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Results for “Approximation methods”

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At least 667 records · Page 37

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NASA NTRS1973

Role of pressure transients in the detection and identification of lunar surface gas sources.

The dynamic behavior of neutral gases emitted from lunar surface sources is investigated. Pressure transients to be expected from several types of possible lunar surface sources are constructed. An approximate method is developed to estimate the source-sensor separation distance and the amount of effluent release. The case for which the source location and effluent molecular weight can be determined from ancillary data is discussed. It is shown that, if such data are available, pressure transients detected by either Apollo lunar surface experiment package ion spectrometers or cold cathode gages can be used to determine the release rate and the total amount of effluent release from the source.

Hall, F. G.↗

NASA NTRS1974

Signal-to-noise ratios in coherent soft limiters

Expressions for the output signal-to-noise power ratio of a bandpass soft limiter followed by a coherent detection device are presented and discussed. It is found that a significant improvement in the output signal-to-noise ratio (SNR) at low input SNR's can be achieved by such soft limiters as compared to hard limiters. This indicates that the soft limiter may be of some use in the area of threshold extension. Approximation methods for determining output signal-to-noise spectral densities are also presented.

Lesh, J. R.↗

NASA NTRS1974

Analysis of bilinear stochastic systems

Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.

Willsky, A. S.↗

NASA NTRS1975

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗

NASA NTRS1974

A numerical study of electromagnetic scattering from ocean-like surfaces

The integral equations describing electromagnetic scattering from cylindrical, perfectly conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometrical optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root-mean-square surface roughness is less than one tenth of a wavelength.

Lentz, R. R.↗

NASA NTRS1975

Shape of the 5 mm oxygen band in the atmosphere

The problem of absorption of microwaves by molecular oxygen in the atmosphere is treated by means of a first-order approximation to the impact theory of overlapping spectral lines. By including only the coupling between adjacent rotational states in molecular collisions, we have devised a simple approximate method for computing the interference between lines from measurements on the resolved lines. The need for an empirically determined function describing the linewidth/pressure ratio is eliminated. Comparisons with measurements at atmospheric pressures show that the first-order interference accounts for the low absorption at the band wings near 1 atm pressure. It also predicts the correct amount of asymmetry between high and low frequency wings.

Source record↗

NASA NTRS1975

Analysis of bilinear stochastic systems

Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.

Willsky, A. S.↗

NASA NTRS1975

An approximation technique for predicting the transient response of a second order nonlinear equation

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

Laurenson, R. M.↗

NASA NTRS1975

Charge-transfer energy in closed-shell ion-atom interactions

The importance of charge-transfer energy in the interactions between closed-shell ions and atoms is investigated. Ab initio calculations on H(plus)-He and Li(plus)-He are used as a guide for the construction of approximate methods for the estimation of the charge-transfer energy for more complicated systems. For many alkali ion-rate gas systems the charge-transfer energy is comparable to the induction energy in the region of the potential minimum, although for doubly charged alkaline-earth ions in rare gases the induction energy always dominates. Surprisingly, an empirical combination of repulsion energy plus asymptotic induction energy plus asymptotic dispersion energy seems to give a fair representation of the total interaction, especially if the repulsion energy is parameterized, despite the omission of any explicit charge-transfer contribution. More refined interaction models should consider the charge-transfer energy contribution.

Alvarez-Rizzatti, M.↗

NASA NTRS1976

Evaluation of the 'mean frequency' technique

The 'mean frequency' technique, a simple procedure introduced by Bebb and Gold for the approximate evaluation of sums occurring in high-order perturbation theory, represents a useful approximation method. Its predictions compare favorably to exact results obtained by Gontier and Trahin for multiphoton bound-bound transitions in hydrogen. However, the technique can be in error if the 'mean frequency' lies near certain integers.

Gaddy, E. M.↗

NASA NTRS1977

A mathematical study of a random process proposed as an atmospheric turbulence model

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Sidwell, K.↗

NASA NTRS1977

Drive Train Normal Modes Analysis for the ERDA/NASA 100-Kilowatt Wind Turbine Generator

Natural frequencies, as a function of power were determined using a finite element model. Operating conditions investigated were operation with a resistive electrical load and operation synchronized to an electrical utility grid. The influence of certain drive train components on frequencies and mode shapes is shown. An approximate method for obtaining drive train natural frequencies is presented.

