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NASA NTRS2005

Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity

Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.

Kolecki, Joseph C.↗

NASA NTRS2007

Deep Space Network Antenna Logic Controller

The Antenna Logic Controller (ALC) software controls and monitors the motion control equipment of the 4,000-metric-ton structure of the Deep Space Network 70-meter antenna. This program coordinates the control of 42 hydraulic pumps, while monitoring several interlocks for personnel and equipment safety. Remote operation of the ALC runs via the Antenna Monitor & Control (AMC) computer, which orchestrates the tracking functions of the entire antenna. This software provides a graphical user interface for local control, monitoring, and identification of faults as well as, at a high level, providing for the digital control of the axis brakes so that the servo of the AMC may control the motion of the antenna. Specific functions of the ALC also include routines for startup in cold weather, controlled shutdown for both normal and fault situations, and pump switching on failure. The increased monitoring, the ability to trend key performance characteristics, the improved fault detection and recovery, the centralization of all control at a single panel, and the simplification of the user interface have all reduced the required workforce to run 70-meter antennas. The ALC also increases the antenna availability by reducing the time required to start up the antenna, to diagnose faults, and by providing additional insight into the performance of key parameters that aid in preventive maintenance to avoid key element failure. The ALC User Display (AUD) is a graphical user interface with hierarchical display structure, which provides high-level status information to the operation of the ALC, as well as detailed information for virtually all aspects of the ALC via drill-down displays. The operational status of an item, be it a function or assembly, is shown in the higher-level display. By pressing the item on the display screen, a new screen opens to show more detail of the function/assembly. Navigation tools and the map button allow immediate access to all screens.

Ahlstrom, Harlow↗

NASA NTRS2004

Indoor Navigation using Direction Sensor and Beacons

A system for indoor navigation of a mobile robot includes (1) modulated infrared beacons at known positions on the walls and ceiling of a room and (2) a cameralike sensor, comprising a wide-angle lens with a position-sensitive photodetector at the focal plane, mounted in a known position and orientation on the robot. The system also includes a computer running special-purpose software that processes the sensor readings to obtain the position and orientation of the robot in all six degrees of freedom in a coordinate system embedded in the room.

Shields, Joel↗

NASA NTRS2015

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

NASA NTRS2015

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

Impact↗

NASA NTRS2020

Generation and Calibration of Linear Models of Aircraft with Highly Coupled Aeroelastic and Flight Dynamics

The lightweight structures and unconventional configurations being considered for the next generation of aircraft mean that any effort to predict or control the flight dynamics is impacted by the structural dynamics. One of the most severe forms of coupling between aeroelasticity and flight dynamics is an instability called body freedom flutter. The existing tools often assume a relatively weak effect of structural dynamics on the flight dynamics, and are therefore incapable of modeling strong interactions like body freedom flutter. A method of combining different sources of data traditionally used for aeroelasticity and flight dynamics is described by reconciling many of the differences between these models. By building upon past modeling efforts, a level of familiarity in the approach is achieved. Generally the differences from the traditional approaches are subtle but significant. The traditional frequency domain flutter model in a modal coordinate system is converted to a form consistent with a time domain flight dynamics model. The time domain rational function approximation about a non-inertial coordinate system and the unique constraints for the conversion between the inertial and non-inertial coordinate systems are discussed. A consistent transformation of the states of aeroelastic models to flight dynamics models is derived, which enables the integration of data from higher fidelity computational fluid dynamics models or wind-tunnel testing. The present method of integrating multidisciplinary data was used to create models that compare well with X-56A flight-test data, including conditions past the flutter speed.

