The international geomagnetic reference field 1965.0 in dipole coordinates
Computer program for transforming spherical harmonic coefficients to geomagnetic dipole coordinates
Mead, G. D.↗
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Results for “Coordinate transformations”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Finite difference solution to the three-dimensional, incompressible thermal energy boundary-layer equation
An implicit numerical method has been adopted for the solution to the three-dimensional, energy boundary-layer equation. The energy equation is written in terms of a dimensionless temperature function, the relative stagnation-enthalpy difference, and transformed by the introduction of a Blasius-type transformation of coordinates as well as dimensionless stream functions. The method is applied to the problem consisting of an infinite cylinder joined with its axis perpendicular to a thin, flat, heated plate. A Prandtl number equal to one is simply considered.
Fillo, J. A.↗
Two concepts for the reduction of payload attitude slewing times.
The concepts presented are particularly valuable in sounding rocket applications, where experiment data-gathering time above the atmosphere is measured in minutes per flight. One concept is a practical nonlinear control law for slewing a payload in one axis, with performance that approaches time-optimal as the uncertainty in angular acceleration approaches zero. The second concept is a practical transformation-of-coordinates system allowing slewing about an axis not coincident with any of the three control axes of the payload, so that the payload experiment axis may move along the great circle arc containing the initial and terminal target points. Implementation of both concepts is facilitated by the availability of variable-thrust cold-gas thrustors. Both concepts can result in significant reductions in slewing times compared with more conventional systems.
Riley, D. C.↗
A new technique for calculating reentry base heating
The laminar base flow field of a two-dimensional reentry body has been studied by Telenin's method. The flow domain was divided into strips along the x-axis, and the flow variations were represented by Lagrange interpolation polynomials in the transformed vertical coordinate. The complete Navier-Stokes equations were used in the near wake region, and the boundary layer equations were applied elsewhere. The boundary conditions consisted of the flat plate thermal boundary layer in the forebody region and the near wake profile in the downstream region. The resulting two-point boundary value problem of 33 ordinary differential equations was then solved by the multiple shooting method. The detailed flow field and thermal environment in the base region are presented in the form of temperature contours, Mach number contours, velocity vectors, pressure distributions, and heat transfer coefficients on the base surface. The maximum heating rate was found on the centerline, and the two-dimensional stagnation point flow solution was adquate to estimate the maximum heating rate so long as the local Reynolds number could be obtained.
Meng, J. C. S.↗
Basic research and data analysis for the national geodetic satellite program and for the earth and ocean physics applications program
Activities related to the National Geodetic Satellite Program are reported and include a discussion of Ohio State University's OSU275 set of tracking station coordinates and transformation parameters, determination of network distortions, and plans for data acquisition and processing. The problems encountered in the development of the LAGEOS satellite are reported in an account of activities related to the Earth and Ocean Physics Applications Program. The LAGEOS problem involves transmission and reception of the laser pulse designed to make accurate determinations of the earth's crustal and rotational motions. Pulse motion, ephemeris, arc range measurements, and accuracy estimates are discussed in view of the problem. Personnel involved in the two programs are also listed, along with travel activities and reports published to date.
Source record↗
The scattering of electromagnetic pulses by a slit in a conducting screen
A direct method for calculating the impulse response of a slit in a conducting screen is presented which is derived specifically for the analysis of transient scattering by two-dimensional objects illuminated by a plane incident wave. The impulse response is obtained by assuming that the total response is composed of two sequences of diffracted waves. The solution is determined for the first two waves in one sequence by using Green's functions and the equivalence principle, for additional waves in the sequence by iteration, and for the other sequence by a transformation of coordinates. The cases of E-polarization and H-polarization are considered.
Ackerknecht, W. E., III↗
Oblique orthographic projections and contour plots
Oblique orthographic projections allow model to be viewed in any selected orientation specified by Euler-angle transformation. This transformation resolves coordinate system of model to principal plane on which display is to be plotted.
