SEARCH · Search NASA

Results for “LOGARITHM”

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.

SourceResearch connectionFrom yearThrough year

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

At least 397 records · Page 22

All sources NASA NTRS DOE OSTI

NASA NTRS1976

A simplified application of the method of operators to the calculation disturbed motions of an airplane

A simplified treatment of the application of Heaviside's operational methods to problems of airplane dynamics is given. Certain graphical methods and logarithmic formulas that lessen the amount of computation involved are explained. The problem of representing a gust disturbance or control manipulation is taken up and it is pointed out that in certain cases arbitrary control manipulations may be dealt with as though they imposed specific constraints on the airplane, thus avoiding the necessity of any integration whatever.

Jones, R. T.↗

NASA NTRS1976

Extended Conformal Mappings for Supersonic Aircraft Calculations

A gasdynamical analysis is presented for a three-dimensional, supersonic, inviscid, steady, shockless flow past an arbitrary airframe, using computational grids. The analysis, which includes special treatments for body points and bow-shock points, relies on the equations of motion written in terms of logarithm of pressure entropy and two angles reprising the velocity vector. A FORTRAN code was employed (sample geometry is shown). The flow analysis is considered reliable for aircraft cross-sections that are elliptical in shape.

Moretti, G.↗

NASA NTRS1975

Gravity shear waves atop the cirrus layer of intense convective storms

Recent visual satellite photographs of certain intense convective storms have revealed concentric wave patterns. A model for the generation and growth of these waves is proposed. The proposed initial generating mechanism is similar to the effect noticed when a pebble is dropped into a calm pond. The penetration of the tropopause by overshooting convection is analogous to the pebble's penetration of the water's surface. The model for wave growth involves instability due to the wind shear resulting from the cirrus outflow. This model is based on an equation for the waves' phase speed which is similar to the Helmholtz equation. It, however, does not assume an incompressible atmosphere, but rather assumes density is a logarithmic function of height. Finally, the model is evaluated on the two mid-latitude and three tropical cases. The data indicate that shearing instability may be a significant factor in the appearance of these waves.

Stobie, J. G.↗

NASA NTRS1976

An analog technique for the measurement of damping from transient decay signals

A tracking filter that includes an output that is logarithmically proportional to the amplitude of the filtered signal is used to measure the damping exponent of a transient decay. This method is analogous to the digital technique referred to as the moving-block or peak-plot method. The method is simple to use and quite accurate, avoids the numerical computations associated with similar digital techniques, but is constrained by the poor time-domain response characteristics of commercial tracking filters presently available.

Bousman, W. G.↗

NASA NTRS1976

Perturbation theory in thermosphere dynamics

It is shown that density and pressure throughout the thermosphere can be adequately described in a logarithmic expansion that provides a sound basis for the application of perturbation theory. This expansion eliminates most of the important nonlinearities associated with density variations. On the basis of this expansion, the validity of perturbation theory can be extended to cover a large variety of atmospheric conditions in which the relative temperature amplitude is less than 0.5 and wind velocities are significantly less than the speed of sound.

Mayr, H. G.↗

NASA NTRS1976

On the relation of J sub I to work done per unit uncracked area - Total, or component 'due to crack'

The J sub I relation, introduced by Rice (1968), expresses the work done on a quasiplanar specimen of specified width (or depth) for a fixed uniform crack length when the displacement of the load is increased from zero to some given value. The relation remains the same if the work done and its logarithmic derivative are calculated in terms of the component of the displacement that is 'due to the crack' rather than the total displacement. J sub I is studied as a function of displacement for a precracked, three-point-loaded bend specimen and also in the extremes of linear-elastic, and rigid/perfectly plastic behavior.

Srawley, J. E.↗

NASA NTRS1976

Resonance-line transfer with partial redistribution. VIII - Solution in the comoving frame for moving atmospheres

The effects of partial frequency redistribution in the scattering process for lines formed in moving atmospheres are analyzed using a general method that allows the transfer equation to be solved in the comoving frame of the gas. The same chromospheric and atomic model studied by Cannon and Vardavas (1974) is employed in the calculations, but a depth scale with logarithmically spaced points is adopted. It is found that in both static and moving atmospheres, the profiles obtained with complete and partial frequency redistribution are virtually identical. The large differences in profiles obtained by Cannon and Vardavas when they used complete and partial redistribution are shown to be spurious (and physically unreal) effects resulting from angle averaging in the observer's frame instead of the comoving frame.

