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 433 records · Page 24

All sources NASA NTRS DOE OSTI

NASA NTRS1978

Effects of particle drift on cosmic ray transport. II - Analytical solution to the modulation problem with no latitudinal diffusion

An analytical solution to a model of the modulation of galactic cosmic rays in the presence of particle drifts is presented and discussed. The solution assumes an energy-independent radial diffusion coefficient proportional to distance and no latitudinal diffusion, and includes energy-independent particle drift velocities similar to those expected in a Parker spiral magnetic field with an equatorial current sheet. The solutions clearly demonstrate the large effects of drifts on the modulated cosmic-ray intensity. For values of the radial diffusion coefficient and particle drift velocity which are plausible for 1-GV-rigidity protons, the logarithmic radial gradient in the inner solar system is reduced by more than a factor of 5 over the value calculated in the absence of drifts. It is found that even for much smaller values of particle drift velocity and radial diffusion coefficient, such as might be expected for protons with energies of the order of 10 MeV, the effects of the drifts can be substantial.

Isenberg, P. A.↗

NASA NTRS1978

Observations of interstellar chlorine and phosphorus

Copernicus observations of interstellar Cl I, Cl II, and P II UV lines toward 10 stars are reported. Column densities are estimated for each species, and upper limits are computed for HCl column densities. Derivation of the gas-phase abundances of chlorine and phosphorus indicates that the averages of both the chlorine and the phosphorus logarithmic abundances relative to hydrogen are between 5.0 and 5.1. It is suggested that interstellar chlorine may be depleted by about a factor of 3 relative to the solar abundance and that interstellar phosphorus is depleted by a factor of 2 to 3. The results are shown to support the prediction that chlorine is ionized in regions containing primarily atomic oxygen and is neutral in regions where there is a significant amount of molecular hydrogen. The photoionization rate of neutral chlorine toward 15 Mon is estimated, and it is concluded that most chlorine is contained within the gas phase.

Jura, M.↗

NASA NTRS1978

On the use of relative velocity exponents for jet engine exhaust noise

The effect of flight on jet engine exhaust noise has often been presented in terms of a relative velocity exponent, n, as a function of radiation angle. The value of n is given by the OASPL reduction due to relative velocity divided by 10 times the logarithm of the ratio of relative jet velocity to absolute jet velocity. It is shown in this paper that the exponent n is positive for pure subsonic jet mixing noise and varies, in a systematic manner, as a function of flight conditions and jet velocity. On the basis of calculations from simple empirical models for jet mixing noise, shock noise and internally-generated noise, it is shown that when other sources are present, the resulting range of n is increased over the range for jet mixing noise, and in some cases negative values of n are obtained.

Stone, J. R.↗

NASA NTRS1978

Photochemistry and dynamics of the ozone layer

The paper presents a broad review of the photochemical and dynamic theories of the ozone layer. The two theories are combined into the MIT three-dimensional dynamic-chemical quasi-geostrophic model with 26 levels in the vertical spaced in logarithmic pressure coordinates between the ground and 72-km altitude. The chemical scheme incorporates the important odd nitrogen, odd hydrogen, and odd oxygen chemistry, but is simplified in the sense that it requires specification of the distributions of NO2, OH and HO2. The prognostic equations are the vorticity equation, the perturbation thermodynamic equation, and the global mean and perturbation continuity equations for ozone; diagnostic equations include the hydrostatic equation, the balance condition, and the mass continuity equation. The model is applied to the investigation of the impact of supersonic aircraft on the ozone layer.

Prinn, R. G.↗

NASA NTRS1977

Obstacle detection by rapid estimation scheme with data scaling

A data scaling technique is proposed to improve the performance of a rapid estimation scheme for analyzing rover rangefinder data in the specific area of obstacle outline characterization. The scaling transformation involves multiplying the measured beam length times a scale factor and taking the logarithm in a certain base. Although analysis shows that introducing the scaling transformation has no primary effect on the detection ability and that there is no apparent signal-to-noise ratio improvement, computer simulations show a reduction in the number of false jumps. In the 40-m range the use of data scaling cleared the foreground of obstacles of noise and obtained definition of the near edge of a crater.

