer observations were also performed to provide the comparison of the standard and updated methods with concurrent ozone sound data at Boulder U.S. The comparison has revealed that the present method has some advantages in both resolution and accuracy, as compared to the standard one, especially for the atmospheric layers below ozone maximum.

Frolov, Alexander D.↗

NASA NTRS1993

Using emergent order to shape a space society

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Graps, Amara L.↗

NASA NTRS1994

An investigation of the use of temporal decomposition in space mission scheduling

This research involves an examination of techniques for solving scheduling problems in long-duration space missions. The mission timeline is broken up into several time segments, which are then scheduled incrementally. Three methods are presented for identifying the activities that are to be attempted within these segments. The first method is a mathematical model, which is presented primarily to illustrate the structure of the temporal decomposition problem. Since the mathematical model is bound to be computationally prohibitive for realistic problems, two heuristic assignment procedures are also presented. The first heuristic method is based on dispatching rules for activity selection, and the second heuristic assigns performances of a model evenly over timeline segments. These heuristics are tested using a sample Space Station mission and a Spacelab mission. The results are compared with those obtained by scheduling the missions without any problem decomposition. The applicability of this approach to large-scale mission scheduling problems is also discussed.

Bullington, Stanley E.↗