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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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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Interpolation constants for calculation of transmittance and rate of dissociation of molecular oxygen in the mesosphere and lower thermosphere

Values of band oscillator strengths and rotational line widths for the Schumann-Runge band system have been used to derive interpolation constants from which the transmittance and rate of dissociation of molecular oxygen can be calculated. These constants, valid for temperatures between 150 and 300 K and for column densities between 1 x 10 to the 17th power/cm sq and 7 x 10 to the 24th power/cm sq, cover the wavelength range 1750 and 2050A.

Hudson, R. D.↗
NASA NTRS1972

Interpolation using surface splines.

A surface spline is a mathematical tool for interpolating a function of two variables. It is based upon the small deflection equation of an infinite plate. The surface spline depends upon the solution of a system of linear equations, and thus, will ordinarily require the use of a digital computer. The closed form solution involves no functions more complicated than logarithms, and is easily coded. Several modifications which can be incorporated are discussed.

Harder, R. L.↗
NASA NTRS1973

Generalize aerodynamic coefficient table storage, checkout and interpolation for aircraft simulation

The set of programs described has been used for rapidly introducing, checking out and very efficiently using aerodynamic tables in complex aircraft simulations on the IBM 360. The preprocessor program reads in tables with different names and dimensions and stores then on disc storage according to the specified dimensions. The tables are read in from IBM cards in a format which is convenient to reduce the data from the original graphs. During table processing, new auxiliary tables are generated which are required for table cataloging and for efficient interpolation. In addition, DIMENSION statements for the tables as well as READ statements are punched so that they may be used in other programs for readout of the data from disc without chance of programming errors. A quick data checking graphical output for all tables is provided in a separate program.

Neuman, F.↗
NASA NTRS1972

Data smoothing and error detection based on linear interpolation

A method is presented, based on linear interpolation, for detecting and correcting bad data points in a set of data without contaminating the good data points. The method used is not concerned with the small random errors usually attributed to a noisy system. It assumes that the data points which are in error are relatively isolated from each other and that the number of such points is small compared to the total number of data points.

Guerra, V. M.↗
NASA NTRS1974

Optimal rocket thrust profile shaping using third degree spline function interpolation

Optimal solid-rocket thrust profiles for the parallel-burn, solid-rocket-assisted space shuttle are investigated. Solid-rocket thrust profiles are simulated by using third-degree spline functions, with the values of the thrust ordinates defined as parameters. The profiles are optimized parametrically, using the Davidon-Fletcher-Powell penalty function method, by minimizing propellant weight subject to state and control inequality constraints and to terminal boundary conditions. This study shows that optimizing a control variable parametrically by using third-degree spline function interpolation allows the control to be shaped so that inequality constraints are strictly adhered to and all corners are eliminated. The absence of corners, which is realistic in nature, makes this method attractive from the viewpoint of solid rocket grain design.

Johnson, I. L.↗
NASA NTRS1975

Interpolation in numerical optimization

The present work discusses the generation of the cubic-spline interpolator in numerical optimization methods which use a variable-step integrator with step size control based on local relative truncation error. An algorithm for generating the cubic spline with successive over-relaxation is presented which represents an improvement over that given by Ralston and Wilf (1967). Rewriting the code reduces the number of N-vectors from eight to one. The algorithm is formulated in such a way that the solution of the linear system set up yields the first derivatives at the nodal points. This method is as accurate as other schemes but requires the minimum amount of storage.

Hall, K. R.↗
NASA NTRS1976

Cubic spline function interpolation in atmosphere models for the software development laboratory: Formulation and data

A tabulation of selected altitude-correlated values of pressure, density, speed of sound, and coefficient of viscosity for each of six models of the atmosphere is presented in block data format. Interpolation for the desired atmospheric parameters is performed by using cubic spline functions. The recursive relations necessary to compute the cubic spline function coefficients are derived and implemented in subroutine form. Three companion subprograms, which form the preprocessor and processor, are also presented. These subprograms, together with the data element, compose the spline fit atmosphere package. Detailed FLOWGM flow charts and FORTRAN listings of the atmosphere package are presented in the appendix.

Kirkpatrick, J. C.↗
NASA NTRS1976

First-Order-hold interpolation digital-to-analog converter with application to aircraft simulation

Those who design piloted aircraft simulations must contend with the finite size and speed of the available digital computer and the requirement for simulation reality. With a fixed computational plant, the more complex the model, the more computing cycle time is required. While increasing the cycle time may not degrade the fidelity of the simulated aircraft dynamics, the larger steps in the pilot cue feedback variables (such as the visual scene cues), may be disconcerting to the pilot. The first-order-hold interpolation (FOHI) digital-to-analog converter (DAC) is presented as a device which offers smooth output, regardless of cycle time. The Laplace transforms of these three conversion types are developed and their frequency response characteristics and output smoothness are compared. The FOHI DAC exhibits a pure one-cycle delay. Whenever the FOHI DAC input comes from a second-order (or higher) system, a simple computer software technique can be used to compensate for the DAC phase lag. When so compensated, the FOHI DAC has (1) an output signal that is very smooth, (2) a flat frequency response in frequency ranges of interest, and (3) no phase error. When the input comes from a first-order system, software compensation may cause the FOHI DAC to perform as an FOHE DAC, which, although its output is not as smooth as that of the FOHI DAC, has a smoother output than that of the ZOH DAC.

