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At least 739 records · Page 41

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NASA NTRS1974

Computer extension and analytic continuation of Stokes' expansion for gravity waves

Stokes' infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic. Stokes' expansion has been found to be incapable of yielding the highest wave for any value of the water depth since convergence is limited by a square-root branch-point some distance short of the maximum. By reformulating the problem using a different independent parameter, the highest waves are obtained correctly. Series summation and analytic continuation are facilitated by the use of Pade approximants. The method is valid in principle for any finite value of the wavelength and solutions of high accuracy can be obtained for most values of the wave height and water depth.

Schwartz, L. W.↗

NASA NTRS1974

Analytic approximations in the study of the solar modulation of electrons

Numerical solutions to the transport equation of galactic cosmic rays in the interplanetary medium have been used to investigate the applicability of commonly used approximate analytic solutions for electrons (10 MeV to 10 GeV). We find that for a given cosmic-ray diffusion coefficient the force-field approximation is in reasonable agreement with the numerical solution at energies above 200 MeV, but deviates significantly at lower energies, depending on the shape of the interstellar electron spectrum. The diffusion-convection approximation agrees generally with the numerical solution within a factor of 2 over the entire energy range.

Cummings, A. C.↗

NASA NTRS1974

Analytical investigations employing dynamic mechanical properties

Dynamic mechanical spectroscopy has emerged as an effective laboratory method for analytical investigations of polymers. These methods were applied in investigating the property changes of silicone poppets implanted in artificial heart valves, and for exploring the cause of hardening of certain solid propellants. As a research activity, the property-structure relations which lead to the ability to superimpose dynamic data for epoxy resins were investigated.

Cuddihy, E. F.↗

NASA NTRS1974

Experimental and analytical studies in tilt-rotor aeroelasticity

An overview of an experimental and analytical research program for studying the aeroelastic and dynamic characteristics of tilt-rotor VTOL aircraft is presented. Selected results from several investigations of scaled models in the Langley transonic dynamics tunnel as well as some results from a test of a flight-worthy prop rotor in the NASA Ames full-scale wind tunnel are shown and discussed with a view toward delineating various aspects of dynamic behavior peculiar to prop rotor aircraft. Included are such items as prop rotor pylon stability, whirl flutter, gust response, and blade flapping. Theoretical predictions, based on analyses developed at Langley, are shown to be in agreement with the measured stability and response behavior.

Kvaternik, R. G.↗

NASA NTRS1974

Some analytical results for radiative transfer in thick atmospheres

Singular eigenmode expansions are a convenient analytical tool with which to study problems of monochromatic radiative transfer in thick or semi-infinite atmospheres. Some closed-form solutions are presented for anisotropic scattering, with the neglect of polarization effects. A basic ingredient for applications to the semi-infinite medium is Chandrasekhar's H-function, which is best defined through the Wiener-Hopf factorization. The solutions of the Milne and albedo problems are discussed in order that the method of matched asymptotic approximations may be used to describe the solution for a thick atmosphere adjacent to a diffusely reflecting ground. Expressions for the emerging distributions are quoted. A possible extension of the general scheme to problems involving polarization is indicated.

Kuscer, I.↗

NASA NTRS1974

A three parameter analytic phase function for multiple scattering calculations

A simple procedure was developed to fit the first three moments of an actual phase function with a three parameter analytic phase function. The exact Legendre Polynomial decomposition of this function is, suitable for multiple scattering calculations. The use of this function is expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo omega sub 0 is greater than or equal to 0.9.

Kattawar, G. W.↗

NASA NTRS1975

Experimental and analytical study of an inlet forebody for an airframe-integrated scramjet concept

Preliminary analytical and experimental inlet forebody investigations have been conducted at Mach numbers of 6.0 and 8.5. The forebody design concept consisted of a sharp-nosed right circular cone followed by elliptical cross sections. This concept resulted in swept isentropic compression which would allow swept cowl leading edges. Measurements were made to define the condition of the inviscid flow field developed by the forebody, including flow profiles in the vicinity of cowl leading-edge stations, and the three-dimensional boundary-layer effects. The investigation verified some of the expected differences between the predicted and the experimental results.

Andrews, E. H., Jr.↗

NASA NTRS1974

Analytical and experimental investigation of a 1/8-scale dynamic model of the shuttle orbiter. Volume 3B: Supporting data

The NASA Structural Analysis System (NASTRAN) Model 1 finite element idealization, input data, and detailed analytical results are presented. The data presented include: substructuring analysis for normal modes, plots of member data, plots of symmetric free-free modes, plots of antisymmetric free-free modes, analysis of the wing, analysis of the cargo doors, analysis of the payload, and analysis of the orbiter.

Mason, P. W.↗

NASA NTRS1975

Analytical method for calculation of navigational data for the position of a satellite

A method is described for calculating the position of a satellite at the instants when measurements are made on board. The initial conditions used were the mean orbital elements of the satellite and their time derivatives in one orbit. The results of the calculation are compared with those obtained by numerical integration, and it is found that results are identical at the beginning of an orbit, but change as the orbit progresses. The advantages and disadvantages of the analytical method are presented.

