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At least 595 records · Page 33

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NASA NTRS1971

Computer method for identification of boiler transfer functions

An iterative computer method is described for identifying boiler transfer functions using frequency response data. An objective penalized performance measure and a nonlinear minimization technique are used to cause the locus of points generated by a transfer function to resemble the locus of points obtained from frequency response measurements. Different transfer functions can be tried until a satisfactory empirical transfer function to the system is found. To illustrate the method, some examples and some results from a study of a set of data consisting of measurements of the inlet impedance of a single tube forced flow boiler with inserts are given.

Miles, J. H.↗

NASA NTRS1972

Identification of boiler inlet transfer functions and estimation of system parameters

An iterative computer method is described for identifying boiler transfer functions using frequency response data. An objective penalized performance measure and a nonlinear minimization technique are used to cause the locus of points generated by a transfer function to resemble the locus of points obtained from frequency response measurements. Different transfer functions can be tried until a satisfactory empirical transfer function of the system is found. To illustrate the method, some examples and some results from a study of a set of data consisting of measurements of the inlet impedance of a single tube forced flow boiler with inserts are given.

Miles, J. H.↗

NASA NTRS1971

Higher moment equations and the distribution function of the solar-wind plasma.

Study of the higher-moment equations for a collisionless fully ionized plasma. For a collisionless, heat-conducting plasma, the distribution function f is cylindrically symmetric about the direction of the magnetic field. It is shown that under a certain assumption the fourth moments of f can be expressed as simple functions of lower moments. Thus no higher-moment terms appear in the third-moment equations. The two third-moment equations, which are obtained in a simple form, join other lower-moment equations to form a closed set of moment equations. The new equations can be used to study the thermal anisotropy and the heat flux of the solar-wind proton. A special case of the cylindrically symmetric distribution function f is found to resemble the proton distribution function reconstructed from solar-wind data, and this resemblance justifies the assumption needed for decoupling the moment equations.

Whang, Y. C.↗

NASA NTRS1972

Variational solutions by the use of stepwise constant functions. I - Linear case.

Demonstration that accurate solutions to the integral equation or to the extremal function can be easily obtained by the variational method in many cases when a stepwise constant function is used for the trial function. The evaluation procedure is simple and straightforward; integrals of the kernel function can be evaluated analytically; the method provides, when the solution involves singularities, the best mean value across the singularity; the results are accurate in both the detailed physical quantities and their averages; the resultant solution can be further integrated analytically over the parameters associated with the problem; and the method can be readily applied to nonlinear integral equations.

Yoshikawa, K. K.↗

NASA NTRS1972

Stored energy function of rubberlike materials derived from simple tensile data.

An explicit formulation is developed to obtain the stored energy function, based on the Valanis-Landel separable symmetric stored energy function. This formulation is applicable to any multiaxial stress state, from simple tensile data alone, for those cases in which the stored energy function is a separable function of the stretch ratios. By direct comparison, it is also shown that styrene butadiene rubber, at least over a specific range, follows this postulated separable form.

Peng, T. J.↗

NASA NTRS1972

Digital modeling of human operator dynamics via class of Liapunov functions

A technique is described which is utilized for modeling human operator dynamics. The technique is based upon a model-reference system configuration and a class of Liapunov functions formulated for this purpose which possess variable characteristics. It is shown how such a class of Liapunov functions and their time derivatives is formulated. The crux of the formulation lies in three variable positive definite matrices used for the construction of the class of Liapunov functions. The form and order of these matrices depend upon the form and order of the error differential equation of the human operator model-reference system. These matrices can be modified to include nonlinear functions of the human operator model.

