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At least 343 records · Page 19

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NASA NTRS1991

How to determine spiral bevel gear tooth geometry for finite element analysis

An analytical method was developed to determine gear tooth surface coordinates of face milled spiral bevel gears. The method combines the basic gear design parameters with the kinematical aspects for spiral bevel gear manufacturing. A computer program was developed to calculate the surface coordinates. From this data a 3-D model for finite element analysis can be determined. Development of the modeling method and an example case are presented.

Handschuh, Robert F.↗

NASA NTRS1960

Early orbit determination scheme for the Juno space vehicle

The present status (1959-60) of the ABMA early orbit determination scheme for the Juno space vehicle is described. The design of the scheme was essentially influenced by three factors: its origin centered around postflight vehicle analysis, the flexibility required for accepting varied kinds of data, and the potential of highspeed computers concentrated in ABMA's Computation Laboratory. The scheme is outlined, the tracking stations participating are shortly described, and the physical layout and computational equipment are briefly mentioned. The evaluation techniques used for the various steps of the orbit determination are discussed in detail. Appendices describe briefly the principal coordinate systems used and characteristics of the digital computer programs.

Fletcher Kurtz↗

NASA NTRS1977

TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies

A method for automatic generation of boundary-fitted curvilinear coordinate systems, where the transformed coordinates are solutions of an elliptic differential system in the physical plane, and where the coordinate lines are coincident with all boundaries of a general multiply-connected, two-dimensional region containing any number of arbitrarily shaped bodies, and is described along with a suitable computer code for implementing the method. Any partial differential system can be solved on the boundary-fitted coordinate system by appropriate transformations. The transformed equations are approximated by finite differences and solved numerically in the transformed plane. All computations, whether for generating coordinate system or then solving the transformed equations, can be done on a rectangular field with square mesh with no interpolation required on the boundaries. The physical boundaries may even be time-dependent.

Thompson, J. F.↗

NASA NTRS1992

Computational fluid dynamics for propulsion technology: Geometric grid visualization in CFD-based propulsion technology research

The coordination is examined of necessary resources, facilities, and special personnel to provide technical integration activities in the area of computational fluid dynamics applied to propulsion technology. Involved is the coordination of CFD activities between government, industry, and universities. Current geometry modeling, grid generation, and graphical methods are established to use in the analysis of CFD design methodologies.

Ziebarth, John P.↗

NASA NTRS1999

The Density Matrix of H20 - N2 In the Coordinate Representation: A Monte Carlo Calculation of the Far-Wing Line Shape

The far-wing line shape theory within the binary collision and quasistatic framework has been developed using the coordinate representation. Within this formalism, the main computational task is the evaluation of multidimensional integrals whose variables are the orientational angles needed to specify the initial and final positions of the system during transition processes. Using standard methods, one is able to evaluate the 7-dimensional integrations required for linear molecular systems, or the 7-dimensional integrations for more complicated asymmetric-top (or symmetric-top) molecular systems whose interaction potential contains cyclic coordinates. In order to obviate this latter restriction on the form of the interaction potential, a Monte Carlo method is used to evaluate the 9-dimensional integrations required for systems consisting of one asymmetric-top (or symmetric-top) and one linear molecule, such as H20-N2. Combined with techniques developed previously to deal with sophisticated potential models, one is able to implement realistic potentials for these systems and derive accurate, converged results for the far-wing line shapes and the corresponding absorption coefficients. Conversely, comparison of the far-wing absorption with experimental data can serve as a sensitive diagnostic tool in order to obtain detailed information on the short-range anisotropic dependence of interaction potentials.

Ma, Q.↗

NASA NTRS1996

Aerostructural Vortical Flow Interactions with Applications to F/A-18 and F-117 Tail Buffet

The buffet response of the flexible twin-tail configuration of the F/A-18 and a generic F-111 aircraft are computationally simulated and experimentally validated. The problem is a multidisciplinary one which requires the sequential solution of three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations. The second set is the aeroelastic equations for bending and torsional twin-tail responses. The third set is the grid-displacement equations which are used to update the grid coordinates due to the tail deflections. The computational models consist of a 76 deg. swept back, sharp edged delta wing of aspect ratio of one and a swept-back F/A-18 or F-117 twin-tail. The configuration is pitched at 30 deg. angle-of-attack. The problem is solved for the initial flow conditions with the twin tails kept rigid. Next, the aeroelastic equations of the tails are turned on along with the grid-displacement equations to solve for the bending and torsional tails responses due to the unsteady loads produced by the vortex breakdown flow of the leading-edge vortex cores of the delta wing. Several spanwise locations of the twin tails are investigated. The computational results are validated using several existing experimental data.