Mihalas, D.↗

NASA NTRS1976

Optical computing with laser light

Linear and nonlinear optical processing techniques (Fourier transformation, convolution and correlation, arithmetic operations - addition and subtraction with gratings, generalized orthogonal transformations; theta modulation, half-tone screen process, optical feedback) for mathematical computations are reviewed. The use of gratings and computer holograms in addition, subtraction, differentiation, and application of generalized transformations is discussed. Use of nonlinear optical elements with or without optical coherent feedback in such nonlinear operations as taking logarithms and thresholding is described. Applications in hybrid systems incorporating digital computer and optical processor with real-time interface devices, or optical threshold and logic devices for parallel processing to apply digital techniques to optical information are considered.

Lee, S. H.↗

NASA NTRS1976

Analysis of neutrally stable atmospheric flow over a two-dimensional forward facing step

A mathematical model describing ground-wind induced flow fields around surface obstructions such as buildings, bridges or other man-made structures is presented. The Navier-Stokes equations with a two-equation turbulence model are used to analyze the flow over a two-dimensional forward facing step. A study of the assumed logarithmic approach velocity profile shows that an increase of surface roughness produces a rise to higher turbulence levels in the shear layer originating from the step corner. This rise leads to higher Reynolds stress and to faster reattachment of the separated flow.

Bitte, J.↗

NASA NTRS1976

Atmospheric flow over two-dimensional bluff surface obstructions

The phenomenon of atmospheric flow over a two-dimensional surface obstruction, such as a building (modeled as a rectangular block, a fence or a forward-facing step), is analyzed by three methods: (1) an inviscid free streamline approach, (2) a turbulent boundary layer approach using an eddy viscosity turbulence model and a horizontal pressure gradient determined by the inviscid model, and (3) an approach using the full Navier-Stokes equations with three turbulence models; i.e., an eddy viscosity model, a turbulence kinetic-energy model and a two-equation model with an additional transport equation for the turbulence length scale. A comparison of the performance of the different turbulence models is given, indicating that only the two-equation model adequately accounts for the convective character of turbulence. Turbulence flow property predictions obtained from the turbulence kinetic-energy model with prescribed length scale are only insignificantly better than those obtained from the eddy viscosity model. A parametric study includes the effects of the variation of the characteristics parameters of the assumed logarithmic approach velocity profile. For the case of the forward-facing step, it is shown that in the downstream flow region an increase of the surface roughness gives rise to higher turbulence levels in the shear layer originating from the step corner.

Bitte, J.↗

NASA NTRS1977

Influence of temperature and the role of chromium on the kinetics of sulfidation of 310 stainless steel

The sulfidation of 310 stainless steel was studied over the temperature range from 910 K to 1285 K. By adjusting the ratio of hydrogen sulfide, variations in sulfur potential were obtained. The effect of temperature on sulfidation was determined at three different sulfur potentials: 39/sqNm, 0.014/sqNm, and 0.00015/sqNm. All sulfide scales contained one or two surface layers in addition to a subscale. The second outer layer (OL-II), furthest from the alloy, contained primarily Fe-Ni-S. The first outer layer (OL-I), nearest the subscale, contained FE-Cr-S. The subscale consisted of sulfide inclusions in the metal matrix. At a given temperature and sulfur potential, the weight gain data obeyed the parabolic rate law after an initial transient period. The parabolic rate constants obtained at the sulfur potential of 39/sqNm did not show a break when the logarithm of the rate constant was plotted as a function of the inverse of absolute temperature. Sulfidation carried out at sulfur potentials below 0.02/sqNm, however, did show a break at 1145 K, which is termed as the transition temperature. This break was found to be associated with the changes which had occurred in the Fe:Cr ratio of OL-I. Below the transition temperature the activation energy was found to be approximately 125 kj/mole. Above the transition temperature the rate of sulfidation decreased with temperature but dependent on the Fe:Cr ratio in the iron-chromium-sulfide layers of the OL-I. A reaction mechanism consistent with the experimental results has been proposed.

Rao, D. B.↗

NASA NTRS1977

Study to investigate and evaluate means of optimizing the Ku-band combined radar/communication functions for the space shuttle

The performance of the space shuttle orbiter's Ku-Band integrated radar and communications equipment is analyzed for the radar mode of operation. The block diagram of the rendezvous radar subsystem is described. Power budgets for passive target detection are calculated, based on the estimated values of system losses. Requirements for processing of radar signals in the search and track modes are examined. Time multiplexed, single-channel, angle tracking of passive scintillating targets is analyzed. Radar performance in the presence of main lobe ground clutter is considered and candidate techniques for clutter suppression are discussed. Principal system parameter drivers are examined for the case of stationkeeping at ranges comparable to target dimension. Candidate ranging waveforms for short range operation are analyzed and compared. The logarithmic error discriminant utilized for range, range rate and angle tracking is formulated and applied to the quantitative analysis of radar subsystem tracking loops.