Sullivan, T. L.↗

NASA NTRS1977

Unsteady aerodynamic modeling for arbitrary motions

A study is presented on the unsteady aerodynamic loads due to arbitrary motions of a thin wing and their adaptation for the calculation of response and true stability of aeroelastic modes. In an Appendix, the use of Laplace transform techniques and the generalized Theodorsen function for two-dimensional incompressible flow is reviewed. New applications of the same approach are shown also to yield airloads valid for quite general small motions. Numerical results are given for the two-dimensional supersonic case. Previously proposed approximate methods, starting from simple harmonic unsteady theory, are evaluated by comparison with exact results obtained by the present approach. The Laplace inversion integral is employed to separate the loads into 'rational' and 'nonrational' parts, of which only the former are involved in aeroelastic stability of the wing. Among other suggestions for further work, it is explained how existing aerodynamic computer programs may be adapted in a fairly straightforward fashion to deal with arbitrary transients.

Edwards, J. W.↗

NASA NTRS1977

Effects of roughness size on the position of boundary-layer transition and on the aerodynamic characteristics of a 55 deg. swept delta wing at supersonic speeds

An experimental investigation was conducted to determine the effects of roughness size on the position of boundary layer transition and on the aerodynamic characteristics of a 55 deg swept delta wing model. Results are presented and discussed for wind tunnel tests conducted at free stream Mach numbers from 1.50 to 4.63, Reynolds numbers per meter from 3,300,000 to 1.6 x 10 to the 7th power, angles of attack from -8 to 16 deg, and roughness sizes ranging from 0.027 cm sand grit to 0.127 cm high cylinders. Comparisons were made with existing flat plate data. An approximate method was derived for predicting the drag of roughness elements used in boundary layer trips.

Stallings, R. L., Jr.↗

NASA NTRS1978

An approximate inviscid radiating flow field analysis for outer planet entry probes

An approximate computational technique has been developed for predicting inviscid, radiating flows about blunt probes entering atmospheres consisting of hydrogen and helium. The technique is rapid and versatile and is well suited for performing parametric trade studies for outer planet entries. Details of the computational technique, the thermodynamic correlations, the 58-step absorption coefficient model and the analytic shock shape equations are discussed. Good comparisons of the radiative heating computed by the approximate method and by detailed calculations are obtained.

Zoby, E. V.↗

NASA NTRS1980

Limit cycles of a flexible shaft with hydrodynamic journal bearings in unstable regimes

A symmetric 3 mass rotor supported on hydrodynamic bearings is described. An approximate method of representing finite bearings is used to calculate bearing forces. As the method sums forces from a number of independent circular lobes lemon 3 and 4 lobe bearings are taken into account. The calculations are based on an axial groove bearing. Linear analysis precedes nonlinear simulation of some unstable conditions. The demonstration of small limit cycles suggests that necessarily flexible rotors e.g., helicopter tail rotors, may be practical without either tilt pad bearings or external dampers.

Brown, R. D.↗

NASA NTRS1980

A new theory for rapid calculation of the ground pattern of the incident sound intensity produced by a maneuvering jet airplane

An approximate method for computing the jet noise pattern of a maneuvering airplane is described. The method permits one to relate the noise pattern individually to the influences of airplane speed and acceleration, jet velocity and acceleration, and the flight path curvature. The analytic formulation determines the ground pattern directly without interpolation and runs rapidly on a minicomputer. Calculated examples including a climbing turn and a simple climb pattern with a gradual throttling back are presented.

Barger, R. L.↗

NASA NTRS1980

Scattering by non-spherical particles of size comparable to a wavelength - A new semi-empirical theory

An approximate method is proposed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. When the particle size parameter, x, the ratio of particle circumference to wavelength, is less than some upper bound x(o) (about 5), Mie theory is used. For x greater than x(o), the interaction is divided into three components: diffraction, external reflection, and transmission. Physical optics theory is used to obtain the first of these components; geometrical optics theory is applied to the second; and a simple parameterization is employed for the third. The predictions of this theory are found to be in very good agreement with laboratory measurements for a wide variety of particle shapes, sizes, and refractive indexes. Limitations of the theory are also noted.

Pollack, J. B.↗