Marynowski, R. C.↗

NASA NTRS1978

The law of constant rejection

Improvements in analytical technique, study of multielement partitioning in natural systems, and improvements in ionic radius values have permitted construction of Onuma diagrams, in which the logarithm of partition coefficient is plotted versus ionic radius. The optimum radii, corresponding to crystallographic sites, do change in response to changes in major element composition for any particular mineral-type. In natural systems elements compete for sites rather than substituting for another element. It is proposed on empirical grounds, for equilibrium ionic bonding, that Onuma diagram curves for a particular lattice site are parabolic near optimum radius, linear elsewhere, parallel for different valences, and mirror images on opposite sides of optimum. Deviations may be due to overlapping peaks, liquid structure, polyvalence, bonding differences, contamination, kinetics, alteration, etc. However, dominant crystal-chemical control is indicated.

Philpotts, J. A.↗

NASA NTRS1978

Strain-rate/temperature behavior of high density polyethylene in compression

The compressive strain rate/temperature behavior of highly linear, high density polyethylene was analyzed in terms of the predictive relations developed for metals and other crystalline materials. For strains of 5 percent and above, the relationship between applied strain rate, dotted epsilon, and resulting flow stress, sigma, was found to be: dotted epsilon exp times (Q sub f/RT) = k'(sigma/sigma sub c) to the nth power; the left-hand side is the activation-energy-compensated strain rate, where Q sub f is activation energy for flow, R is gas constant, and T is temperature; k is a constant, n is temperature-independent stress exponent, and sigma/sigma sub c is structure-compensated stress. A master curve resulted from a logarithmic plot of activation-energy-compensated strain rate versus structure-compensated stress.

Clements, L. L.↗

NASA NTRS1978

Effect of concentration dependence of the diffusion coefficient on homogenization kinetics in multiphase binary alloy systems

Diffusion calculations were performed to establish the conditions under which concentration dependence of the diffusion coefficient was important in single, two, and three phase binary alloy systems. Finite-difference solutions were obtained for each type of system using diffusion coefficient variations typical of those observed in real alloy systems. Solutions were also obtained using average diffusion coefficients determined by taking a logarithmic average of each diffusion coefficient variation considered. The constant diffusion coefficient solutions were used as reference in assessing diffusion coefficient variation effects. Calculations were performed for planar, cylindrical, and spherical geometries in order to compare the effect of diffusion coefficient variations with the effect of interface geometries. In most of the cases considered, the diffusion coefficient of the major-alloy phase was the key parameter that controlled the kinetics of interdiffusion.

Tenney, D. R.↗

NASA NTRS1979

Dynamic mechanical analysis of fiber reinforced composites

Dynamic mechanical and thermal properties were determined for unidirectional epoxy/glass composites at various fiber orientation angles. Resonant frequency and relative logarithmic decrement were measured as functions of temperature. In low angle and longitudinal specimens a transition was observed above the resin glass transition temperature which was manifested mechanically as an additional damping peak and thermally as a change in the coefficient of thermal expansion. The new transition was attributed to a heterogeneous resin matrix induced by the fiber. The temperature span of the glass-rubber relaxation was found to broaden with decreasing orientation angle, reflecting the growth of fiber contribution and exhibiting behavior similar to that of Young's modulus. The change in resonant frequency through the glass transition was greatest for samples of intermediate fiber angle, demonstrating behavior similar to that of the longitudinal shear modulus.

Reed, K. E.↗

NASA NTRS1979

Data acquisition and path selection decision making for an autonomous roving vehicle

The feasibility of using range/pointing angle data such as might be obtained by a laser rangefinder for the purpose of terrain evaluation in the 10-40 meter range on which to base the guidance of an autonomous rover was investigated. The decision procedure of the rapid estimation scheme for the detection of discrete obstacles has been modified to reinforce the detection ability. With the introduction of the logarithmic scanning scheme and obstacle identification scheme, previously developed algorithms are combined to demonstrate the overall performance of the intergrated route designation system using laser rangefinder. In an attempt to cover a greater range, 30 m to 100 mm, the problem estimating gradients in the presence of positioning angle noise at middle range is investigated.

Shen, C. N.↗

NASA NTRS1979

Solar cycle variations in IMF intensity

Annual averages of logarithms of hourly interplanetary magnetic field intensities, obtained from geocentric spacecraft between November 1963 and December 1977, reveal the following solar cycle variation. For 2 to 3 years at each solar minimum period, the IMF intensity is depressed by 10-15 percent relative to its mean value realized during a broad nine-year period centered at solar maximum. No systematic variations occur during this nine-year period. The solar minimum decrease, although small relative to variations in some other solar wind parameters, is both statistically and physically significant.

