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NASA NTRS1981

Baseline mathematics and geodetics for tracking operations

Various geodetic and mapping algorithms are analyzed as they apply to radar tracking systems and tested in extended BASIC computer language for real time computer applications. Closed-form approaches to the solution of converting Earth centered coordinates to latitude, longitude, and altitude are compared with classical approximations. A simplified approach to atmospheric refractivity called gradient refraction is compared with conventional ray tracing processes. An extremely detailed set of documentation which provides the theory, derivations, and application of algorithms used in the programs is included. Validation methods are also presented for testing the accuracy of the algorithms.

James, R.↗

NASA NTRS1983

An interactive system for compositing digital radar and satellite data

This paper describes an approach for compositing digital radar data and GOES satellite data for meteorological analysis. The processing is performed on a user-oriented image processing system, and is designed to be used in the research mode. It has a capability to construct PPIs and three-dimensional CAPPIs using conventional as well as Doppler data, and to composite other types of data. In the remapping of radar data to satellite coordinates, two steps are necessary. First, PPI or CAPPI images are remapped onto a latitude-longitude projection. Then, the radar data are projected into satellite coordinates. The exact spherical trigonometric equations, and the approximations derived for simplifying the computations are given. The use of these approximations appears justified for most meteorological applications. The largest errors in the remapping procedure result from the satellite viewing angle parallax, which varies according to the cloud top height. The horizontal positional error due to this is of the order of the error in the assumed cloud height in mid-latitudes. Examples of PPI and CAPPI data composited with satellite data are given for Hurricane Frederic on 13 September 1979 and for a squall line on 2 May 1979 in Oklahoma.

Heymsfield, G. M.↗

NASA NTRS1989

Phoebe: A preliminary control network and rotational elements

A preliminary control network for the Saturnian satellite Phoebe was determined based upon 6 distinct albedo features mapped on 16 Voyager 2 images. Using an existing map and an analytical triangulation program which minimized the measurement error, the north pole of Phoebe was calculated to be alpha sub 0 = 355.0 deg + or - 9.6 deg, delta sub 0 = 68.7 deg + or - 7.9 deg, where alpha sub 0, delta sub 0 are standard equatorial coordinates with equinox J2000 at epoch J2000. The prime meridian of Phoebe was computed to be W = 304.7 deg + 930.833872d, where d is the interval in days from JD 2451545.0 TDB.

Colvin, Tim R.↗

NASA NTRS1991

Preliminary calibration plan for the Advanced Particles and Field Observatory (APAFO) magnetometer experiment

Prelaunch and postlaunch calibration plans for the APAFO magnetometer experiment are presented. A study of tradeoffs between boom length and spacecraft field is described; the results are summarized. The prelaunch plan includes: calibration of the Vector Fluxgate Magnetometer (VFM), Star Sensors, and Scalar Helium Magnetometer (SHM); optical bench integration; and acquisition of basic spacecraft field data. Postlaunch calibration has two phases. In phase one, SHM data are used to calibrate the VFM, total vector magnetic field data are used to calibrate a physical model of the spacecraft field, and both calibrations are refined by iteration. In phase two, corrected vector data are transformed into geocentric coordinates, previously undetected spacecraft fields are isolated, and initial geomagnetic field models are computed. Provided the SHM is accurate to the required 1.0 nT and can be used to calibrate the VFM to the required 3.0- nT accuracy, the tradeoff study indicates that a 12 m boom and a spacecraft field model uncertainty of 5 percent together allow the 1.0 nT spacecraft field error requirement to be met.

Voorhies, C. V.↗

NASA NTRS1991

Computation of three-dimensional flows using two stream functions

An approach to compute 3-D flows using two stream functions is presented. The method generates a boundary fitted grid as part of its solution. Commonly used two steps for computing the flow fields are combined into a single step in the present approach: (1) boundary fitted grid generation; and (2) solution of Navier-Stokes equations on the generated grid. The presented method can be used to directly compute 3-D viscous flows, or the potential flow approximation of this method can be used to generate grids for other algorithms to compute 3-D viscous flows. The independent variables used are chi, a spatial coordinate, and xi and eta, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since for a 3-D flow there is no unique way to define two sets of intersecting stream surfaces to cover the given flow, different types of two sets of intersecting stream surfaces are considered. First, the metric of the (chi, xi, eta) curvilinear coordinate system associated with each type is presented. Next, equations for the steady state transport of mass, momentum, and energy are presented in terms of the metric of the (chi, xi, eta) coordinate system. Also included are the inviscid and the parabolized approximations to the general transport equations.

Greywall, Mahesh S.↗

NASA NTRS1993

Earth system dynamics: The interrelation of atmospheric, ocean and solid earth dynamics

The research work performed during the time period 16 Oct. 1992 through 31 Dec. 1993 is summarized. The overall research activity, including a list of the major findings of the EOS IDS research to date, is described, the publications and presentations are listed, and a budget request for the subsequent year is attached. Specifically, the report covers: EOS panel activities; major findings of research; team member contributions; new research directions; EOS restructuring effect; changes in requirements; plans for using existing data; collaborations with other EOS and non-EOS investigations; EOS instrument team interaction; instrument development verification and validation; interaction with EOSDIS and DAAC's; team coordination; overall management; summary of response to site review questions and comments; science computing facility; and additional new research activities.