Mekel, R.↗

NASA NTRS1972

The measurement of driver describing functions in simulated steering control tasks

Measurements of driver describing functions in steering control tasks have been made using a driving simulator. The task was to regulate against a random crosswind gust input on a straight roadway, in order to stay in the center of the lane. Although driving is a multiloop task in general, the forcing function and situation were configured so that an inner-loop visual cue feedback of heading angle of heading rate would dominate, and the driver's response was interpreted to be primarily single-loop. The driver describing functions were measured using an STI describing function analyzer. Three replications for each subject showed good repeatability within a subject. There were some intersubject differences as expected, but the crossover frequencies, effective time delays, and stability margins were generally consistent with the prior data and models for similar manual control tasks. The results further confirm the feasibility of measuring human operator response properties in nominal control tasks with full (real-world) visual field displays.

Weir, D. H.↗

NASA NTRS1972

Estimation of automobile-driver describing function from highway tests using the double steering wheel

The automobile-driver describing function for lateral position control was estimated for three subjects from frequency response analysis of straight road test results. The measurement procedure employed an instrumented full size sedan with known steering response characteristics, and equipped with a lateral lane position measuring device based on video detection of white stripe lane markings. Forcing functions were inserted through a servo driven double steering wheel coupling the driver to the steering system proper. Random appearing, Gaussian, and transient time functions were used. The quasi-linear models fitted to the random appearing input frequency response characterized the driver as compensating for lateral position error in a proportional, derivative, and integral manner. Similar parameters were fitted to the Gabor transformed frequency response of the driver to transient functions. A fourth term corresponding to response to lateral acceleration was determined by matching the time response histories of the model to the experimental results. The time histories show evidence of pulse-like nonlinear behavior during extended response to step transients which appear as high frequency remnant power.

Delp, P.↗

NASA NTRS1972

Energy distribution functions of kilovolt ions in a modified Penning discharge

The distribution function of ion energy parallel to the magnetic field of a Penning discharge was measured with a retarding potential energy analyzer. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field were made with a charge-exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and their kinetic temperatures are equal within experimental error. This suggests that turbulent processes previously observed Maxwellianize the velocity distribution along a radius in velocity space, and result in an isotropic energy distribution. The kinetic temperatures are on the order of kilovolts, and the tails of the ion energy distribution functions are Maxwellian up to a factor of 7 e-folds in energy. When the distributions depart from Maxwellian, they are enhanced above the Maxwellian tail. Above densities of about 10 to the 10th power particles/cc, this enhancement appears to be the result of a second, higher temperature Maxwellian distribution. At these high particle energies, only the ions perpendicular to the magnetic field lines were investigated.

Roth, J. R.↗

NASA NTRS1972

Generalized Airy functions for use in one-dimensional quantum mechanical problems

The solution of the one dimensional, time independent, Schroedinger equation in which the energy minus the potential varies as the nth power of the distance is obtained from proper linear combinations of Bessel functions. The linear combinations called generalized Airy functions, reduce to the usual Airy functions Ai(x) and Bi(x) when n equals 1 and have the same type of simple asymptotic behavior. Expressions for the generalized Airy functions which can be evaluated by the method of generalized Gaussian quadrature are obtained.

Eaves, J. O.↗

NASA NTRS1973

The luminosity function of quasars and its evolution: A comparison of optically selected quasars and quasars found in radio catalogs

The luminosity function of quasars and its evolution are discussed, based on comparison of available data on optically selected quasars and quasars found in radio catalogs. It is assumed that the red shift of quasars is cosmological and the results are expressed in the framework of the Lambda = 0, Q sub Q = 1 cosmological model. The predictions of various density evolution laws are compared with observations of an optically selected sample of quasars and quasar samples from radio catalogs. The differences between the optical luminosity functions, the red shift distributions and the radio to optical luminosity ratios of optically selected quasars and radio quasars rule out luminosity functions where there is complete absence of correlation between radio and optical luminosities. These differences also imply that Schmidt's (1970) luminosity function, where there exists a statistical correlation between radio and optical luminosities, although may be correct for high red shift objects, disagrees with observation at low red shifts. These differences can be accounted for by postulating existence of two classes (1 and 2) of objects.