Ouellette, Jeffrey↗

NASA NTRS2002

Systems Architecture for Fully Autonomous Space Missions

The NASA Goddard Space Flight Center is working to develop a revolutionary new system architecture concept in support of fully autonomous missions. As part of GSFC's contribution to the New Millenium Program (NMP) Space Technology 7 Autonomy and on-Board Processing (ST7-A) Concept Definition Study, the system incorporates the latest commercial Internet and software development ideas and extends them into NASA ground and space segment architectures. The unique challenges facing the exploration of remote and inaccessible locales and the need to incorporate corresponding autonomy technologies within reasonable cost necessitate the re-thinking of traditional mission architectures. A measure of the resiliency of this architecture in its application to a broad range of future autonomy missions will depend on its effectiveness in leveraging from commercial tools developed for the personal computer and Internet markets. Specialized test stations and supporting software come to past as spacecraft take advantage of the extensive tools and research investments of billion-dollar commercial ventures. The projected improvements of the Internet and supporting infrastructure go hand-in-hand with market pressures that provide continuity in research. By taking advantage of consumer-oriented methods and processes, space-flight missions will continue to leverage on investments tailored to provide better services at reduced cost. The application of ground and space segment architectures each based on Local Area Networks (LAN), the use of personal computer-based operating systems, and the execution of activities and operations through a Wide Area Network (Internet) enable a revolution in spacecraft mission formulation, implementation, and flight operations. Hardware and software design, development, integration, test, and flight operations are all tied-in closely to a common thread that enables the smooth transitioning between program phases. The application of commercial software development techniques lays the foundation for delivery of product-oriented flight software modules and models. Software can then be readily applied to support the on-board autonomy required for mission self-management. An on-board intelligent system, based on advanced scripting languages, facilitates the mission autonomy required to offload ground system resources, and enables the spacecraft to manage itself safely through an efficient and effective process of reactive planning, science data acquisition, synthesis, and transmission to the ground. Autonomous ground systems in turn coordinate and support schedule contact times with the spacecraft. Specific autonomy software modules on-board include mission and science planners, instrument and subsystem control, and fault tolerance response software, all residing within a distributed computing environment supported through the flight LAN. Autonomy also requires the minimization of human intervention between users on the ground and the spacecraft, and hence calls for the elimination of the traditional operations control center as a funnel for data manipulation. Basic goal-oriented commands are sent directly from the user to the spacecraft through a distributed internet-based payload operations "center". The ensuing architecture calls for the use of spacecraft as point extensions on the Internet. This paper will detail the system architecture implementation chosen to enable cost-effective autonomous missions with applicability to a broad range of conditions. It will define the structure needed for implementation of such missions, including software and hardware infrastructures. The overall architecture is then laid out as a common thread in the mission life cycle from formulation through implementation and flight operations.

Esper, Jamie↗

NASA NTRS1990

Application of a patched-grid algorithm to the F/A-18 forebody-leading-edge extension configuration

A patched-grid algorithm for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver is presented. Results from both a spatial-flux and a time-flux conservation approach to patching across zonal boundaries are presented. A generalized coordinate transformation with a biquadratic geometric element is used at the zonal interface in order to treat highly stretched viscous grids and arbitrarily shaped zonal boundaries. Applications are made to the F/A-18 forebody-Ieading-edge extension configuration at subsonic, high-alpha conditions. Computed surface flow patterns compare well with ground-based and flight-test results; the large effect of Reynolds number on the forebody flowfield is shown.

Leading edge extension↗

NASA NTRS1995

Calculation of three-dimensional (3-D) internal flow by means of the velocity-vorticity formulation on a staggered grid

A method has been developed to accurately compute the viscous flow in three-dimensional (3-D) enclosures. This method is the 3-D extension of a two-dimensional (2-D) method developed for the calculation of flow over airfoils. The 2-D method has been tested extensively and has been shown to accurately reproduce experimental results. As in the 2-D method, the 3-D method provides for the non-iterative solution of the incompressible Navier-Stokes equations by means of a fully coupled implicit technique. The solution is calculated on a body fitted computational mesh incorporating a staggered grid methodology. In the staggered grid method, the three components of vorticity are defined at the centers of the computational cell sides, while the velocity components are defined as normal vectors at the centers of the computational cell faces. The staggered grid orientation provides for the accurate definition of the vorticity components at the vorticity locations, the divergence of vorticity at the mesh cell nodes and the conservation of mass at the mesh cell centers. The solution is obtained by utilizing a fractional step solution technique in the three coordinate directions. The boundary conditions for the vorticity and velocity are calculated implicitly as part of the solution. The method provides for the non-iterative solution of the flow field and satisfies the conservation of mass and divergence of vorticity to machine zero at each time step. To test the method, the calculation of simple driven cavity flows have been computed. The driven cavity flow is defined as the flow in an enclosure driven by a moving upper plate at the top of the enclosure. To demonstrate the ability of the method to predict the flow in arbitrary cavities, results will he shown for both cubic and curved cavities.