Lala, P.↗

NASA NTRS1975

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 1: Analytical manual for earth orbital MAPSEP

An introduction to the MAPSEP organization and a detailed analytical description of all models and algorithms are given. These include trajectory and error covariance propagation methods, orbit determination processes, thrust modeling, and trajectory correction (guidance) schemes. Earth orbital MAPSEP contains the capability of analyzing almost any currently projected low thrust mission from low earth orbit to super synchronous altitudes. Furthermore, MAPSEP is sufficiently flexible to incorporate extended dynamic models, alternate mission strategies, and almost any other system requirement imposed by the user. As in the interplanetary version, earth orbital MAPSEP represents a trade-off between precision modeling and computational speed consistent with defining necessary system requirements. It can be used in feasibility studies as well as in flight operational support. Pertinent operational constraints are available both implicitly and explicitly. However, the reader should be warned that because of program complexity, MAPSEP is only as good as the user and will quickly succumb to faulty user inputs.

Source record↗

NASA NTRS1975

Analytical modeling requirements for tilting proprotor aircraft dynamics

Proprotor and cantilever wing aeroelastic behavior is applied to a gimballed rotor and a hingeless rotor to develop an analytical model for prediction of tilting proprotor aircraft dynamics. Particular attention is given to: the influence of coupled flap/lag bending modes; the influence of rotor blade torsion degrees of freedom on proprotor dynamics; and, to a constant coefficient approximation representing the dynamics in nonaxial flow through the rotor. The following are also examined: the number of blade bending and torsion modes required; the influence of the rotor aerodynamic model; the influence of the blade trim bending deflection; the importance of the rotor rotational speed degree of freedom; and the effect of the wing aerodynamic forces. The origin of the significant influence of the blade pitch motion on the proprotor dynamics is discussed.

Johnson, W.↗

NASA NTRS1975

Analytical simulation of the far-field jet noise and the unsteady jet flow-field by a model of periodic shedding of vortex ring from the jet exit

The construction of a theoretical flow field due to shedding of vortex rings, the identification of the controlling parameters, and the determination of whether the theoretical model successfully simulated the unsteady pressure field near jet (and consequently the far field noise) was studied. The basic parameters contained in the analytic solutions were the epoch at which a vortex ring was shed near the jet exit and the eddy viscosity coefficient. These parameters were identified from the experimental data for the real-time pressure and from the spread of the mixing layer of the jet. Results of the theoretical analysis show good qualitative agreement with the experimental data.

Liu, C. H.↗

NASA NTRS1975

Analytical techniques: A compilation

A compilation, containing articles on a number of analytical techniques for quality control engineers and laboratory workers, is presented. Data cover techniques for testing electronic, mechanical, and optical systems, nondestructive testing techniques, and gas analysis techniques.

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NASA NTRS1975

Analytical and test equipment: A compilation

A compilation is presented of innovations in testing and measuring technology for both the laboratory and industry. Topics discussed include spectrometers, radiometers, and descriptions of analytical and test equipment in several areas including thermodynamics, fluid flow, electronics, and materials testing.

Source record↗

NASA NTRS1975

Analytic aerotriangulation utilizing Skylab earth terrain camera (S-190B) photography

The author has identified the following significant results. Inherent errors in using nonmetric Skylab photography and office-identified photo control made it necessary to perform numerous block adjustment solutions involving different combinations of control and weights. The final block adjustment was executed holding to 14 of the office-identified photo control points. Solution accuracy was evaluated by comparing the analytically computed ground positions of the withheld photo control points with their known ground positions and also by determining the standard errors of these points from variance values. A horizontal position RMS error of 15 meters was attained. The maximum observed error in position at a control point was 25 meters.

Keller, M.↗

NASA NTRS1975

Spectroscopic analysis of solar and cosmic X-ray spectra. 1: The nature of cosmic X-ray spectra and proposed analytical techniques

Techniques for the study of the solar corona are reviewed as an introduction to a discussion of modifications required for the study of cosmic sources. Spectroscopic analysis of individual sources and the interstellar medium is considered. The latter was studied via analysis of its effect on the spectra of selected individual sources. The effects of various characteristics of the ISM, including the presence of grains, molecules, and ionization, are first discussed, and the development of ISM models is described. The expected spectral structure of individual cosmic sources is then reviewed with emphasis on supernovae remnants and binary X-ray sources. The observational and analytical requirements imposed by the characteristics of these sources are identified, and prospects for the analysis of abundances and the study of physical parameters within them are assessed. Prospects for the spectroscopic study of other classes of X-ray sources are also discussed.

Walker, A. B. C., Jr.↗

NASA NTRS1974

Experimental and analytical sonic nozzle discharge coefficients for Reynolds numbers up to 8,000,000

Sonic discharge coefficients are presented for two different geometry flow nozzles using nitrogen gas at high pressures where real-gas corrections are significant. Throat Reynolds number range extended up to 8,000,000. Experimentally obtained coefficients for a nozzle with a continuous and finite radius of curvature agreed with those obtained analytically to within 0.2 per cent. Experimental coefficients for a long-radius ASME nozzle agreed to within 0.25 per cent to an empirical equation representing the most probable subsonic discharge coefficient.

Szaniszlo, A. J.↗

NASA NTRS1974

On the analytic lunar and solar perturbations of a near earth satellite

The disturbing function of the moon (sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the moon (sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elements l, l prime, F, D and Gamma of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements omega and Omega of the satellite, so that analytic integration is simple and the results are accurate over a long period of time.-

Estes, R. H.↗