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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Multigrid applications to three-dimensional elliptic coordinate generation

The multigrid algorithm was applied to solve the coupled set of elliptic quasilinear partial differential equations associated with three-dimensional coordinate generation. The results indicate that the multigrid scheme is more than twice as fast as conventional relaxation schemes on moderate-size grids. Convergence factors of order 0.90 per work unit were achieved on 36,000-point grids. The paper covers the form of transformation, develops the set of generation equations, and gives details on the multigrid approach used. Included are a development of the full-approximation storage scheme, details of the smoothing-rate analysis, and a section devoted to rational programming techniques applicable to the multigrid algorithm.

Thames, F. C.↗
NASA NTRS1988

Dual periodicity of the Jovian magnetosphere

Using data from the 1979 Voyager flybys of Jupiter and two sets of ground-based observations of the Io torus, this paper presents an extensive analysis concerning the nature of the second magnetospheric periodicity of the Jupiter's magnetic field, along with a definition of a new Jovian matching coordinate system (referred to as system IV). It is shown that available independent data sets covering a time interval of 4 years, which either drift or show no particular organization in system III, fit mutually consistent patterns in system IV. Provisional values are derived for a transformation between systems III and IV. It is emphasized that system IV needs to be tested against additional data before its durability is assured.

Sandel, B. R.↗
NASA NTRS1991

Terrestrial reference systems related to the TOPEX/Poseidon project

In the TOPEX/POSEIDON project, several satellite positioning systems, such as Laser, Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and Global Positioning Satellite (GPS) (on an experimental basis), will be used to track the satellite and to provide accurate orbits. Unfortunately, these systems will provide their dedicated tracking-station coordinates and the satellite orbits in different reference frames. Each technique will use, de facto, a different reference frame. In fact, even for the same technique, each group, depending on the hypothesis used in its computation, will use a different reference frame. This problem is not new for geodesists and can be overcome, in large part, but could create trouble for other scientists when they compare or combine different coordinate data sets. The main purpose of this investigation is to determine a consistent terrestrial system for TOPEX/POSEIDON in which all the tracking-station coordinates, all the orbit ephemerides, and all the other station coordinates of specific interest (such as tide gauges) could be expressed. Another issue of this investigation is the provision of reliable information concerning the relationships between all the possible reference frames of interest for th TOPEX/POSEIDON project. To be more explicit, we plan to provide the possible transformation formula between the TOPEX/POSEIDON terrestrial reference frame and the Laser, DORIS, GPS, and other internationally recognized frames such as the International Terrestrial Reference Frame (ITRF).

Boucher, Claude↗
NASA NTRS2005

Generating Solid Models from Topographical Data

A method of generating solid models of terrain involves the conversion of topographical data into a form useable by a rapid-prototyping (RP) machine. The method was developed to enable the use of the RP machine to make solid models of Martian terrain from Mars Orbiter laser-altimeter topographical data. The method is equally applicable to the generation of models of the terrains of other astronomical bodies, including other planets, asteroids, and Earth. Topographical data describe a terrain in terms of a set of three-dimensional coordinates [e.g., Cartesian (x,y,z) or polar (latitude, longitude, radius) coordinates] of points or nodes on the terrain surface. The input data for the RP machines are required to provide a three-dimensional description, not of a single surface, but of a volume in this case, a ground volume that underlies the terrain surface. The description is required to be in the form of triangular elements that connect the nodes of all the surfaces and that completely bound the volume, with no open areas, no overlap of triangles, and no extraneous geometric elements. The software used in the present model-generation method was written in IDL - an advanced programming language that affords a number of tools, including subroutines that triangularize surfaces. The software creates a volume from the topographical surface data by adding sides to the edges of the terrain surface and joining the sides with a bottom surface. Each of the sides is triangularized by use of IDL subroutines, and then the software searches for extraneous elements and removes them. Topographical data are usually presented in a grid corresponding to polar coordinates, so that a model generated from such data is equivalent to a topographical map in Mercator projection. However an RP machine is fully capable of including the curvature of a planetary body in a model that it makes. Therefore, the software also offers a capability to transform the topographical data to a projection onto a surface having a curvature corresponding to that of the surface of the modeled planet.