Tapley, Byron D.↗

NASA NTRS1994

Multi-dimensional combustor flowfield analyses in gas-gas rocket engine

The objectives of the present research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustions processes. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an on-going experimental program at NASA LeRC. Detailed computational modeling requires the application of the full three-dimensional Navier Stokes equations, coupled with species diffusion equations. The numerical procedure is performed on both time-marching and time-accurate algorithms and using an LU approximate factorization in time, flux split upwinding differencing in space. The emphasis in this paper is focused on using numerical analysis to understand detailed combustor flowfields, including the shear layer dynamics created between fuel film cooling and the core gas in the vicinity on the nearby combustor wall; the integrity and effectiveness of the coolant film; three-dimensional fuel jets injection/mixing/combustion characteristics; and their impacts on global engine performance.

Tsuei, Hsin-Hua↗

NASA NTRS1995

Effect of baffle on slosh reaction forces in rotating liquid helium subjected to a lateral impulse in microgravity

Sloshing dynamics within a partially filled rotating Dewar of superfluid He II are investigated in response to a lateral impulse. The study investigates several factors, including how the rotating bubble of superfluid He II reacts to the impulse in microgravity, how the amplitudes of slosh reaction forces act on the Dewar with various rotating speeds, how the frequencies of the sloshing modes excited differ in terms of differences in rotating speeds, and how the sloshing dynamics differ with and without a baffle. The numerical computation of sloshing dynamics is based on the noninertial frame spacecraft-bound coordinates. Results of the simulations are illustrated.

Hung, R. J.↗

NASA NTRS1996

NASA flow fields analysis

The objectives of the present research are to improve design capabilities for low thrust rocket engines through understanding the detailed mixing and combustion processes in a representative combustor. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an on-going experimental program at NASA LERC. Detailed computational modeling involves the solution of both the two- and three-dimensional Navier Stokes equations, coupled with chemical reactions and the species diffusion equations. Computations of interest include both steady state and time-accurate flowfields and are obtained by means of LU approximate factorization in time and flux split upwinding differencing in space. The emphasis in the research is focused on using numerical analysis to understand detailed combustor flowfields, including the shear layer dynamics created between fuel film cooling and the core gas in the vicinity on the nearby combustor wall; the integrity and effectiveness of the coolant film; and three-dimensional fuel and oxidizer jet injection/mixing/combustion characteristics in the primary combustor along with their joint impacts on global engine performance.

Merkle, Charles L.↗

NASA NTRS1996

An MHD Study of the Interaction Between the Solar Wind and the Interstellar Medium

The overall objective of this research program is to obtain a better understanding of the interaction between the solar wind and the interstellar medium through the use of numerical solutions of the time-dependent magnetohydrodynamic (MHD) equations. The simulated results have been compared with observations where possible and with the results from previous analytic and numerical studies. The primary accomplishment of this project has been the development of codes for 2-D models in both spherical and cylindrical coordinates and the application of the codes to the solar wind/interstellar medium interaction. Computations have been carried out for both a relatively simple gas-dynamic interaction and a flow-aligned interstellar magnetic field. The results have been shown to compare favorably with models that use more approximations and to modify and extend the previous results as would be expected. The simulations have also been used along with a data analysis study to provide a quantitative estimate of the distance to the termination and bow shocks. Some of the specific topics that have been studied are: (1) gas dynamic models of the solar wind/interstellar medium interaction, (2) termination shock response to large-scale solar wind fluctuations, and (3) distances to the termination shock and heliopause. The main results from each of these studies are summarized. The results were published in three papers which are included as attachments.

Steinolfson, R. S.↗

NASA NTRS1995

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Hung, R. J.↗

NASA NTRS1998

Implementation of a Parallel Kalman Filter for Stratospheric Chemical Tracer Assimilation

A Kalman filter for the assimilation of long-lived atmospheric chemical constituents has been developed for two-dimensional transport models on isentropic surfaces over the globe. An important attribute of the Kalman filter is that it calculates error covariances of the constituent fields using the tracer dynamics. Consequently, the current Kalman-filter assimilation is a five-dimensional problem (coordinates of two points and time), and it can only be handled on computers with large memory and high floating point speed. In this paper, an implementation of the Kalman filter for distributed-memory, message-passing parallel computers is discussed. Two approaches were studied: an operator decomposition and a covariance decomposition. The latter was found to be more scalable than the former, and it possesses the property that the dynamical model does not need to be parallelized, which is of considerable practical advantage. This code is currently used to assimilate constituent data retrieved by limb sounders on the Upper Atmosphere Research Satellite. Tests of the code examined the variance transport and observability properties. Aspects of the parallel implementation, some timing results, and a brief discussion of the physical results will be presented.

