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NASA NTRS1980

A three-dimensional body-fitted coordinate system for flow field calculations on asymmetric nosetips

A three dimensional body-fitted coordinate system developed for use in the calculation of inviscid flows over ablated, asymmetric reentry vehicle nosetips is described. Because of the potential geometric asymmetries, no standard coordinate system (e.g., spherical, axisymmetric reference surface-normal) is capable of being closely aligned with the nosetip surface. To generate a 3-D, body-fitted coordinate system an analytic mapping procedure is applied that is conformal within each meridional plane of the nosetip; these transformations are then coupled circumferentially to yield a three dimensional coordinate system. The mappings used are defined in terms of hinge points, which are points selected to approximate the body contours in each meridional plane. The selection of appropriate hinge points was automated to facilitate the use of the resulting nosetip flow field code.

Hall, D. W.↗

NASA NTRS1981

Transformation from proper time on earth to coordinate time in solar system barycentric space-time frame of reference. I. II

It is noted that in order to obtain accurate computed values of earth-based range and Doppler observables of a deep space probe, an expression is required for the difference between coordinate time (t) in the solar system barycentric space-time frame of reference and proper time (tau) recorded on a fixed atomic clock on earth. This is part 1 of a two-part article which obtains an expression for the coordinate time/proper time difference that can be used in deriving computed values of observations of a spacecraft or celestial body located anywhere in the solar system. The expression can also be used in computing Very Long Baseline Interferometry data types. In part 1, expression for the coordinate time/proper time difference is obtained that is a function of position and velocity vectors of the major celestial bodies of the solar system and the atomic clock on earth which reads proper time. This expression is transformed in part 2 to a function of time and the earth-fixed coordinates of the atomic clock.

Moyer, T. D.↗

NASA NTRS1983

A comparison of methods for computing the sigma-coordinate pressure gradient force for flow over sloped terrain in a hybrid theta-sigma model

In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.

Johnson, D. R.↗

NASA NTRS1985

Users manual for coordinate generation code CRDSRA

Generation of a viable coordinate system represents an important component of an isolated airfoil Navier-Stokes calculation. The manual describes a computer code for generation of such a coordinate system. The coordinate system is a general nonorthogonal one in which high resolution normal to the airfoil is obtained in the vicinity of the airfoil surface, and high resolution along the airfoil surface is obtained in the vicinity of the airfoil leading edge. The method of generation is a constructive technique which leads to a C type coordinate grid. The method of construction as well as input and output definitions are contained herein. The computer code itself as well as a sample output is being submitted to COSMIC.

Shamroth, S. J.↗

NASA NTRS1985

Generation of Surface Coordinates by Elliptic Partial Differential Equations

The problem of generating spatial coordinates by numerical methods through carefully selected mathematical models is of current interest both in mechanics and physics. The problem of generation of a desired system of coordinates in a given surface was considered, which essentially is an effort directed to the problem of grid generation in a two-dimensional non-Euclidean space. The mathematical model selected for this purpose is based on the formulae of Gauss for a surface. The proposed equations can be used to generate a new coordinate system from the data of an already given coordinate system in a surface. If the coefficients of the first and second fundamental forms have been given, then the proposed equations can be used to generate a surface satisfying the given data (surface fitting). The proposed equations can also be used to generate surfaces in the space between two arbitrary given surfaces, thus providing 3D grids in an Euclidean space.

Warsi, Z. U. A.↗

NASA NTRS1983

Computer programs for smoothing and scaling airfoil coordinates

Detailed descriptions are given of the theoretical methods and associated computer codes of a program to smooth and a program to scale arbitrary airfoil coordinates. The smoothing program utilizes both least-squares polynomial and least-squares cubic spline techniques to smooth interatively the second derivatives of the y-axis airfoil coordinates with respect to a transformed x-axis system which unwraps the airfoil and stretches the nose and trailing-edge regions. The corresponding smooth airfoil coordinates are then determined by solving a tridiagonal matrix of simultaneous cubic-spline equations relating the y-axis coordinates and their corresponding second derivatives. A technique for computing the camber and thickness distribution of the smoothed airfoil is also discussed. The scaling program can then be used to scale the thickness distribution generated by the smoothing program to a specific maximum thickness which is then combined with the camber distribution to obtain the final scaled airfoil contour. Computer listings of the smoothing and scaling programs are included.