Kandil, Osama A.↗

NASA NTRS1980

A three-dimensional turbulent compressible subsonic duct flow analysis for use with constructed coordinate systems

An approximate analysis, applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline, is presented for computation of three-dimensional subsonic flow in straight and curved diffusers. The formulation is intended to facilitate the use of constructed coordinates in circumstances where it is difficult to maintain smooth behavior in higher derivatives; the use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation. The analysis is applied to a particular family of duct and diffuser geometries having curved centerlines and superelliptic cross sections. Qualitative agreement with experimental measurements is observed with regard to streamwise vortices and distortion of the primary flow.

Levy, R.↗

NASA NTRS1996

Computation and Validation of Fluid/Structure Twin Tail Buffet Response

The buffet response of the flexible twin-tail/delta wing configuration, a multidisciplinary problem, is solved using three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations which are used for obtaining the flow-field vector and the aerodynamic loads on the twin tails. The second set is the coupled aeroelastic equations which are used for obtaining the bending and torsional deflections of the twin tails. The third set is the grid-displacement equations which are used for updating the grid coordinates due to the tail deflections. The computational model is similar to the one used by Washburn et. al. which consists of a delta wing of aspect ratio one and twin tails with taper ratios of 0.23. The vortex of the twin tails are located at the wing trailing edge. The configuration is pitched at 30 deg angle of attack, and the freestream Mach number and Reynolds number are 0.3 and 1.25 million, respectively. With the twin tails fixed as rigid surfaces, the problem is solved for the initial flow conditions. Next, the problem is solved for the twin tail response for uncoupled bending and torsional vibrations due to the unsteady loads produced by the vortex breakdown flow of the leading-edge vortex cores. The configuration is investigated for three spanwise positions of the twin tails; inboard, midspan and outboard locations. The computational results are validated and are in very good agreement with the experimental data of Washburn, et. al.

Massey, Steven J.↗

NASA NTRS1977

Interactive LORAN-C to geographic and geographic-to-LORAN-C computation

The LORAN program is stored in CMS disk files for use by Avionics Engineering Center terminal users. A CMS EXEC file named LORAN controls program operation. The user types LORAN and the program then prompts for data input and produces output on the terminal. The FORTRAN program refers to a disk file of LORAN master data giving station locations, coding delays, repetition rate and station pair identification letters. For Geographic-to-LORAN conversion, no iterative computations are required; the program is a straightforward coordinate conversion based upon the techniques described by the Navy. For LORAN-to-Geographic conversion, the original Navy program required a dead-reckoned position, near the actual unknown fix, to begin computations. No iteration was performed to obtain the LORAN fix, but internal program errors occurred at execution time if the dead-reckoned fix were displaced from the actual fix by more than a few minutes of latitude or longitude. In order to enhance usefulness of the program for the terminal user, an iterative routine was added which allows a single dead-reckoned position to be entered from the master data file for each LORAN chain. The results compare exactly with the LORAN-C navigation chart, and provide adequate benchmark data for general aviation flight planning and data analysis.

Piecuch, L. M.↗

NASA NTRS1981

Approximate and exact numerical computation of supersonic flow over an airfoil

The computation of inviscid supersonic flow over a two-dimensional airfoil is considered. There are two main nonlinear approaches which lead to approximate solutions. Small-amplitude theory gives valid solutions provided the airfoil thickness is not too great and the Mach number is not too high. The second type of approximation, shock expansion theory, employs the fact that even for flows with strong shocks the effect of the down-running characteristics remains small. This leads to an analytic solution at the airfoil. It is pointed out that the approximate solution is accurate enough for many cases of interest. The numerical method furnishes a rapid correction to the solution in those cases where it is not. The characteristic-streamline coordinate system is useful both for the computation of the approximate solution and the corrections, and is also convenient for displaying and interpreting the results.

Lewis, T. S.↗

NASA NTRS1998

Polarization Considerations

As light passes through a optical system the reflections and refractions will in general change the polarization state of the light. If we assume that all of the materials in the thin film coatings and substrate are isotropic and homogeneous then calculating the amount of "instrumental" polarization is a relatively straight forward task. In the following sections we will present a of the steps required to perform a 'polarization ray trace' calculation for a single ray and monochromatic and hence polarized light. The thin film portion of the calculation is also shown. The reason for explicitly showing the thin film equations is that there are sign conventions imposed on the boundary value equations by the orientation and handedness of the various coordinate frames which are attached to the geometric rays. The attenuation of light through a optical system, is relatively simple, and requires at the very least a lens (average) reflectivity or transmissivity. Determining the polarization sensitivity of a optical system is still relatively straight forward requiring at least a knowledge of the behavior of the "s" and "p" components at each interface for the chief ray. Determining the thin film induced aberrations of a optical system are somewhat more demanding. Questions about the arithmetic sign of the phase factors and how this relates to the overall "OPD" of a ray are ubiquitous. Many rays are required to construct a wavefront. Thin film codes which modify the OPD's of rays are a requirement for this last mentioned computation. This requires a consistent scheme of coordinate frames and sign conventions and is probably the most demanding task of a polarization ray trace. Only the electric field will used in the discussion. This is not a restriction as the Stokes parameters are functions of the electric field. The following does not attempt to explain, but only to present all of the required concepts and formulas.

