Search NASASearch

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 289 records · Page 16

Scale effects on supercritical airfoils

A survey of research relative to scale effects on supercritical airfoils has been conducted. The results of this survey indicated that Reynolds number scale effects have a significant impact on airfoil design and performance. Further, this impact is greater for supercritical airfoils than for conventional airfoils. It was found that low Reynolds number drag data could be extrapolated to high Reynolds number conditions provided the flow was attached and the pressure distribution shape did not change appreciably. Airfoil lift and pitching-moment data obtained at low Reynolds numbers cannot be extrapolated to full-scale values. Viscous theoretical transonic analysis methods currently under development will significantly improve the ability of the designer to account for scale effects. Boundary-layer manipulation in low Reynolds number facilities using natural transition or aft located transition strips to simulate high Reynolds number conditions was shown to be an uncertain test procedure and reliance should be made on high Reynolds number facilities if available.

Blackwell, J. A., Jr.

Elastic moduli of transversely isotropic graphite fibers and their composites

The paper demonstrates that it is possible to calculate the complete set of elastic mechanical properties for graphite-epoxy fiber-reinforced materials at any fiber-volume fraction by modifying equations previously developed to include transversely isotropic graphite-fiber properties. Experimental verification of the modified equations is demonstrated by using these equations to curve fit elastic-property data obtained ultrasonically over a range of fiber-volume fractions. Material systems under consideration are T300/5208, AS-3501 and Modomor II/LY558 graphite epoxy. Using the modified equations it is possible to extrapolate for fiber properties. From Modomor II/LY558 ultrasonic data, it is shown that five out of seven extrapolated graphite-fiber properties are consistent with the assumption that graphite fibers are transversely isotropic. Elastic properties for T300/5208 and AS-3501 are ultrasonically evaluated by propagating stress waves through six individual specimens cut at various angles from a block of unidirectional material. Particular attention is devoted to specimen dimensions. To demonstrate the need for accurately calculating or experimentally measuring all lamina elastic properties, a brief discussion is included on the effect that variations in lamina elastic properties have on calculating interlaminar stresses.

Kriz, R. D.

The geometry of the partial realization problem

It is shown that the space of sequences of length n which have an extrapolation of McMillan degree k, and no extrapolations of lower McMillan degree can be given the structure of a differentiable manifold. This approach makes the proof of certain known results on the partial realization problem quite straightforward and makes it possible to establish some important new results as well. A key tool is the fact, proven here, that the set of n by a real Hankel matrices of rank r is a manifold with r+1 connected components.

Brockett, R. W.

Computer and laboratory simulation of interactions between spacecraft surfaces and charged-particle environments

There are two categories of interactions considered in this report. The first, spacecraft passive, refers to cases where the charged-particle environment acts on the spacecraft (e.g., spacecraft charging phenomena). The second, spacecraft active, refers to cases where a system on the spacecraft causes the interaction (e.g., high voltage space power systems). Both categories are studied in ground simulation facilities to understand the processes involved and to measure the pertinent parameters. Computer simulations are based on the NASA Charging Analyzer Program (NASCAP) code. Analytical models are developed in this code and verified against the experimental data. Extrapolation from the small test samples to space conditions are made with this code. Typical results from laboratory and computer simulations are presented for both types of interactions. Extrapolations from these simulations to performance in space environments are discussed.

Stevens, N. J.

A study of the sonic-boom characteristics of a blunt body at a Mach number of 6

An experimental and analytical study of the sonic boom static pressure signatures generated by a blunt body at mach 6 has shown that finite difference computer programs can be used to give reasonable estimates of the signatures. The calculated near field static pressure signature was extrapolated to the far field by a program using the method of characteristics. A comparison of this extrapolated signature with the signature predicted by far field sonic boom theory (linearized) shows that peak overpressures are about the same, at least up to mach, but the far field theory overestimates the length of the signature.

Ashby, G. C., Jr.

Computer program for pulsed thermocouples with corrections for radiation effects

A pulsed thermocouple was used for measuring gas temperatures above the melting point of common thermocouples. This was done by allowing the thermocouple to heat until it approaches its melting point and then turning on the protective cooling gas. This method required a computer to extrapolate the thermocouple data to the higher gas temperatures. A method that includes the effect of radiation in the extrapolation is described. Computations of gas temperature are provided, along with the estimate of the final thermocouple wire temperature. Results from tests on high temperature combustor research rigs are presented.

Will, H. A.

Influence of boundary approximations and conditions on finite difference solutions

Numerical representations of boundary approximations and conditions for three problems are investigated to determine the resulting global accuracy of the steady state solution. Numerical accuracy with various boundary approximations is determined for quasi-one-dimensional inviscid flow in a duct with the interior grid points evaluated using the MacCormack scheme. When an extrapolation approximation with first order local truncation error is used, the global second order accuracy of the difference scheme can be destroyed. For one dimensional flow in a porous medium, an implicit midpoint difference scheme which is consistent with the boundary conditions is developed without the need of boundary approximations. A dissipative model problem is solved with the boundary conditions discretized with first and second order accuracy. The overall second order accuracy of the difference scheme is destroyed if first order numerical representation of one of the boundary conditions is used. With a boundary approximation, the second order global accuracy of the model problem is retained if either second order extrapolation or first order representation of the governing equation is used.

Blottner, F. G.

Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations

Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.

Beam, R. M.

Sources of atmospheric methane - Measurements in rice paddies and a discussion

Field measurements of methane fluxes from rice paddies, fresh water lakes, and saltwater marshes have been made to infer estimates of the size of these sources of atmospheric methane. The rice-paddy measurements, the first of their kind, show that the principal means of methane escape is through the plants themselves as opposed to transport across the water-air interface via bubbles or molecular diffusion. Nitrogen-fertilized plants release much more methane than unfertilized plants but even these measured rates are only one fourth as large as those inferred earlier by Koyama (1963, 1964) and on which all global extrapolations have been based to date. Measured methane fluxes from lakes and marshes are also compared to similar earlier data and it is found that extant data and flux-measurement methods are insufficient for reliable global extrapolations.