Morgan, H. L., Jr.↗

NASA NTRS1986

The coordinate frame of the lunar laser ranging network

The geocentric coordinates for four instruments, which were derived using lunar laser ranging, are compared with the 84L02 coordinates determined from the Lageos satellite. The determination of the geocentric coordinates for the 2.7 m and McDonald Observatory laser ranging system telescopes at McDonald Observatory, the Haleakala site, and the CERGA site near Grasse, France is described. Consideration is given to the McDonald Observatory colocation and station motion due to continential drift. A rms difference of 18 cm is determined for the two sets of geocentric coordinates; however, removing a data anomaly reduces the rms difference to 13 cm.

Williams, J. G.↗

NASA NTRS1988

Reference coordinate systems: An update. Supplement 11

A common requirement for all geodetic investigations is a well-defined coordinate system attached to the earth in some prescribed way, as well as a well-defined inertial coordinate system in which the motions of the terrestrial frame can be monitored. The paper deals with the problems encountered when establishing such coordinate systems and the transformations between them. In addition, problems related to the modeling of the deformable earth are discussed. This paper is an updated version of the earlier work, Reference Coordinate Systems for Earth Dynamics: A Preview, by the author.

Mueller, Ivan I.↗

NASA NTRS1989

Model reduction in the physical coordinate system

In the dynamics modeling of a flexible structure, finite element analysis employs reduction techniques, such as Guyan's reduction, to remove some of the insignificant physical coordinates, thus producing a dynamics model that has smaller mass and stiffness matrices. But this reduction is limited in the sense that it removes certain degrees of freedom at a node points themselves in the model. From the standpoint of linear control design, the resultant model is still too large despite the reduction. Thus, some form of the model reduction is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. However, a problem arises from the placement of sensors and actuators in the reduced model, because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, a method is developed that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this point, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed, however, this reduced model is expressed by a subset of the original states.

Yae, K. Harold↗

NASA NTRS1991

A General-Coordinate Formulation For Boundary-Layer Flow

Formulation for solution of equations of boundary-layer flow in general body-fitted curvilinear coordinates retains velocities in Cartesian coordinates. Increases stability of numerical simulations by avoiding coordinate source terms. In formulation, curvilinear coordinates do not have to be orthogonal, and much of software developed previously for use in numerical simulations of flow based on Navier-Stokes equations used.

Steger, Joseph L.↗

NASA NTRS1990

Tracking algorithms using log-polar mapped image coordinates

The use of log-polar image sampling coordinates rather than conventional Cartesian coordinates offers a number of advantages for visual tracking and docking of space vehicles. Pixel count is reduced without decreasing the field of view, with commensurate reduction in peripheral resolution. Smaller memory requirements and reduced processing loads are the benefits in working environments where bulk and energy are at a premium. Rotational and zoom symmetries of log-polar coordinates accommodate range and orientation extremes without computational penalties. Separation of radial and rotational coordinates reduces the complexity of several target centering algorithms, described below.

Weiman, Carl F. R.↗

NASA NTRS1991

Noninertial coordinate time: A new concept affecting time standards, time transfers, and clock synchronization

Relativity compensations must be made in precise and accurate measurements whenever an observer is accelerated. Although many believe the Earth-centered frame is sufficiently inertial, accelerations of the Earth, as evidenced by the tides, prove that it is technically a noninertial system for even an Earth-based observer. Using the constant speed of light, a set of fixed remote clocks in an inertial frame can be synchronized to a fixed master clock transmitting its time in that frame. The time on the remote clock defines the coordinate time at that coordinate position. However, the synchronization procedure for an accelerated frame is affected, because the distance between the master and remote clocks is altered due to the acceleration of the remote clock toward or away from the master clock during the transmission interval. An exact metric that converts observations from noninertial frames to inertial frames was recently derived. Using this metric with other physical relationships, a new concept of noninertial coordinate time is defined. This noninertial coordinate time includes all relativity compensations. This new issue raises several timekeeping issues, such as proper time standards, time transfer process, and clock synchronization, all in a noninertial frame such as Earth.

