Search NASA⌕ Search

SEARCH · Search NASA

Results for “extrapolate”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

The accuracy of far-field noise obtained by the mathematical extrapolation of near-field noise data

Results are presented for an analytical study of the accuracy and limitations of a technique that permits the mathematical extrapolation of near-field noise data to far-field conditions. The effects of the following variables on predictive accuracy of the far-field pressure were examined: (1) number of near-field microphones; (2) length of source distribution; (3) complexity of near-field and far-field distributions; (4) source-to-microphone distance; and (5) uncertainties in microphone data and imprecision in the location of the near-field microphones. It is shown that the most important parameters describing predictive accuracy are the number of microphones, the ratio of source length to acoustic wavelength (L/lambda), and the error in location of near-field microphones. For maximum microphone location errors of plus or minus 1 cm, only an accuracy of plus or minus 2.5 dB can be attained with approximately 40 microphones for the highest L/lambda of 10.

Ahtye, W. F.↗
NASA NTRS1978

Extrapolation methods for dynamic partial differential equations

Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.

Turkel, E.↗
NASA NTRS1979

Correlation of data related to shock-induced trailing-edge separation and extrapolation to flight Reynolds number

Pressure data from a number of previous wind tunnel and flight investigations of high speed transport type wings were analyzed with the intent of developing a procedure for extrapolating low Reynolds number data to flight conditions. These analyses produced a correlation of the development of trailing-edge separation resulting from increases in Mach number and/or angle of attack and show that scale effects on this correlated separation development and the resulting shock location changes fall into a regular and apparently universal pattern. Further studies appear warranted to refine the correlation through a detailed consideration of boundary layer characteristics, and to evaluate scale effects on supercritical wings.

Cahill, J. F.↗
NASA NTRS1981

MEGA16 - Computer program for analysis and extrapolation of stress-rupture data

The computerized form of the minimum commitment method of interpolating and extrapolating stress versus time to failure data, MEGA16, is described. Examples are given of its many plots and tabular outputs for a typical set of data. The program assumes a specific model equation and then provides a family of predicted isothermals for any set of data with at least 12 stress-rupture results from three different temperatures spread over reasonable stress and time ranges. It is written in FORTRAN 4 using IBM plotting subroutines and its runs on an IBM 370 time sharing system.

Ensign, C. R.↗
NASA NTRS1983

Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms

The minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods for sequences of vectors. In a recent survey these methods were tested and compared with the scalar, vector, topological epsilon algorithms, and were observed to be more efficient than the latter. It was also observed that the two methods have similar convergence properties. The convergence and stability properties of these methods are analyzed and the performance of the acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods is discussed.

Sidi, A.↗
NASA NTRS1983

New considerations on scale extrapolation of wing pressure distributions affected by transonic shock-induced separations

Use of this analytical parameter, it is shown, highlights the distinction between cases which are dominated by trailing-edge separation, and those for which separation at the shock foot is dominant. Use of the analytical parameter and the distinction noted above greatly improves the correlation of separation data and the extrapolation of wind tunnel data to flight conditions.

Kahn, M. M. S.↗
NASA NTRS1984

An objective analysis technique for extrapolating tidal fields

An interpolation technique which allows accurate extrapolation of tidal height fields in the ocean basins by making use of selected satellite altimetry measurements and/or conventional gauge measurements was developed and tested. A normal mode solution for the Atlantic and Indian Oceans was obtained by means of a finite difference grid. Normal mode amplitude maps are presented.

Sanchez, B. V.↗
NASA NTRS1982

Impact ejecta dynamics in an atmosphere - Experimental results and extrapolations

It is noted that the impacts of 0.635-cm aluminum projectiles at 6 km/sec into fine pumice dust, at 1 atm, generate a ball of ionized gas behind an expanding curtain of upward moving ejecta. The gas ball forms a toroid which dissolves as it is driven along the interior of the ejecta curtain, by contrast to near-surface explosions in which a fireball envelops early-time crater growth. High frame rate Schlieren photographs show that the atmosphere at the base of the ejecta curtain is initially turbulent, but later forms a vortex. These experiments suggest that although small size ejecta may be decelerated by air drag, they are not simply lofted and suspended but become incorporated in an ejecta cloud that is controlled by air flow which is produced by the response of the atmosphere to the impact. The extrapolation of these results to large body impacts on the earth suggests such contrasts with laboratory experiments as a large quantity of impact-generated vapor, the supersonic advance of the ejecta curtain, the lessened effect of air drag due to the tenuous upper atmosphere, and the role of secondary cratering.

Schultz, P. H.↗
NASA NTRS1986

Extrapolation of Earth-based solar irradiance measurements to exoatmospheric levels for broad-band and selected absorption-band observations

Techniques for extrapolating Earth-based spectral band measurements of directly transmitted solar irradiance to equivalent exoatmospheric signal levels were used to aid in determining system gain settings of the Halogen Occultation Experiment (HALOE) sunsensor system being developed for the NASA Upper Atmosphere Research Satellite and for the Stratospheric Aerosol and Gas (SAGE) 2 instrument on the Earth Radiation Budget Satellite. A band transmittance approach was employed for the HALOE sunsensor which has a broad-band channel determined by the spectral responsivity of a silicon detector. A modified Langley plot approach, assuming a square-root law behavior for the water vapor transmittance, was used for the SAGE-2 940 nm water vapor channel.