Keller, John W.↗
NASA NTRS2014

America's Next Great Ship: Space Launch System Core Stage Transitioning from Design to Manufacturing

The Space Launch System (SLS) Program is essential to achieving the Nation's and NASA's goal of human exploration and scientific investigation of the solar system. As a multi-element program with emphasis on safety, affordability, and sustainability, SLS is becoming America's next great ship of exploration. The SLS Core Stage includes avionics, main propulsion system, pressure vessels, thrust vector control, and structures. Boeing manufactures and assembles the SLS core stage at the Michoud Assembly Facility (MAF) in New Orleans, LA, a historical production center for Saturn V and Space Shuttle programs. As the transition from design to manufacturing progresses, the importance of a well-executed manufacturing, assembly, and operation (MA&O) plan is crucial to meeting performance objectives. Boeing employs classic techniques such as critical path analysis and facility requirements definition as well as innovative approaches such as Constraint Based Scheduling (CBS) and Cirtical Chain Project Management (CCPM) theory to provide a comprehensive suite of project management tools to manage the health of the baseline plan on both a macro (overall project) and micro level (factory areas). These tools coordinate data from multiple business systems and provide a robust network to support Material & Capacity Requirements Planning (MRP/CRP) and priorities. Coupled with these tools and a highly skilled workforce, Boeing is orchestrating the parallel buildup of five major sub assemblies throughout the factory. Boeing and NASA are transforming MAF to host state of the art processes, equipment and tooling, the most prominent of which is the Vertical Assembly Center (VAC), the largest weld tool in the world. In concert, a global supply chain is delivering a range of structural elements and component parts necessary to enable an on-time delivery of the integrated Core Stage. SLS is on plan to launch humanity into the next phase of space exploration.

Birkenstock, Benjamin↗
NASA NTRS2016

Managing a Safe and Successful Multi-User Spaceport

Encouraged by the creation of the Office of Commercial Space Transportation within the U.S. Federal Aviation Administration (FAA) in 1984 and the Commercial Space Act of 1998, the National Aeronautics and Space Administration (NASA) now relies on an extensive network of support from commercial companies and organizations. At NASA's Kennedy Space Center (KSC), this collaboration opens competitive opportunities for launch providers, including repurposing underutilized Shuttle Program resources, constructing new facilities, and utilizing center services and laboratories. The resulting multi-user spaceport fosters diverse activity, though it engenders risk from hazards associated with various spaceflight processing activities. The KSC Safety & Mission Assurance (S&MA) Directorate, in coordination with the center's Spaceport Integration and Center Planning & Development organizations, has developed a novel approach to protect NASA's workforce, critical assets, and the public from hazardous, space-related activity associated with KSC's multi-user spaceport. For NASA KSC S&MA, the transformation to a multi-user spaceport required implementing methods to foster safe and successful commercial activity while resolving challenges involving: Retirement of the Space Shuttle program; Co-location of multiple NASA programs; Relationships between the NASA programs; Complex relationships between NASA programs and commercial partner operations in exclusive-use facilities; Complex relationships between NASA programs and commercial partner operations in shared-use facilities. NASA KSC S&MA challenges were met with long-term planning and solutions involving cooperation with the Spaceport Integration and Services Directorate. This directorate is responsible for managing active commercial partnerships with customer advocacy and services management, providing a dedicated and consistent level of support to a wide array of commercial operations. This paper explores these solutions, their relevance to the current commercial space industry, and the challenges that continue to drive improvement with a focus on areas of safety management and risk assessment that have been crucial in KSC's evolution into a multi-user spaceport. These solutions may be useful to government entities and private companies looking to partner with the commercial space industry.

Range↗
NASA NTRS1972

Determination of a third orthogonal velocity component using two rotationally displaced laser Doppler velocimeter systems.

Transformation equations are derived that may be used to determine a third orthogonal velocity component from measurements made at a common point by two rotationally displaced, two orthogonal component laser Doppler velocimeter (LDV) systems. These equations also may be used to relate velocity measurements made in a particular coordinate system to any other coordinate system. It is shown that the set of smallest angles that may be used to separate the two, two component, LDV systems is very sensitive to the relative magnitudes and directions of the individual velocity components. When the magnitudes of all velocity components are about the same, it is found that the minimum angle of separation is of the same order as the instrumental error of the LDV systems.

Farmer, W. M.↗
NASA NTRS1987

Quaternions as astrometric plate constants

A new method for solving problems in relative astrometry is proposed. In it, the relationship between the measured quantities and the components of the position vector of a star is modeled using quaternions, in effect replacing the plate constants of a standard four-plate-constant solution with the four components of a quaternion. The method allows a direct solution for the position vectors of the stars, and hence for the equatorial coordinates. Distortions, magnitude, and color effects are readily incorporated into the formalism, and the method is directly applicable to overlapping-plate problems. The advantages of the method include the simplicity of the resulting equations, their freedom from singularities, and the fact that trigonometric functions and tangential point transformations are not needed to model the plate material. A global solution over the entire sky is possible.