Giles, G. L.↗
Volumetric pattern analysis of fuselage-mounted airborne antennas
A volumetric pattern analysis of fuselage-mounted airborne antennas at high frequencies was investigated. The primary goal of the investigation was to develop a numerical solution for predicting radiation patterns of airborne antennas in an accurate and efficient manner. An analytical study of airborne antenna pattern problems is presented in which the antenna is mounted on the fuselage near the top or bottom. Since this is a study of general-type commercial aircraft, the aircraft was modeled in its most basic form. The fuselage was assumed to be an infinitely long perfectly conducting elliptic cylinder in its cross-section and a composite elliptic cylinder in its elevation profile. The wing, cockpit, stabilizers (horizontal and vertical) and landing gear are modeled by "N" sided bent or flat plates which can be arbitrarily attached to the fuselage. The volumetric solution developed utilizes two elliptic cylinders, namely, the roll plane and elevation plane models to approximate the principal surface profile (longitudinal and transverse) at the antenna location. With the belt concept and the aid of appropriate coordinate system transformations the solution can be used to predict the volumetric patterns of airborne antennas in an accurate and efficient manner. Applications of this solution to various airborne antenna problems show good agreement with scale model measurements. Extensive data are presented for a microwave landing antenna system.
Yu, C. L.↗
Numerical calculation of transonic flow past a swept wing by a finite volume method
The utility of numerical methods for predicting transonic flows over wings and bodies is well established. The computer program FLO22, based on a method presented earlier, has actually been widely used to calculate the aerodynamic performance of wings of transport aircraft. Provided that a correction is made for the displacement effect of the viscous boundary layer, this code has been found to give predictions which are accurate enough to serve as a useful design guide. The main disadvantages of the scheme used in FLO22 are the use of nonconservative difference formulas, which result in a failure to satisfy conservation of mass across shock waves, and the difficulty of finding suitable transformations of coordinates to permit the treatment of more complex geometric configurations. The method described here is an attempt to overcome these shortcomings, while retaining the successful features of the previous method. The basic idea is to use a discrete approximation which directly represents a balance of the mass flow through small volume elements. This leads to a relatively simple treatment of the potential flow equation in conservation form.
Jameson, A.↗
Airplane stability calculations with a card programmable pocket calculator
Programs are presented for calculating airplane stability characteristics with a card programmable pocket calculator. These calculations include eigenvalues of the characteristic equations of lateral and longitudinal motion as well as stability parameters such as the time to damp to one-half amplitude or the damping ratio. The effects of wind shear are included. Background information and the equations programmed are given. The programs are written for the International System of Units, the dimensional form of the stability derivatives, and stability axes. In addition to programs for stability calculations, an unusual and short program is included for the Euler transformation of coordinates used in airplane motions. The programs have been written for a Hewlett Packard HP-67 calculator. However, the use of this calculator does not constitute an endorsement of the product by the National Aeronautics and Space Administration.
Sherman, W. L.↗
Finite difference solutions of heat conduction problems in multi-layered bodies with complex geometries
A numerical procedure is presented for analyzing a wide variety of heat conduction problems in multilayered bodies having complex geometry. The method is based on a finite difference solution of the heat conduction equation using a body fitted coordinate system transformation. Solution techniques are described for steady and transient problems with and without internal energy generation. Results are found to compare favorably with several well known solutions.
Masiulaniec, K. C.↗
The method of complex characteristics for design of transonic blade sections
A variety of computational methods were developed to obtain shockless or near shockless flow past two-dimensional airfoils. The approach used was the method of complex characteristics, which determines smooth solutions to the transonic flow equations based on an input speed distribution. General results from fluid mechanics are presented. An account of the method of complex characteristics is given including a description of the particular spaces and coordinates, conformal transformations, and numerical procedures that are used. The operation of the computer program COMPRES is presented along with examples of blade sections designed with the code. A user manual is included with a glossary to provide additional information which may be helpful. The computer program in Fortran, including numerous comment cards is listed.
Bledsoe, M. R.↗
Lagrangian mean circulations in the stratosphere
The mean Lagrangian motion in the winter stratosphere is computed on the basis of three-dimensional winds derived from the 1978/1979 winter LIMS satellite observations, initializing material tubes of air parcels every 4 days and following them for periods of 10 days each. When the wave amplitudes are large, the tubes break and the parcels disperse; during the major sudden warming, every material tube in the stratosphere was broken, leading to extensive mixing between low and high amplitude parcels. The Lagrangian mean vertical motion tended to be smaller than the motion in the transformed Eulerian coordinate system.