Cicerone, R. J.

The effects of sunspots on solar irradiance

It is pointed out that the darkness of a sunspot on the visible hemisphere of the sun will reduce the solar irradiance on the earth. Approaches are discussed for obtaining a crude estimate of the irradiance deficit produced by sunspots and of the total luminosity reduction for the whole global population of sunspots. Attention is given to a photometric sunspot index, a global measure of spot flux deficit, and models for the compensating flux excess. A model is shown for extrapolating visible-hemisphere spot areas to the invisible hemisphere. As an illustration, this extrapolation is used to calculate a very simple model for the reradiation necessary to balance the flux deficit.

Hudson, H. S.

Pole-strength of the earth from Magsat and magnetic determination of the core radius

A model based on two days of Magsat data is used to numerically evaluate the unsigned magnetic flux linking the earth's surface, and a comparison of the 16.054 GWb value calculated with values from earlier geomagnetic field models reveals a smooth, monotonic, and recently-accelerating decrease in the earth's pole strength at a 50-year average rate of 8.3 MWb, or 0.052%/year. Hide's (1978) magnetic technique for determining the radius of the earth's electrically-conducting core is tested by (1) extrapolating main field models for 1960 and 1965 downward through the nearly-insulating mantle, and then separately comparing them to equivalent, extrapolated models of Magsat data. The two unsigned fluxes are found to equal the Magsat values at a radius which is within 2% of the core radius; and (2) the 1960 main field and secular variation and acceleration coefficients are used to derive models of 1930, 1940 and 1950. The same core magnetic radius value, within 2% of the seismic value, is obtained. It is concluded that the mantle is a nearly-perfect insulator, while the core is a perfect conductor, on the decade time scale.

Voorhies, G. V.

Observation of additional low-degree 5-min modes of solar oscillation

High-order solar oscillations with degrees l=3, 4, and 5 could be detected. The observations were made by measuring the difference between the shifts in the Fe 5,124 spectrum line from light integrated from a central circular portion of the solar disk and from an annular portion exterior to it. The frequencies of the octupole modes agree well with the values obtained from whole-disk measurements at the South Pole. A least-squares fit of the observed frequencies to values interpolated between and extrapolated from the predictions of a sequence of solar models with different chemical compositions selects two models. One, a helium-rich solution, agrees with that of similar analyses of whole-disk data. The extrapolated solution has a relatively deep convection zone, and is thus consistent with analyses of 5-min oscillations of high degree.

Scherrer, P. H.

On the procedure for deriving ozone variations from satellite observations

It is noted that for the years 1970-1972 global ozone may be calculated by using extrapolated values for polar night regions and then deriving direct daily averages. After 1972, regions larger than the polar night often lack data, increasing the error of extrapolation. It is shown that problems of this type can be overcome by using zonal averages, calculating the annual wave through harmonic analysis, and subtracting the annual wave so derived. Linear fits can then be employed to obtain long-term zonal changes and yearly zonal averages. Global results can be derived in the form of an area-weighted average of the zonal results. It is pointed out that no values need be assumed for ozone when data are lacking. The uncertainty from this procedure is estimated at + or - 0.4% of the yearly average. However, other uncertainties in the backscatter ultraviolet experiment may be larger.

Schlesinger, B. M.

Measuring High Gas Temperatures

Program provides extrapolation calculations of high gas temperature based on theoretical heating curve of pulsed thermocouples. Program requires as input mach number, wall temperature, and total pressure in addition to thermocouple data. Tests indicate program extrapolates reasonably-accurate gas temperatures from pulsed-thermocouple data.

Will, H. A.

Noise of the 10-bladed 60 deg swept SR-5 propeller in a wind tunnel

Noise generated by supersonic helical tip speed propellers is a possible cabin environment problem for future airplanes powered by these propellers. Noise characteristics of one of these propellers, designated SR-5, are presented. A matrix of tests was conducted to provide as much acoustic information as possible. During aerodynamic testing it was discovered that the propeller had an aeroelastic instability which prevented testing the propeller at its design advance ratio of 4.08 at axial Mach numbers over 0.7. Plots of the variation of the maximum blade passage tone with helical tip Mach number indicate that, at higher helical tip Mach numbers, the propeller operated on sharply increasing portion of the noise curve; therefore, extrapolations to the design condition would not be accurate. A possible extrapolation indicated that SR-5 at its design point should be quieter than SR-3 at its design point. Directivity plots at the higher helical tip Mach numbers indicate a lobed directivity pattern as was observed previously on the SR-3 propeller.

Dittmar, J. H.

Subsonic panel method for designing wing surfaces from pressure distribution

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Bristow, D. R.

Electron impact cross sections for the 2,2P state excitation of lithium

Electron impact excitation of the 2p 2P state of Li was studied at 10, 20, 60, 100, 150 and 200 eV. Relative differential cross sections in the angular range 3-120 deg were measured and then normalized to the absolute scale by using the optical f value. Integral and momentum transfer cross sections were obtained by extrapolating the differential cross sections to 0 deg and to 180 deg. The question of normalizing electron-metal-atom collision cross sections in general was examined and the method of normalization to optical f values in particular was investigated in detail. It has been concluded that the extrapolation of the apparent generalized oscillator strength (obtained from the measured differential cross sections) to the zero momentum transfer limit with an expression using even powers of the momentum transfer and normalization of the limit to the optical f value yields reliable absolute cross sections.

Vuskovic, L.