Chang, Lang-Ping↗

NASA NTRS2002

GPS Modeling and Analysis. Summary of Research: GPS Satellite Axial Ratio Predictions

This report outlines the algorithms developed at the Colorado Center for Astrodynamics Research to model yaw and predict the axial ratio as measured from a ground station. The algorithms are implemented in a collection of Matlab functions and scripts that read certain user input, such as ground station coordinates, the UTC time, and the desired GPS (Global Positioning System) satellites, and compute the above-mentioned parameters. The position information for the GPS satellites is obtained from Yuma almanac files corresponding to the prescribed date. The results are displayed graphically through time histories and azimuth-elevation plots.

Axelrad, Penina↗

NASA NTRS1999

A Simple Tool for the Design and Analysis of Multiple-reflector Antennas in a Multi-disciplinary Environment

The process of designing and analyzing a multiple-reflector system has traditionally been time-intensive, requiring large amounts of both computational and human time. At many frequencies, a discrete approximation of the radiation integral may be used to model the system. The code which implements this physical optics (PO) algorithm was developed at the Jet Propulsion Laboratory. It analyzes systems of antennas in pairs, and for each pair, the analysis can be computationally time-consuming. Additionally, the antennas must be described using a local coordinate system for each antenna, which makes it difficult to integrate the design into a multi-disciplinary framework in which there is traditionally one global coordinate system, even before considering deforming the antenna as prescribed by external structural and/or thermal factors. Finally, setting up the code to correctly analyze all the antenna pairs in the system can take a fair amount of time, and introduces possible human error.

Katz, Daniel, S.↗

NASA NTRS2006

Montage Version 3.0

The final version (3.0) of the Montage software has been released. To recapitulate from previous NASA Tech Briefs articles about Montage: This software generates custom, science-grade mosaics of astronomical images on demand from input files that comply with the Flexible Image Transport System (FITS) standard and contain image data registered on projections that comply with the World Coordinate System (WCS) standards. This software can be executed on single-processor computers, multi-processor computers, and such networks of geographically dispersed computers as the National Science Foundation s TeraGrid or NASA s Information Power Grid. The primary advantage of running Montage in a grid environment is that computations can be done on a remote supercomputer for efficiency. Multiple computers at different sites can be used for different parts of a computation a significant advantage in cases of computations for large mosaics that demand more processor time than is available at any one site. Version 3.0 incorporates several improvements over prior versions. The most significant improvement is that this version is accessible to scientists located anywhere, through operational Web services that provide access to data from several large astronomical surveys and construct mosaics on either local workstations or remote computational grids as needed.

Jacob, Joseph↗

NASA NTRS2022

On-board Absolute Localization Based on Orbital Imagery for a Future Mars Science Helicopter

Future Mars Rotorcraft require advanced navigationcapabilities to enable all terrain access over long distance flightsthat are executed fully autonomously. A critical component toenable precision navigation during long traverses is the abilityto perform on-board absolute localization to eliminate drift inposition estimates of the on-board odometry algorithm. Inthis paper, we present an approach for on-board map-basedlocalization to provide global reference position based on orbitalor aerial image maps. Our approach builds on a vision-basedlocalization method to localize against a map derived fromHiRISE image products – an ortho-projected image (orthoimage) and a corresponding digital elevation map. The mapis pre-computed using a feature-based approach. Features arestored with their 3D world coordinates, and a descriptor to codethe local image intensity information in the vicinity of the featurelocation. An on-board matching algorithm uses this informationto match visual features in a query image acquired during flight,guided by a pose prior from the on-board range-visual-inertialstate estimator (Range-VIO). Valid matches are then used bya perspective-n-point (PnP) algorithm to estimate the absolutepose of the vehicle in a global frame. We demonstrate andevaluate our approach on simulated data, and data from UASflights.

Balaram, J. Bob↗

NASA NTRS1986

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗

NASA NTRS1992

Structural optimization of thin shells using finite element method

The objective of the present work was the structural optimization of thin shell structures that are subjected to stress and displacement constraints. In order to accomplish this, the structural optimization computer program DESAP1 was modified and improved. In the static analysis part of the DESAP1 computer program the torsional spring elements, which are used to analyze thin, shallow shell structures, were eliminated by modifying the membrane stiffness matrix of the triangular elements in the local coordinate system and adding a fictitious rotational stiffness matrix. This simplified the DESAP1 program input, improved the accuracy of the analysis, and saved computation time. In the optimization part of the DESAP1 program the stress ratio formula, which redesigns the thickness of each finite element of the structure, was solved by an analytical method. This scheme replaced the iterative solution that was previously used in the DESAP1 program, thus increasing the accuracy and speed of the design. The modified program was used to design a thin, cylindrical shell structure with optimum weight, and the results are reported in this paper.

Gotsis, Pascal K.↗