Steven D. Deines↗

NASA NTRS1992

Global coordinates with centimeter accuracy in the International Terrestrial Reference Frame using GPS

Using 21 days of GPS data from 21 globally distributed receivers operating during early 1991, a 7-parameter transformation between a GPS free-network solution and coordinates of 12 stations listed in the International Terrestrial Reference Frame (ITRF) is solved. Standard errors of GPS coordinates are derived by applying an orthogonal projection operator to the free-network covariance. The weighted rms difference between 33 transformed GPS and ITRF coordinates is 12 mm in the Northern Hemisphere. Best results are obtained by mapping ITRF coordinates to the epoch of this experiment assuming no vertical site motions. Fixing selected sites in the GPS solution to ITRF '90 does not improve the agreement. It is concluded that the use of fiducial constraints is unnecessary for global networks.

Blewitt, Geoffrey↗

NASA NTRS1992

Lazy checkpoint coordination for bounding rollback propagation

Independent checkpointing allows maximum process autonomy but suffers from potential domino effects. Coordinated checkpointing eliminates the domino effect by sacrificing a certain degree of process autonomy. In this paper, we propose the technique of lazy checkpoint coordination which preserves process autonomy while employing communication-induced checkpoint coordination for bounding rollback propagation. The introduction of the notion of laziness allows a flexible trade-off between the cost for checkpoint coordination and the average rollback distance. Worst-case overhead analysis provides a means for estimating the extra checkpoint overhead. Communication trace-driven simulation for several parallel programs is used to evaluate the benefits of the proposed scheme for real applications.

Wang, Yi-Min↗

NASA NTRS1993

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Lee, Jong-Hun↗

NASA NTRS1993

Connecting science and operations: The operations coordinator

For a current space mission under development at the Applied Physics Laboratory, the Mission Operations staff includes a team of 'Operations Coordinators' who have been working with the Mission Science and Spacecraft Development teams since completion of mission conceptual design. The Operations Coordinators are responsible for bringing knowledge of the spacecraft to the Mission Science team and bringing knowledge of the experiment requirements to the Spacecraft Development and Mission Operations teams. Once on-orbit operations begin, the Operations Coordinators will be responsible for implementation of specific science experiments from analysis through scheduling, generation of spacecraft command sequences, delivery of science data to the end user, and operations assessment. The Operations Coordinator concept is proving very effective during the development phase of the current mission.

Marshall, Madeleine H.↗

NASA NTRS1993

Lazy checkpoint coordination for bounding rollback propagation

Wang, Yi-Min↗

NASA NTRS1996

Coordinated Fuel Cell System Programs for Government and Commercial Applications: Are We in a New Era?

Though the fuel cell was invented in 1839, it was not until the early 1960's that the fuel cell power system was developed and used for a real application, for the NASA Space Mission Gemini. Unfortunately, fuel cell power systems did not, as a result, become in widespread use. Nevertheless, a great deal of progress has been made by both government and industry, culminating in many successful fuel cell power system demonstrations. Initially, each government agency and each private organization went its own way. Later, it became evident that coordination among programs was essential. An overview is presented of the current coordinated efforts by government and industry in fuel cells, with a sufficient historical background. The primary barriers to coordination of programs were institutional and differing application requirements. Initially, in the institutional area, it was the energy crisis and the formation of DOE which fostered close working relationships among government, manufacturers, and users. The authors discuss the fuel cell power system programs (of NASA, DOE, DOT, DOC, EPRI, GRI, industry, and universities), including missions and applications, technology advances, and demonstrations. The discussion covers the new Solar Regenerative Fuel Cell (RFC) program which has space, defense, and commercial terrestrial applications, and which is an excellent example of both program coordination and the Clinton Administration's dual-use application policy.

Warshay, Marvin↗