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NASA NTRS1982

Expansion series of integral functions occurring in unsteady aerodynamics

Attention is given to two real integral functions which occur in the kernel of singular integral equations for subsonic unsteady lifting surfaces. The arguments k, r, and X of the functions correspond to the reduced frequency, spanwise distance, and modified coordinate in the flow direction, respectively. The value of the parameter nu in the functions depends on geometrical conditions. The considered investigation has the objective to present a series for general values of the nonnegative integer nu in order to compute efficiently the integral functions. The approach makes it possible to avoid any approximation or numerical quadrature.

Ueda, T.↗

NASA NTRS1982

Interaction of a cumulus cloud ensemble with the large-scale environment. IV - The discrete model

The Arakawa-Schubert (1974) parameterization is applied to a prognostic model of large-scale atmospheric circulations and used to analyze data in a general circulation model (GCM). The vertical structure of the large-scale model and the solution for the cloud subensemble thermodynamical properties are examined to choose cloud levels and representative regions. A mass flux distribution equation is adapted to formulate algorithms for calculating the large-scale forcing and the mass flux kernel, using either direct solution or linear programming. Finally, the feedback of the cumulus ensemble on the large-scale environment for a given subensemble mass flux is calculated. All cloud subensemble properties were determined from the conservation of mass, moist static energy, and total water.

Lord, S. J.↗

NASA NTRS1982

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Sharma, A.↗

NASA NTRS1982

Chordwise and compressibility corrections for arbitrary planform slender wings

The Lomax and Sluder method for adapting slender-wing theory to delta or rectangular wings by making chordwise and compressibility corrections is extended to cover wings of any arbitrary planform in subsonic and supersonic flows. The numerical accuracy of the present work is better than that of the Lomax-Sluder results. Comparison of the results of this work with those of the vortex-lattice method and Kernel function method for a family of Gothic and arrowhead wings shows good agreement. A universal curve is proposed for the evaluation of the lift coefficient of a low aspect ratio wing of an arbitrary planform in subsonic flow. The location of the center of pressure can also be estimated.

Levin, D.↗

NASA NTRS1982

Smoothing splines: Regression, derivatives and deconvolution

The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel intergral equation. These results are derived by developing a Fourier representation for a smoothing spline.

Rice, J.↗

NASA NTRS1980

Systems architecture for distributed applications

This paper describes the kernel of a distributed operating system called ADAPT. The system runs on top of existing single host operating systems that are networked together. It's purpose is to transform this network of individual systems into a single system that will be easier for application programmers to use. This single system need not be monolithic; ADAPT facilitates the construction of both integrated and modular distributed systems.

Peebles, R.↗

NASA NTRS1983

Transonic pressure distributions on a rectangular supercritical wing oscillating in pitch

Steady and unsteady aerodynamic data were measured on a rectangular wing with a 12 percent thick supercritical airfoil mounted in the NASA Langley Transonic Dynamics Tunnel. The wing was oscillated in pitch to generate the unsteady aerodynamic data. The purpose of the wind-tunnel test was to measure data for use in the development and assessment of transonic analytical codes. The effects on the wing pressure distributions of Mach number, mean angle of attack, and oscillation frequency and amplitude were measured. Results from the newly-developed XTRAN3S program (a non-linear transonic small disturbance code) and from the RHOIV program (a linear lifting surface kernel function code) were compared to measured data for a Mach number of 0.7 and for oscillation frequencies ranging from 0 to 20 Hz. The XTRAN3S steady and unsteady results agreed fairly well with the measured data. The RHOIV unsteady-result agreement was fair but, of course, did not predict shock effects.

Ricketts, R. H.↗

NASA NTRS1983

The water factor in harvest-sprouting of hard red spring wheat

Sprouting in unthreshed, ripe, hard red spring wheat (Triticum aestivum L.) is induced by rain, but sprouting does not necessarily occur because the crop is wetted. The spike and grain water conditions conducive to sprouting were determined in a series of laboratory experiments. Sprouting did not occur in field growing wheat wetted to 110% water concentration until the spike water concentration was reduced to 12% and maintained at this concentration for 2 days before wetting. When cut at growth stage 11.3, Feekes scale, Saratovskaya 20 (USSR) sprouted after 4 days drying, Olaf and Alex between 7 and 15 days drying and Columbus, recognized for its resistance to harvest time sprouting, after more than 15 days drying. Sprouting potential was enhanced after 4 wetting drying cycles in which any wetted interval was too brief to permit sufficient water imbibition to initiate sprouting. At harvest ripeness, grain water concentration exceeded spike water concentration by 0.7 percentage units. Following 6 months storage, 20% of the kernels in 300 spike bundles (simulating windrows) sprouted within 28 hrs after initiation of wetting to saturation (150% water concentration). Ninety percent sprouting occurred within 8 days in bundles maintained at 75% water concentration and higher, but less sprouting occurred in bundles dried to 50% water concentration before resaturation.

Bauer, A.↗

NASA NTRS1983

Approximation of the optimal compensator for a large space structure

This paper considers the approximation of the optimal compensator for a Large Space Structure. The compensator is based upon a solution to the Linear Stochastic Quadratic Regulator problem. Colocation of sensors and actuators is assumed. A small gain analytical solution for the optimal compensator is obtained for a single input/single output system, i.e., certain terms in the compensator can be neglected for sufficiently small gain. The compensator is calculated in terms of the kernel to a Volterra integral operator using a Neumann series. The calculation of the compensator is based upon the C sub 0 semigroup for the infinite dimensional system. A finite dimensional approximation of the compensator is, therefore, obtained through analysis of the infinite dimensional compensator which is a compact operator.