Lyjak, Lawrence V.↗
Navier-Stokes solutions about the F/A-18 forebody-LEX configuration
Three-dimensional viscous How computations are presented for the F/A-18 fore body-LEX geometry. Solutions are obtained from an algorithm for the compressible Navier-Stokes equations which incorporates an upwind-biased, flux-difference-splitting approach along with longitudinally-patched grids. Results are presented for both laminar and fully turbulent flow assumptions and include correlations with wind tunnel as well as flight-test results. A good quantitative agreement for the forebody surface pressure distribution is achieved between the turbulent computations and wind tunnel measurements at M ∞ = 0.6. The computed turbulent surface flow patterns on the forebody qualitatively agree well with in-flight surface flow patterns obtained on an F/A-18 aircraft at M ∞ = 0.34.
Transitional flow↗
An interactive chemical dynamical radiative two-dimensional model of the middle atmosphere
A new two-dimensional model of the stratosphere and the mesosphere was formulated in transformed Eulerian coordinates, in which dynamics, radiation, and chemistry are treated interactively. The model includes a detailed radiative scheme which derives the diabatic heating rates consistently with calculated distributions of temperature and trace species densities. Results are presented on the present-day and perturbed atmosphere, showing that the calculated distributions of source gases, such as nitrous oxide and methane, are very sensitive to the calculated (and parameterized) dynamical quantities, and that species produced in the atmosphere, like carbon monoxide and odd nitrogen, can provide valuable information on the role of atmospheric transport.
Brasseur, G.↗
An approach for targeting landers and penetrators using orbital optical navigation
Onboard orbital optical navigation data is analyzed with the purpose of generating topographic maps for selecting a landing site. It is suggested that a near-real time orbit-determination process be used for solving a large set of parameters including the spacecraft orbit and primary-body gravity field, the rotational properties of the planetary body, the coordinates of surface features, and the camera-pointing and orientation angles of each picture. A batch-sequential formulation of the standard least-squares problem is employed, along with backward smoothing and a square-root formation filter. An experiment in which over 100 images of Phobos are processed to estimate about 2000 parameters is presented, with emphasis on coordinate systems, transforming points on the reference surface to images in the picture, parameter estimation, and cartographic accuracy.
Wang, Tseng-Chan↗
The chemical composition of the dust-free Martian atmosphere - Preliminary results of a two-dimensional model
This paper describes a two-dimensional model of the Martian atmosphere, in which chemical, radiative and dynamical processes are treated interactively. The model is developed for a carbon dioxide-hydrogen-oxygen-nitrogen atmosphere and provides estimates of concentrations for 19 chemical species. The dynamical equations are expressed in the transformed Eulerian coordinates. The wave driving and eddy mixing coefficients resulting from gravity and Rossby wave absorption are computed consistently with the evolving distribution of the mean zonal wind. The net diabatic heating/cooling rate is derived from a detailed radiative scheme including the contributions of CO2, O3, H2O and O2, and is computed consistently with the calculated distribution of temperature and trace species quantities. The computed temperature field as well as the meridional and seasonal variations of ozone column abundance are in good agreement with the distributions observed by Mariner 9 and Viking spacecrafts and the results obtained by previous studies. The present version of the model does not include the effects of dust, clouds and polar hood and only the chemistry in a dust-free atmosphere is considered.
Moreau, D.↗
High-order ENO methods for the unsteady compressible Navier-Stokes equations
The adaptive stencil concepts of ENO (Essentially Non-Oscillatory) methods are applied to the laminar Navier-Stokes equations to yield a high-order, time-accurate algorithm with a shock-capturing capability. The method targets problems in the areas of nonlinear acoustics, compressible transition, and turbulence which, due to the presence of shocks or complex geometries, are not easily solved by spectral methods. The present approach has been implemented and tested for the full three-dimensional Navier-Stokes equations in a transformed curvilinear coordinate system. Validation results are presented for a variety of problems which verify the method's accuracy properties and shock capturing capabilities, as well as demonstrate its use as a direct simulation tool.
Atkins, H. L.↗