Stremel, Paul M.↗

NASA NTRS2019

Earth Science Technology Office (ESTO) New Observing Strategies (NOS) and NOS-Testbed (NOS-T)

With the advancement of space hardware technologies such as smaller spacecraft, component and instrument miniaturization and high performance space processors, and with the advancement of software technologies in artificial intelligence, big data analysis and autonomous decision making, Earth Science is looking at novel ways to observe phenomena that previously could not have been studied or would have been too expensive to study with traditional missions. In particular, the New Observing Strategies (NOS) component of the NASA Earth Science Technology Office (ESTO) Advanced Information Systems Technology (AIST) Program aims at leveraging these novel technologies as well as low cost and easy access to space to acquire multi-temporal or simultaneous multi-angular, multi-locations, multi-resolution and multi-spectral observations that will provide better multi-source measurements and will build a more dynamic and comprehensive picture of Earth Science phenomena that need to be studied and analyzed. For applications such as water resources management, air quality monitoring, biodiversity studies or disaster management, NOS will integrate the use of small instruments, small spacecraft, constellations of spacecraft and networks of sensors to design new missions that will provide the necessary measurements to improve future forecast and science modeling systems.Measurement acquisition will therefore be approached as a system of systems rather than on a mission basis, and a system of this complexity should not be expected to work without full integration and experimental characterization. Although most of the individual technologies enabling to link and coordinate multi-source observations are more or less mature, a few technologies need to be developed and all of them need to be integrated and tested as a system. In order for this validation to occur, the AIST Program is developing the NOS Testbed that includes 3 main goals:1.Validate novel NOS technologies, independently and as a system2.Demonstrate novel distributed operations concepts3.Socialize new Distributed Spacecraft Mission (DSM) and SensorWeb (SW) technologies and concepts to the science community by significantly retiring the risk of integrating these new technologies.The NOS Testbed will consist of multiple sensing nodes, simulated or actual, representing space, air and/or ground measurements, that are interconnected by a communications fabric (infrastructure that permits nodes to transmit and receive data between one another and interact with each other). Each node will be supported by hardware capabilities required to perform nodes monitoring and command & control, as well as intelligent "onboard" computing. The nodes will work together in a collaborative manner to demonstrate optimal science capabilities. The testbed will enable to validate technologies such as inter-node communication models, techniques and protocols; inter-node coordination; real-time data fusion and understanding; planning; sensor re-targeting; etc. Additionally, the testbed will have the capability to interact with various mission design tools, OSSEs and one or several forecast models. More details about the NOS Testbed will be presented at the confererence.

Earth Science missions; Advanced information Syste↗

NASA NTRS2010

Lunar Pole Illumination and Communications Statistics Computed from GSSR Elevation Data

The Goldstone Solar System RADAR (GSSR) group at JPL produced a Digital Elevation Model (DEM) of the lunar south pole using data obtained in 2006. This model has 40-meter horizontal resolution and about 5-meter relative vertical accuracy. This paper uses that Digital Elevation Model to compute average solar illumination and Earth visibility near the lunar south pole. This data quantifies solar power and Earth communications resources at proposed lunar base locations. The elevation data were converted into local terrain horizon masks, then converted into selenographic latitude and longitude coordinates. The horizon masks were compared to latitude, longitude regions bounding the maximum Sun and Earth motions relative to the moon. Proposed lunar south pole base sites were examined in detail, with the best site showing multi-year averages of solar power availability of 92% and Direct-To-Earth (DTE) communication availability of about 50%. Results are compared with a theoretical model, and with actual sun and Earth visibility averaged over the years 2009 to 2028. Results for the lunar North pole were computed using the GSSR DEM of the lunar North pole produced in 1997. The paper also explores using a heliostat to reduce the photovoltaic power system mass and complexity.

Lunar base↗

NASA NTRS1993

Multigrid methods for numerical simulation of laminar diffusion flames

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

Liu, C.↗

NASA NTRS1997

Preconditioning for Numerical Simulation of Low Mach Number Three-Dimensional Viscous Turbomachinery Flows

A preconditioning scheme has been implemented into a three-dimensional viscous computational fluid dynamics code for turbomachine blade rows. The preconditioning allows the code, originally developed for simulating compressible flow fields, to be applied to nearly-incompressible, low Mach number flows. A brief description is given of the compressible Navier-Stokes equations for a rotating coordinate system, along with the preconditioning method employed. Details about the conservative formulation of artificial dissipation are provided, and different artificial dissipation schemes are discussed and compared. The preconditioned code was applied to a well-documented case involving the NASA large low-speed centrifugal compressor for which detailed experimental data are available for comparison. Performance and flow field data are compared for the near-design operating point of the compressor, with generally good agreement between computation and experiment. Further, significant differences between computational results for the different numerical implementations, revealing different levels of solution accuracy, are discussed.