Petrosian, V.↗

NASA NTRS1972

Geopotential representation with sampling functions.

Satellite-to-ocean altitudes measured to meter accuracy eventually can yield a geoid representation with significant short-wavelength structure over ocean areas. To cope conveniently with this expected detail, one suggested analytical technique would represent the geopotential or the geoid as an expansion in sampling functions that are linear combinations of spherical harmonics. Each of the sampling functions makes its principal contribution to the geopotential in a single geographical region. For a representation truncated after degree N, there are (N + 1) squared such functions associated with a like number of points distributed nearly regularly on the globe. The features of this geopotential representation can be illustrated by considering the case N = 22, for which an expansion in sampling functions can be produced that is equivalent to the geopotential of the 1969 Smithsonian standard earth.

Lundquist, C. A.↗

NASA NTRS1974

Function generation subprograms for use in digital simulations

Function generation subprograms were developed for handling functions of one variable and two types of functions of two variables. These subprograms can be used in any digital or hybrid simulation requiring function generation. Use of these programs can often lower overall program execution time.

Hart, C. E.↗

NASA NTRS1973

Lunar electromagnetic scattering. II - Magnetic fields and transfer functions for parallel propagation

Magnetic field and transfer function amplitudes, resulting from a transverse electromagnetic wave in the interplanetary medium scattering from the moon and its diamagnetic cavity, are presented. Calculations are made using an asymmetric scattering theory for a spherical two-layer model of the lunar electrical conductivity profile and a nonconducting cylindrical model of the downstream lunar plasma void. Both the field and transfer function magnitudes are calculated as functions of position on the surface of the moon for frequencies relevant to the observations of the lunar surface and orbiting magnetometers. The amplitudes of the magnetic field components on the cavity boundary are also computed as functions of frequency and distance downstream from the lunar limb. Comparisons of the results are made with those of (1) spherically symmetric descriptions of lunar electromagnetic scattering, (2) the quasi-static approximation to asymmetric scattering theory, and (3) observations of the scattering phenomenon by lunar surface and orbiting magnetometers.

Schubert, G.↗

NASA NTRS1974

Shuttle ascent trajectory optimization with function space quasi-Newton techniques

A Space Shuttle ascent trajectory optimization problem from lift-off to orbital insertion is solved with a function space version of a quasi-Newton parameter optimization method developed by Broyden. The problem includes five parameter and one bounded-function controls, two state-variable constraints, and four terminal conditions. The bounded controls are treated directly, while the remaining constraints are adjoined to the performance index (maximum payload) with penalty functions. The problem is formulated as a four-phase variational problem (liftoff, pitch-over, gravity-turn, linear tangent steering), and the appropriate gradients are developed by first variation theory. A projection operator is introduced to aid in the interpretation of the algorithm with mixed parameter and function controls.

Edge, E. R.↗

NASA NTRS1974

Performance monitor system functional simulator, environmental data, orbiter 101(HFT)

Information concerning the environment component of the space shuttle performance monitor system simulator (PMSS) and those subsystems operational on the shuttle orbiter 101 used for horizontal flight test (HFT) is provided, along with detailed data for the shuttle performance monitor system (PMS) whose software requirements evolve from three basic PMS functions: (1) fault detection and annunciation; (2) subsystem measurement management; and (3) subsystem configuration management. Information relative to the design and operation of Orbiter systems for HFT is also presented, and the functional paths are identified to the lowest level at which the crew can control the system functions. Measurement requirements are given which are necessary to adequately monitor the health status of the system. PMS process requirements, relative to the measurements which are necessary for fault detection and annunciation of a failed functional path, consist of measurement characteristics, tolerance limits, precondition tests, and correlation measurements.

Parker, F. W.↗

NASA NTRS1974

Symbolic integration of a class of algebraic functions

An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.

Ng, E. W.↗

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.↗