Reagan, J. A.↗
NASA NTRS1987

Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability

In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability and that the W-transformation can be applied to them without any modifications. Convergence results are stated and numerical examples given.

Sidi, Avram↗
NASA NTRS1987

Extrapolation of earth-based solar irradiance measurements to exoatmospheric levels for broad-band and selected absorption-band observations

Techniques for extrapolating earth-based spectral band measurements of directly transmitted solar irradiance to equivalent exoatmospheric signal levels were used to aid in determining system gain settings of the Halogen Occultation Experiment (HALOE) sunsensor being developed for the NASA Upper Atmosphere Research Satellite and for the Stratospheric Aerosol and Gas (SAGE) 2 instrument on the Earth Radiation Budget Satellite. A band transmittance approach was employed for the HALOE sunsensor which has a broad-band channel determined by the spectral responsivity of a silicon detector. A modified Langley plot approach, assuming a square-root law behavior for the water vapor transmittance, was used for the SAGE-2 940 nm water vapor channel.

Reagan, John A.↗
NASA NTRS1990

A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere

This paper presents a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, viz the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized, and the accuracy and numerical instability are discussed. On the basis of this investigation, it is claimed that the two methods do resemble each other qualitatively.

Wu, S. T.↗
NASA NTRS1992

Schroedinger's radial equation - Solution by extrapolation

A high-accuracy numerical method for the solution of a 1D Schroedinger equation that is suitable for a diatomic molecule, obtained by combining a finite-difference method with iterative extrapolation to the limit, is presently shown to have several advantages over more conventional methods. Initial guesses for the term values are obviated, and implementation of the algorithm is straightforward. The method is both less sensitive to round-off error, and faster than conventional methods for equivalent accuracy. These advantages are illustrated through the solution of Schroedinger's equation for a Morse potential function suited for HCl and a numerically derived Rydberg-Klein-Rees potential function for the X 1Sigma(+) state of CO.

Goorvitch, D.↗
NASA NTRS1992

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗
NASA NTRS1992

Ground signature extrapolation of three-dimensional near-field CFD predictions for several HSCT configurations

A CFD analysis of the near-field sonic boom environment of several low boom High Speed Civilian Transport (HSCT) concepts is presented. The CFD method utilizes a multi-block Euler marching code within the context of an innovative mesh topology that allows for the resolution of shock waves several body lengths from the aircraft. Three-dimensional pressure footprints at one body length below three-different low boom aircraft concepts are presented. Models of two concepts designed by NASA to cruise at Mach 2 and Mach 3 were built and tested in the wind tunnel. The third concept was designed by Boeing to cruise at Mach 1.7. Centerline and sideline samples of these footprints are then extrapolated to the ground using a linear waveform parameter method to estimate the ground signatures or sonic boom ground overpressure levels. The Mach 2 concept achieved its centerline design signature but indicated higher sideline booms due to the outboard wing crank of the configuration. Nacelles are also included on two of NASA's low boom concepts. Computations are carried out for both flow-through nacelles and nacelles with engine exhaust simulation. The flow-through nacelles with the assumption of zero spillage and zero inlet lip radius showed very little effect on the sonic boom signatures. On the other hand, it was shown that the engine exhaust plumes can have an effect on the levels of overpressure reaching the ground depending on the engine operating conditions. The results of this study indicate that engine integration into a low boom design should be given some attention.

Siclari, M. J.↗
NASA NTRS1992

Limitations on wind-tunnel pressure signature extrapolation

Analysis of some recent experimental sonic boom data has revived the hypothesis that there is a closeness limit to the near-field separation distance from which measured wind tunnel pressure signatures can be extrapolated to the ground as though generated by a supersonic-cruise aircraft. Geometric acoustic theory is used to derive an estimate of this distance and the sample data is used to provide a preliminary indication of practical separation distance values.

Mack, Robert J.↗
NASA NTRS1993

Emissions of sulfur gases from marine and freshwater wetlands of the Florida Everglades - Rates and extrapolation using remote sensing

Rates of emissions of the biogenic sulfur (S) gases carbonyl sulfide (COS), methyl mercaptan (MSH), dimethyl sulfide (DMS), and carbon disulfide (CS2) were measured in a variety of marine and freshwater wetland habitats in the Florida Everglades during a short duration period in October using dynamic chambers, cryotrapping techniques, and gas chromatography. The most rapid emissions of over 500 nmol/sq m/h occurred in red mangrove-dominated sites that were adjacent to open seawater and contained numerous crab burrows. Poorly drained red mangrove sites exhibited lower fluxes of about 60 nmol/sq m/h, which were similar to fluxes from the black mangrove areas which dominated the marine-influenced wetland sites in the Everglades. DMS was the dominant organo-S gas emitted especially in the freshwater areas. Spectral data from a scene from the Landsat TM were used to map habitats in the Everglades. Six vegetation categories were delineated using geographical information system software and S gas emissions were extrapolated for the entire Everglades National Park. The black mangrove-dominated areas accounted for the largest portion of S gas emissions to the area. The large area extent of the saw grass communities accounted for about 24 percent of the total S emissions.

Hines, Mark E.↗