Jefferys, William H.↗
NASA NTRS1989

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗
NASA NTRS2002

The Burst and Transient Source Experiment Earth Occultation Technique

An Earth orbiting detector sensitive to gamma-ray photons will see step-like occultation features in its count rate when a gamma-ray point source crosses the Earth's limb. This is due to the change in atmospheric attenuation of the gamma rays along the line of sight. In an uncollimated detector, these occultation features can be used to locate and monitor astrophysical sources provided their signals can be individually separated from the detector background. We show that the Earth occultation technique applied to the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) is a viable and flexible all-sky monitor in the low-energy gamma-ray and hard X-ray energy range (20 keV-1 MeV). The method is an alternative to more sophisticated photon imaging devices for astronomy and can serve well as a cost-effective science capability for monitoring the high energy sky. Here we describe the Earth occultation technique for locating new sources and for measuring source intensity and spectra without the use of complex background models. Examples of transform imaging, step searches, spectra, and light curves are presented. Systematic uncertainties due to source confusion, detector response, and contamination from rapid background fluctuations are discussed and analyzed for their effect on intensity measurements. A sky location-dependent average systematic error is derived as a function of Galactic coordinates. The sensitivity of the technique is derived as a function of incident photon energy and also as a function of angle between the source and the normal to the detector entrance window. Occultations of the Crab Nebula by the Moon are used to calibrate Earth occultation flux measurements independent of possible atmospheric scattering effects.

Harmon, B. A.↗
NASA NTRS1991

Forward and inverse kinematics of double universal joint robot wrists

A robot wrist consisting of two universal joints can eliminate the wrist singularity problem found on many individual robots. Forward and inverse position and velocity kinematics are presented for such a wrist having three degrees of freedom. Denavit-Hartenberg parameters are derived to find the transforms required for the kinematic equations. The Omni-Wrist, a commercial double universal joint robot wrist, is studied in detail. There are four levels of kinematic parameters identified for this wrist; three forward and three inverse maps are presented for both position and velocity. These equations relate the hand coordinate frame to the wrist base frame. They are sufficient for control of the wrist standing alone. When the wrist is attached to a manipulator arm; the offset between the two universal joints complicates the solution of the overall kinematics problem. All wrist coordinate frame origins are not coincident, which prevents decoupling of position and orientation for manipulator inverse kinematics.

Williams, Robert L., II↗
NASA NTRS2020

The “Gearamid” Model: Transforming NASA Langley’s Role in the Aerospace Technology Ecosystem

NASA’s operating environment is evolving: numerous new emerging technologies are converging to create breakthrough solutions, many nontraditional players are partnering to create those solutions, and a diverse array of new public-private funding models are being employed. A team at NASA’s Langley Research Center (LaRC) developed a model to describe the challenges that must be addressed for an emerging breakthrough technology to penetrate the appropriate market sector, and how all the players in the relevant ecosystem can collaborate to accelerate the market infusion process. This model, which the team dubbed the “Gearamid,” originated from a narrower study to determine what LaRC should do to capitalize on and advance autonomous technology as a “game changer” in the civil aerospace domain. The elements in the original version of the Gearamid depict the various challenges that need to be addressed as an autonomous technology proceeds from initial development to market infusion. In addition, the Gearamid indicates the “actors” best suited to address each challenge element. The study team noted that all challenge elements in the Gearamid must be worked concurrently to assure successful infusion of autonomous solutions. The team also found that NASA expertise naturally positions Agency organizations—including LaRC—to lead contributions that address certain challenge elements and to play a supplemental role in other areas where entities external to NASA are actively working and investing to solve challenges. Furthermore, the team concluded that NASA can play a leadership role in coordinating efforts of the diverse entities across the civil aerospace community. After determining the center’s optimal role in the autonomous technology development ecosystem, the study team then extrapolated the Gearamid model for autonomous technologies into a broader, more general model depicting the challenge elements that must be overcome to develop and infuse any emerging technology. LaRC has embraced the Gearamid model and is using it to drive changes that will transform the center and allow it to function optimally in the evolving landscape. Given LaRC’s successes, the study team suggests that other organizations may also be able to use the Gearamid model to inform future planning/strategy efforts.