Tweedt, Daniel L.↗

NASA NTRS1972

The 4-D guidance of STOL aircraft in the terminal area

Advanced STOL aircraft for the improvement of the nation's air transportation system by the elimination of delays and congestions associated with today's air travel are discussed. A new guidance technique, referred to as 4-D guidance, is being developed for STOL aircraft. The 4-D guidance technique synthesizes complex three-dimensional flight paths from a minimum set of input and files the aircraft along the paths according to a prespecified time schedule. The two major elements of a 4-D guidance system are the trajectory synthesizer and the control law. Inputs to the trajectory synthesizer are the three-dimensional coordinates of way points, the turning radii, the speed ranges, the acceleration limits, and the arrival times at time control way points. First, the three-dimensional trajectory is computed by using circular arcs and straight lines. Then the airspeed profile, compensated for wind, is calculated to achieve the desired arrival times. The synthesized trajectory is stored as a time sequence of reference states which the aircraft is forced to track by using a linear feedback law.

Pecsvaradi, T.↗

NASA NTRS1972

Four-D guidance of STOL aircraft in the terminal area

The primary objective of advanced STOL aircraft is the improvement of the nation's air transportation system by the elimination of delays and congestions associated with today's air travel. A new guidance technique, referred to as 4-D guidance, is being developed to achieve this objective. The 4-D guidance technique synthesizes complex three-dimensional flight paths from a minimum set of input data and flies the aircraft along the paths according to a prespecified time schedule. The two major elements of a 4-D guidance system are the trajectory synthesizer and the control law. Inputs to the trajectory synthesizer are the three-dimensional coordinates of way points, the turning radii, the speed ranges, the acceleration limits, and the arrival times at time control way points. First, the three-dimensional trajectory is computed by using circular arcs and straight lines. Then the airspeed profile, compensated for wind, is calculated to achieve the desired arrival times. The synthesized trajectory is stored as a time sequence of reference states which the aircraft is forced to track by using a linear feedback law.

Pecsvaradi, T.↗

NASA NTRS1975

Propagation predictions and studies using a ray tracing program combined with a theoretical ionospheric model

Radio wave propagation predictions are described in which modern comprehensive theoretical ionospheric models are coupled with ray-tracing programs. In the computer code described, a network of electron density and collision frequency parameters along a band about the great circle path is calculated by specifying the transmitter and receiver geographic coordinates, time, the day number, and the 2800-MHz solar flux. The ray paths are calculated on specifying the frequency, mode, range of elevation angles, and range of azimuth angles from the great circle direction. The current program uses a combination of the Penn State MKI E and F region models and the Mitra-Rowe D and E region model. Application of the technique to the prediction of satellite to ground propagation and calculation of oblique incidence propagation paths and absorption are described. The implications of the study to the development of the next generation of ionospheric models are discussed.

Lee, M. K.↗

NASA NTRS1980

State estimation and absolute image registration for geosynchronous satellites

Spacecraft state estimation and the absolute registration of Earth images acquired by cameras onboard geosynchronous satellites are described. The basic data type of the procedure consists of line and element numbers of image points called landmarks whose geodetic coordinates, relative to United States Geodetic Survey topographic maps, are known. A conventional least squares process is used to estimate navigational parameters and camera pointing biases from observed minus computed landmark line and element numbers. These estimated parameters along with orbit and attitude dynamic models are used to register images, using an automated grey level correlation technique, inside the span represented by the landmark data. In addition, the dynamic models can be employed to register images outside of the data span in a near real time mode. An important application of this mode is in support of meteorological studies where rapid data reduction is required for the rapid tracking and predicting of dynamic phenomena.

Nankervis, R.↗

NASA NTRS1980

Development of a computer program data base of a navigation aid environment for simulated IFR flight and landing studies

A general aviation single pilot instrument flight rule simulation capability was developed. Problems experienced by single pilots flying in IFR conditions were investigated. The simulation required a three dimensional spatial navaid environment of a flight navigational area. A computer simulation of all the navigational aids plus 12 selected airports located in the Washington/Norfolk area was developed. All programmed locations in the list were referenced to a Cartesian coordinate system with the origin located at a specified airport's reference point. All navigational aids with their associated frequencies, call letters, locations, and orientations plus runways and true headings are included in the data base. The simulation included a TV displayed out-the-window visual scene of country and suburban terrain and a scaled model runway complex. Any of the programmed runways, with all its associated navaids, can be referenced to a runway on the airport in this visual scene. This allows a simulation of a full mission scenario including breakout and landing.

Bergeron, H. P.↗