Cleveland, W. B.↗
NASA NTRS1977

Software for C1 interpolation

The problem of mathematically defining a smooth surface, passing through a finite set of given points is studied. Literature relating to the problem is briefly reviewed. An algorithm is described that first constructs a triangular grid in the (x,y) domain, and first partial derivatives at the modal points are estimated. Interpolation in the triangular cells using a method that gives C sup.1 continuity overall is examined. Performance of software implementing the algorithm is discussed. Theoretical results are presented that provide valuable guidance in the development of algorithms for constructing triangular grids.

Lawson, C. L.↗
NASA NTRS1976

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗
NASA NTRS1981

RAWINPROC: Computer program for decommutating, interpreting, and interpolating Rawinsonde meteorological balloon sounding data

The FORTRAN computer program RAWINPROC accepts output from NASA Wallops computer program METPASS1; and produces input for NASA computer program 3.0.0700 (ECC-PRD). The three parts together form a software system for the completely automatic reduction of standard RAWINSONDE sounding data. RAWINPROC pre-edits the 0.1-second data, including time-of-day, azimuth, elevation, and sonde-modulated tone frequency, condenses the data according to successive dwells of the tone frequency, decommutates the condensed data into the proper channels (temperature, relative humidity, high and low references), determines the running baroswitch contact number and computes the associated pressure altitudes, and interpolates the data appropriate for input to ACC-PRD.

Staffanson, F. L.↗
NASA NTRS1982

Variational methods in simultaneous optimum interpolation and initialization

The duality between optimum interpolation and variational objective analysis, is reviewed. This duality is used to set up a variational approach to objective analysis which uses prior information concerning the atmospheric spectral energy distribution, in the variational problem. In the wind analysis example, the wind field is partitioned into divergent and nondivergent parts, and a control parameter governing the relative energy in the two parts is estimated from the observational data being analyzed by generalized cross validation, along with a bandwidth parameter. A variational approach to combining objective analysis and initialization in a single step is proposed. In a simple example of this approach, data, forecast, and prior information concerning atmospheric energy distribution is combined into a single variational problem. This problem has (at least) one bandwidth parameter, one partitioning parameter governing the relative energy in fast slow modes, and one parameter governing the relative weight to be given to observational and forecast data.

Wahba, G.↗
NASA NTRS1984

Comparison of Optimum Interpolation and Cressman Analyses

The objective of this investigation is to develop a state-of-the-art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies. A three-dimensional multivariate O/I analysis scheme has been developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

Baker, W. E.↗
NASA NTRS1985

Interpolation Methods for GTD Analysis of Shaped Reflectors

The finding of smooth analytic representations for antenna reflector surfaces which are prescribed only by discretized data obtained by various synthesis methods is examined. Frequently the data are distributed in a nonuniform grid and contain noise. The smoothness required is to C sub 1 for physical optics diffraction analysis and to C sub 2 for geometrical theory of diffraction (GTD) analysis. The GTD analysis approach requires a surface description which returns data very rapidly. Two methods of interpolation, the global and the local methods, are discussed. They each have advantages and disadvantages; characteristics are discussed and examples are presented.

Galindo-Israel, V.↗
NASA NTRS1985

Convex Interpolating Splines of Arbitrary Degree

Shape preserving approximations are constructed by interpolating the data with polynomial splines of arbitrary degree. A regularity condition is formulated on the data which insures the existence of such a shape preserving spline, an algorithm is presented for its construction, and the uniform norm of the error is bound which results when the algorithm is used to produce an approximation to a given f epsilon Ca,b.

Neuman, E.↗
NASA NTRS1985

Comparison of Optimum Interpolation and Cressman Analyses

The development of a state of the art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies was investigated. A three dimensional multivariate O/I analysis scheme was developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

Baker, W. E.↗
NASA NTRS1985

Developement of an Optimum Interpolation Analysis Method for the CYBER 205

A state-of-the-art technique to assimilate the diverse observational database obtained during FGGE, and thus create initial conditions for numerical forecasts is described. The GLA optimum interpolation (OI) analysis method analyzes pressure, winds, and temperature at sea level, mixing ratio at six mandatory pressure levels up to 300 mb, and heights and winds at twelve levels up to 50 mb. Conversion to the CYBER 205 required a major re-write of the Amdahl OI code to take advantage of the CYBER vector processing capabilities. Structured programming methods were used to write the programs and this has resulted in a modular, understandable code. Among the contributors to the increased speed of the CYBER code are a vectorized covariance-calculation routine, an extremely fast matrix equation solver, and an innovative data search and sort technique.

Nestler, M. S.↗