Jill M Marlowe↗
NASA NTRS2008

Algorithm for Wavefront Sensing Using an Extended Scene

A recently conceived algorithm for processing image data acquired by a Shack-Hartmann (SH) wavefront sensor is not subject to the restriction, previously applicable in SH wavefront sensing, that the image be formed from a distant star or other equivalent of a point light source. That is to say, the image could be of an extended scene. (One still has the option of using a point source.) The algorithm can be implemented in commercially available software on ordinary computers. The steps of the algorithm are the following: 1. Suppose that the image comprises M sub-images. Determine the x,y Cartesian coordinates of the centers of these sub-images and store them in a 2xM matrix. 2. Within each sub-image, choose an NxN-pixel cell centered at the coordinates determined in step 1. For the ith sub-image, let this cell be denoted as si(x,y). Let the cell of another subimage (preferably near the center of the whole extended-scene image) be designated a reference cell, denoted r(x,y). 3. Calculate the fast Fourier transforms of the sub-sub-images in the central NxN portions (where N < N and both are preferably powers of 2) of r(x,y) and si(x,y). 4. Multiply the two transforms to obtain a cross-correlation function Ci(u,v), in the Fourier domain. Then let the phase of Ci(u, v) constitute a phase function, phi(u,v). 5. Fit u and v slopes to phi (u,v) over a small u,v subdomain. 6. Compute the fast Fourier transform, Si(u,v) of the full NxN cell si(x,y). Multiply this transform by the u and phase slopes obtained in step 4. Then compute the inverse fast Fourier transform of the product. 7. Repeat steps 4 through 6 in an iteration loop, cumulating the u and slopes, until a maximum iteration number is reached or the change in image shift becomes smaller than a predetermined tolerance. 8. Repeat steps 4 through 7 for the cells of all other sub-images.

Sidick, Erkin↗
NASA NTRS1985

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg, (2) Re = 1000, alpha = 15 deg, (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗
NASA NTRS1986

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg., (2) Re =1000, alpha = 15 deg., (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗
NASA NTRS2016

Space Launch System Vibration Analysis Support

The ultimate goal for my efforts during this internship was to help prepare for the Space Launch System (SLS) integrated modal test (IMT) with Rodney Rocha. In 2018, the Structural Engineering Loads and Dynamics Team will have 10 days to perform the IMT on the SLS Integrated Launch Vehicle. After that 10 day period, we will have about two months to analyze the test data and determine whether the integrated vehicle modes/frequencies are adequate for launching the vehicle. Because of the time constraints, NASA must have newly developed post-test analysis methods proven well and with technical confidence before testing. NASA civil servants along with help from rotational interns are working with novel techniques developed and applied external to Johnson Space Center (JSC) to uncover issues in applying this technique to much larger scales than ever before. We intend to use modal decoupling methods to separate the entangled vibrations coming from the SLS and its support structure during the IMT. This new approach is still under development. The primary goal of my internship was to learn the basics of structural dynamics and physical vibrations. I was able to accomplish this by working on two experimental test set ups, the Simple Beam and TAURUS-T, and by doing some light analytical and post-processing work. Within the Simple Beam project, my role involves changing the data acquisition system, reconfiguration of the test set up, transducer calibration, data collection, data file recovery, and post-processing analysis. Within the TAURUS-T project, my duties included cataloging and removing the 30+ triaxial accelerometers, coordinating the removal of the structure from the current rolling cart to a sturdy billet for further testing, preparing the accelerometers for remounting, accurately calibrating, mounting, and mapping of all accelerometer channels, and some testing. Hammer and shaker tests will be performed to easily visualize mode shapes at low frequencies. Short analytical projects using MATLAB were also assigned to aid in research efforts. These included integration of acceleration data for comparison to measured displacement data. Laplace and Fourier transforms were also investigated to determine viability as a method of modal decoupling. In addition to these projects, I was also able contribute work that would benefit future interns and the division as a whole. I gave a short presentation and answered questions to aid in the recruitment of subsequent interns and co-ops for the division. I also assisted in revisions and additions to Intern/Co-Op Handbook to provide incoming employees with background information on the organization they are about to work for. I further developed tutorial on Pulse software, which was used for data acquisition for both experiments and will be helpful to interns and engineers that may be unfamiliar to the software. I gained a diverse range of experience throughout my internship. I was introduced to advanced dynamics and analytical techniques. This was through new experience with both hands on experimentation and analytical post processing methods. I was exposed to the benefits of interdepartmental collaboration and developed stronger skills in time management by coordinating two different tests at once. This internship provided an excellent opportunity to see how engineering theories applied to real life scenarios, and an introduction to how NASA/JSC solves technical problems.

Johnson, Katie↗
NASA NTRS1974

Finite element solution algorithm for incompressible fluid dynamics

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.

Baker, A. J.↗
NASA NTRS2018

Acoustic Radiation Pressure

The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in Lagrangian coordinates (not Eulerian coordinates) and that the terms in the BST are not the momentum flux density and mean excess Eulerian stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in Eulerian coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean Eulerian pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the Eulerian pressure. It is shown that the transformation between Lagrangian and Eulerian quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the Lagrangian and Eulerian radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the Lagrangian radiation pressure in the propagation direction is equal to (2K) and the BST result that the Eulerian radiation pressure in that direction is the momentum flux density.

Finite deformation theory↗