Mackay, M. K.↗

NASA NTRS1983

Observations of H-alpha and microwave brightening caused by a distant solar flare

Synthesized maps with integration times of 10 and 30 sec, based on the observation of three subflares at 6 cm and H-alpha 6563 A, indicate that most of the 6 cm burst emission originated in 10-15 arcsec features coincident with, or adjacent to, H-alpha flare kernels. During the onset of one of the subflares, 6 cm emission was discovered in a loop stretching over 100,000 km from the primary flare site in association with H-alpha flare-like brightness at the remote footpoint of the loop. Assuming a primary flare site origin for the energy of the distant brightening, about 4 x 10 to the 24th ergs/sec propagated along the connecting magnetic loop at a velocity of more than 6000 km/sec. It is suggested that the energy may have been carried by electrons originating in the high energy tail of the electron thermal velocity distribution, escaping from the primary flare site.

Kundu, M. R.↗

NASA NTRS1983

Transonic pressure distributions on a rectangular supercritical wing oscillating in pitch

Steady and unsteady aerodynamic data were measured on a rectangular wing with a 12 percent thick supercritical airfoil mounted in the NASA Langley Transonic Dynamics Tunnel. The wing was oscillated in pitch to generate the unsteady aerodynamic data. The purpose of the wind-tunnel test was to measure data for use in the development and assessment of transonic analytical codes. The effects on the wing pressure distributions of Mach number, mean angle of attack, and oscillation frequency and amplitude were measured. Results from the newly-developed XTRAN3S program (a nonlinear transonic small disturbance code) and from the RHOIV program (a linear lifting surface kernel function code) were compared to measured data for a Mach number of 0.7 and for oscillation frequencies ranging from 0 to 20 Hz. The XTRAN3S steady and unsteady results agreed fairly well with the measured results. The RHOIV unsteady-result agreement was fair but, of course, did not predict shock effects.

Ricketts, R. H.↗

NASA NTRS1983

The Queen's flare - Its structure and development; precursors, pre-flare brightenings, and aftermaths

A limb flare, which started at about 20:20 UT on April 30, 1980, was observed by several of the instruments on the Solar Maximum Mission (SMM) spacecraft. This flare has been the subject of a joint analysis of the SMM instruments. The present investigation represents a continuation of research reported in part by Woodgate et al. (1981) and Gabriel et al. (1981). Several questions are explored regarding the preflare activity, the evolution of the flare, and its decay. It is concluded that the X-ray brightenings observed before the flare were indicative only of the generally high level of activity from this region. They were not connected with the build-up of energy before the flare since similar brightenings were observed in the region after the flare. At least one brightening occurred at the site of the kernel before the flare. There is also some evidence of a tongue.

De Jager, C.↗

NASA NTRS1983

The crack problem for a nonhomogeneous plane

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Delale, F.↗

NASA NTRS1983

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

A cylindrical shell having a very stiff and plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flaw which may be modeled as a part through surface crack or a through crack. The effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter is studied. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the Mode 1 stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part through crack problem is treated by using a line spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equations of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem.

Yahsi, O. S.↗

NASA NTRS1984

LANDSAT-D investigations in snow hydrology

Two stream methods provide rapid approximate calculations of radiative transfer in scattering and absorbing media. Although they provide information on fluxes only, and not on intensities, their speed makes them attractive to more precise methods. The methods provide a comprehensive, unified review for a homogeneous layer, and solve the equations for reflectance and transmittance for a homogeneous layer over a non reflecting surface. Any of the basic kernels for a single layer can be extended to a vertically inhomogeneous medium over a surface whose reflectance properties vary with illumination angle, as long as the medium can be subdivided into homogeneous layers.

Dozier, J.↗

NASA NTRS1984

Two-dimensional splines

Noteworthy properties of one-dimensional splines are presented. Stochastic processes, kernel functions, interpolation, and data smoothing were discussed. Theorems and concomitant proofs are provided.

Utreras, F. I.↗

NASA NTRS1984

Correlated observations of impulsive UV and hard X-ray bursts in solar flares from the solar maximum mission

An investigation is conducted of the temporal and spatial structures of UV and hard X-ray bursts in a disk and a limb flare observed with instruments on the Solar Maximum Mission satellite. Attention is given to the transient UV brightening before the flare, the impulsive enhancement of UV continuum emission, the relationship between emission source region and particle acceleration region, and large scale excitations. The most active part of the active region appears to be the most flare-productive region. These regions exhibit high UV activities with numerous UV transient bursts occurring in many small kernels.

Cheng, C.-C.↗

NASA NTRS1984

First-flight escape from spheres with R(-2) density distribution

Energy-independent first-flight transport kernels are evaluated for a spherical region with an R(-2) density distribution. The uncollided angular-flux distribution is obtained and integrated for a source distribution that is proportional to the density to give the uncollided emitted particle flux and current density. These are useful for the calculation of mass, energy, and momentum carried away by fast particles born in the medium. The data are relevant to estimate escape from weakly bound atmospheres such as comet comae, dilute circumstellar envelopes, and some unconfined laboratory plasmas.

Huebner, W. F.↗