Waluschka, Eugene↗

NASA NTRS1975

A generalized tensor formulation of atmosphere and seas dynamics

A generalized mathematical model was developed for simulation of the dynamics and transport of both the atmosphere and seas. A nearly horizontal bottom coordinate surface conforms to the land-to-air interface and the sea-floor-to-water interface, which simplifies computations. General vertical motion of the other quasi-horizontal coordinate surfaces is allowed; external gravity waves can be represented by the top coordinate surface, and meteorological fronts and inversion layers in the atmosphere and refractive layers in the seas can be represented with enhanced resolution by the internal quasi-horizontal coordinate surfaces. A tensor reformulation of the standard subgrid mixing theory departs significantly from the standard theory in allowing, as a solution under adiabatic conditions, rigid-body rotation of the atmosphere.

Avis, L. M.↗

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 NTRS1989

A direct procedure for interpolation on a structured curvilinear two-dimensional grid

A direct procedure is presented for locally bicubic interpolation on a structured, curvilinear, two-dimensional grid. The physical (Cartesian) space is transformed to a computational space in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. Required partial derivative information is obtained by finite differences in the computational space. The partial derivatives in physical space are determined by repeated application of the chain rule for partial differentiation. A bilinear transformation is used to analytically transform the individual quadrilateral cells in physical space into unit squares. The interpolation is performed within each unit square using a piecewise bicubic spline.

Zingg, David W.↗

NASA NTRS1991

Polynomials

In this 'Project Mathematics! series, sponsored by California Institute for Technology (CalTech), the mathematical concept of polynomials in rectangular coordinate (x, y) systems are explored. sing film footage of real life applications and computer animation sequences, the history of, the application of, and the different linear coordinate systems for quadratic, cubic, intersecting, and higher degree of polynomials are discussed.

Apostol, Tom M.↗

NASA NTRS1983

Numerical simulation of the leading-edge separation vortex for a wing and strake-wing configuration

In the present investigation, the 'thin layer' Navier-Stokes equations are used to compute the flow about a delta wing and a strake-delta wing configuration. Both configurations possess blunt noses and rounded leading edges. The computational grid about these configurations is generated using a newly developed three-dimensional grid-generation code which solves a set of Poisson equations with spherical coordinate variables using an alternating direction implicit (ADI) scheme. Computational results are obtained for an isolated wing with 60 deg sweep and a strake-wing configuration with 80-60 deg sweep. Computations for angles of attack in the range from 6 to 30 deg are presented. Attention is given to the effect of the angle of attack, the Mach number, and the Reynolds number. Theoretical results are compared with experimental data.

Fujii, K.↗

NASA NTRS1978

The influence of earth tides on earth's coordinates

The importance of the Earth's tides on Earth coordinates were examined for the following reasons: (1) the precision for obtaining the Earth's coordinates shows that the effects of Earth tides appear on the values obtained for the coordinates; (2) the possibility of determining the values of the Earth tides; and (3) the consideration of theoretical models that can compute the values of Earth tides. The astronomical and geodetic coordinates of a point at the Earth's surface are described.

Vincente, R. O.↗

NASA NTRS2008

Small-Body Extensions for the Satellite Orbit Analysis Program (SOAP)

An extension to the SOAP software allows users to work with tri-axial ellipsoid-based representations of planetary bodies, primarily for working with small, natural satellites, asteroids, and comets. SOAP is a widely used tool for the visualization and analysis of space missions. The small body extension provides the same visualization and analysis constructs for use with small bodies. These constructs allow the user to characterize satellite path and instrument cover information for small bodies in both 3D display and numerical output formats. Tri-axial ellipsoids are geometric shapes the diameters of which are different in each of three principal x, y, and z dimensions. This construct provides a better approximation than using spheres or oblate spheroids (ellipsoids comprising two common equatorial diameters as a distinct polar diameter). However, the tri-axial ellipsoid is considerably more difficult to work with from a modeling perspective. In addition, the SOAP small-body extensions allow the user to actually employ a plate model for highly irregular surfaces. Both tri-axial ellipsoids and plate models can be assigned to coordinate frames, thus allowing for the modeling of arbitrary changes to body orientation. A variety of features have been extended to support tri-axial ellipsoids, including the computation and display of the spacecraft sub-orbital point, ground trace, instrument footprints, and swathes. Displays of 3D instrument volumes can be shown interacting with the ellipsoids. Longitude/latitude grids, contour plots, and texture maps can be displayed on the ellipsoids using a variety of projections. The distance along an arbitrary line of sight can be computed between the spacecraft and the ellipsoid, and the coordinates of that intersection can be plotted as a function of time. The small-body extension supports the same visual and analytical constructs that are supported for spheres and oblate spheroids in SOAP making the implementation of the more complex algorithms largely transparent to the user.

Carnright, Robert↗