Weber, C. L.↗

NASA NTRS1976

The EUV chromospheric network in the quiet sun

Investigations on the structure and intensity of the chromospheric network from quiet solar regions have been carried out with EUV data obtained with a spectroheliometer on the Apollo Telescope Mount of Skylab. The distribution of intensities within supergranulation cell interiors follows a near-normal function, where the standard deviation exceeds the value expected from the counting rate, which indicates fine-scale structure below the 5 arcsec resolution of the data. The intensities from the centers of supergranulation cells appear to be the same in both quiet regions and coronal holes, although the network is significantly different in the two types of regions. The average halfwidth of the network elements was measured as 10 arcsec and was independent of the temperature of formation of the observing line for effective-temperature logarithms (log Te) from 3.8 to 5.8. The contrast between the network and the centers of cells is greatest for lines with log Te about equal to 5.2, where the network contributes approximately 75% of the intensity of quiet solar regions. The contrast and fractional-intensity contributions decrease to higher and lower temperatures characteristic of the corona and chromosphere.

Reeves, E. M.↗

NASA NTRS1976

Spectrophotometry of the X-ray binary HZ Herculis

An extensive set of absolute spectrophotometric observations of HZ Her over the wavelength range from 3300 to 10,000 A is presented and analyzed to determine to what extent the observations can be interpreted in terms of a model for the system. The specific model to be tested consists of a large star (HZ Her) with a hot cap beneath the X-ray source, an accretion disk around the X-ray source, and a gas stream flowing between the primary star and the disk. It is found that the model is compatible to a large extent with the detailed observations and that the physical characteristics of the various components can be derived. The mass, luminosity, and radius of the primary star, the mass of the X-ray object, and the orbital dimensions are obtained by analyzing the energy distribution at minimum light and X-ray eclipse data. The angle and effective temperature of the hot cap on the primary are also determined along with the energy distribution, diameter, and thickness of the accretion disk. It is concluded that HZ Her fills its Roche lobe and is an A7 V star, that the logarithm of its surface gravity is about 3.6, and that the mass of the X-ray object is 1.95 solar masses.

Oke, J. B.↗

NASA NTRS1976

A high-sensitivity torsional pendulum for polymeric films and fibres

A free oscillation torsion pendulum is described, which has been designed to measure accurately the dynamic shear modulus and logarithmic decrement of polymeric thin films and fibers, at frequencies of 0.1 to 10 Hz and a temperature range of 4.2 to 450 K. The instrument can also provide in situ tensile deformations of up to 5%. The specimen geometry necessary to obtain reliable modulus measurements with thin films is discussed, and typical data are presented which exhibit hitherto unreported relaxation processes, discernible by this instrument.

Aghili-Kermani, H.↗

NASA NTRS1977

Does the upper main sequence extend across the whole H-R diagram

The effect of using Carson's (1976) radiative opacities in evolutionary sequences of stellar models has been studied over the mass range from 7 to 60 solar masses. The opacities are very large in the outer part of the envelope and induce such enormous radii for masses greater than about 30 solar masses for a heavy-element fraction of 0.02 or about 20 solar masses for a heavy-element fraction of 0.04 that the evolutionary tracks during the phase of core hydrogen burning extend across the whole H-R diagram. The choice of the Schwarschild or Ledoux criterion for convection makes very little difference for the behavior of the tracks. Evolution through the effective-temperature range (in logarithms) of 3.6 to 4.0 occurs in all cases on a rapid (secular) time scale. Core helium burning takes place exclusively in the red-supergiant configuration for stellar masses exceeding 8 solar masses (heavy-element fraction of 0.02) or 6 solar masses (heavy-element fraction of 0.04). These stellar models seem to be in significantly better agreement with the observed distribution of bright stars on the H-R diagram than are the older models based on the Cox-Stewart opacities. It can be inferred that a large envelope opacity (e.g., Carson's) exists and that substantial mass loss takes place in very massive late-type supergiants.

Stothers, R.↗

NASA NTRS1977

The solar boron abundance

Positive evidence for the presence of boron in the sun is reported, and the chemical abundance of boron in the photosphere is derived from photoelectric measurements of the solar spectrum near 2500 A obtained with a rocketborne high-resolution spectrometer. Short sections of the spectrum in the vicinities of the B I lines at 2496.772 and 2497.723 A are plotted. The photospheric boron abundance is determined primarily by analyzing the solar-center spectrum near the first of the two lines in the framework of several single-component photospheric models. The logarithmic boron abundance obtained is 2.6, with an estimated uncertainty of plus or minus 0.3 dex, on the scale where that of hydrogen is 12.0. This value is shown to be in excellent agreement with that predicted for a nucleosynthesis model in which Li, Be, and B are produced by cosmic-ray spallation.

Kohl, J. L.↗

NASA NTRS1977

Asymmetric two-dimensional jet efflux from a channel

Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflection are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises (1917). Results for the asymmetric case improve upon the theoretical values reported by von Mises and compare favorably with existing experimental data.

Martin, C. S.↗