King, J. H.↗

NASA NTRS1979

A depolarization and attenuation experiment using the COMSTAR and CTS satellites

Monthly and annual percent-of-time data on ground rain fall rate and attenuation on satellite downlinks at 11.7 GHz, 19.04 GHz, and 28.56 GHz is presented. Equal probability values of attenuation and rain rate are compared for monthly, quarterly, half-year periods and for the entire year. Regression equations relating cross polarization isolation to the logarithm of attenuation are also presented.

Bostian, C. W.↗

NASA NTRS1979

Some recent developments in the prediction of shock interaction phenomena at hypersonic speeds

The shock strengths for which either Edney type I or type II shock interference patterns can occur when two oblique shocks of opposite families intersect were determined graphically at Mach 10 by using logarithmic shock polar diagrams. The theoretical region of overlap for the two types of interaction was investigated by observing in the Schlieren system of the Langley 15-inch hypersonic flow apparatus the intersection of oblique shocks generated by two sharp 10 degree wedges as the wedge angles of attack and their relative positions were altered. A range of shock strengths for which either of the two interference patterns can exist was demonstrated.

Crawford, D. H.↗

NASA NTRS1978

Limb darkening 1945-3245 A for the quiet sun from Skylab data

Limb-darkening measurements of the quiet sun in the spectral range 1945-3245 A have been made using NRL's SO82B instrument on board Skylab. The spectral intensities have been averaged over 10 A wavelength bands, and coefficients for linear, quadratic, and logarithmic fits to the observed center-to-limb variations have been calculated and tabulated as a function of wavelength. The quadratic fits are found to represent the observations best, the observed and calculated values agreeing to better than plus or minus 15% on the average. Attention is drawn to the value of the results for ultraviolet photometry of eclipsing binaries.

Moe, O. K.↗

NASA NTRS1978

Extensions of the Wilson-Bappu effect among very luminous stars

It has been stated that the technique used by Wilson and Bappu (1957) in their study of the observational correlation of M sub V and the logarithm of the full width at half maximum of the Ca II K-line central emission for G, K, and M stars has a plus or minus 0.5 mag accuracy. A tabulation by Wilson (1976) suggests, however, that the error may be only plus or minus 0.3 mag. This accuracy makes the approach valuable for late-type supergiants since other methods suffer from comparable errors. A description is in this connection presented of a new class of emission lines in late-type giant and supergiant spectra that exhibit M sub V correlated widths, yet are detectable among the brightest stars.

Stencel, R. E.↗

NASA NTRS1979

Development of noise and vibration ride comfort criteria

A laboratory investigation was directed at the development of criteria for the prediction of ride quality in a noise-vibration environment. The stimuli for the study consisted of octave bands of noise centered at 500 and 2000 Hz and vertical floor vibrations composed of either 5 Hz sinusoidal vibrations, or random vibrations centered at 5 Hz and with a 5 Hz bandwidth. Results indicated that the total subjective discomfort response could be divided into two subjective components. One component consisted of subjective discomfort to vibration and was found to be a linear function of vibration acceleration level. The other component consisted of discomfort due to noise which varied logarithmically with noise level (power relationship). A model of subjective discomfort that accounted for the interdependence of noise and vibration was developed. The model was then used to develop a set of criteria (constant discomfort) curves that illustrate the basic design tradeoffs available between noise and vibration.

Dempsey, T. K.↗

NASA NTRS1978

Temperature dependence of the rate constants for reactions of O/1D/ atoms with a number of halocarbons

Results are reported for an experimental study of the reactions of O(1D) with CCl4, CFCl3, CF2Cl2, CHFCl2, CHF2Cl, and CF2ClCFCl2 over the temperature range from 173 to 343 K, based on the time-resolved emission of O(1D) at 630 nm. The experiments involved photolysis of O3 by Nd-YAG laser pulses and measurements of 630-nm emission intensity in mixtures with He and the various halocarbons. Pseudo-first-order rate constants are derived from plots of the logarithms of the 630-nm emission intensities as a function of time for particular He/O3/halocarbon mixtures, and second-order rate constants are then obtained from plots of these pseudo-first-order rate constants as a function of halocarbon concentration at constant He and O3 concentrations. No temperature dependence of the second-order rate constants is observed over the range studied, within the precision of the measurements. It is found that the rate constants decrease as H is substituted for Cl in a halocarbon molecule and as F is substituted for H or Cl.

Davidson, J. A.↗

NASA NTRS1979

Dynamic mechanical analysis of fiber reinforced composites

Reed, K. E.↗