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NASA NTRS1980

Low order equivalent models of highly augmented aircraft determined from flight data using maximum likelihood estimation

This paper presents the results of a study of the feasibility of using low order equivalent mathematical models of a highly augmented aircraft, the F-8 digital fly-by-wire (DFBW), for flying qualities research. Increasingly complex models were formulated and evaluated using flight data and maximum likelihood estimation techniques. The aircraft actuator was modeled alone first. Next the equivalent derivatives were used to model the longitudinal unaugmented F-8 DFBW aircraft dynamics. The most complex model incorporated a pure time shift of the pilot input, a first order lag, and the basic longitudinal airframe model. This same model was then implemented for the F-8 DFBW aircraft in a highly augmented mode. Excellent matching of the dynamics resulted for this model, indicating that low order equivalent models which are good representations of the highly augmented F-8 DFBW aircraft can be formulated with these methods.

Shafer, M. F.↗

NASA NTRS1980

An equivalent source model of the satellite-altitude magnetic anomaly field over Australia

The low-amplitude, long-wavelength magnetic anomaly field measured between 400 and 700 km elevation over Australia by the POGO satellites is modeled by means of the equivalent source technique. Magnetic dipole moments are computed for a latitude-longitude array of dipole sources on the earth's surface such that the dipoles collectively give rise to a field which makes a least squares best fit to that observed. The distribution of magnetic moments is converted to a model of apparent magnetization contrast in a layer of constant (40 km) thickness, which contains information equivalent to the lateral variation in the vertical integral of magnetization down to the Curie isotherm and can be transformed to a model of variable thickness magnetization. It is noted that the closest equivalent source spacing giving a stable solution is about 2.5 deg, corresponding to about half the mean data elevation, and that the magnetization distribution correlates well with some of the principle tectonic elements of Australia.

Mayhew, M. A.↗

NASA NTRS1980

Apparent violation of the principle of equivalence and killing horizons

By means of the principle of equivalence the qualitative behavior of the Schwarzschild horizon about a uniformly accelerating particle was deduced. This result is confirmed for an exact solution of a uniformly accelerating object in the limit of small accelerations. For large accelerations the Schwarzschild horizon appears to violate the qualitative behavior established via the principle of equivalence. When similar arguments are extended to an observable such as the red shift between two observers, there is no departure from the results expected from the principle of equivalence. The resolution of the paradox is brought about by a compensating effect due to the Rindler horizon.

Zimmerman, R. L.↗

NASA NTRS1981

Adaptation of the TH Epsilon Mu formalism for the analysis of the equivalence principle in the presence of the weak and electroweak interaction

The TH epsilon mu formalism, used in analyzing equivalence principle experiments of metric and nonmetric gravity theories, is adapted to the description of the electroweak interaction using the Weinberg-Salam unified SU(2) x U(1) model. The use of the TH epsilon mu formalism is thereby extended to the weak interactions, showing how the gravitational field affects W sub mu (+ or -1) and Z sub mu (0) boson propagation and the rates of interactions mediated by them. The possibility of a similar extension to the strong interactions via SU(5) grand unified theories is briefly discussed. Also, using the effects of the potentials on the baryon and lepton wave functions, the effects of gravity on transition mediated in high-A atoms which are electromagnetically forbidden. Three possible experiments to test the equivalence principle in the presence of the weak interactions, which are technologically feasible, are then briefly outline: (1) K-capture by the FE nucleus (counting the emitted X-ray); (2) forbidden absorption transitions in high-A atoms' vapor; and (3) counting the relative Beta-decay rates in a suitable alpha-beta decay chain, assuming the strong interactions obey the equivalence principle.

Fennelly, A. J.↗

NASA NTRS1982

Equivalence of the generalized Lie-Hori method and the method of averaging

In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence both Duffing's equation and the van der Pol equation are solved using each method.

Ahmed, A.↗

NASA NTRS1982

Measurement of cardiopulmonary performance during acute exposure to a 2440-m equivalent atmosphere

Each of 20 subjects (ranging in age from 18 to 38 years, 15 being male, five female) was given two Bruce Protocol symptom-limited maximum treadmill stress tests, breathing sea-level compressed air (20.9% O2) for one test and a 2440-m equivalent (15.5% O2) for the other. A significant difference was found to exist between measured VO2 max (p less than 0.0002) and exercise time (p less than 0.0004) for the two conditions. No significant differences were observed in heart rate or the recovery time to a respiratory quotient of less than 1. Hemoglobin saturation, as measured by an ear oximeter, averaged 95% for sea-level and 91% for the 2440-m equivalent gases. These results support a 2440-m equivalent contingency atmosphere in the Space Shuttle prior to donning a low-pressure suit for the purpose reducing nitrogen washout times.

Levitan, B. M.↗

NASA NTRS1982

On the validity of equivalent electron fluence for GaAs solar cells

A simple model for particulate radiation damage in shallow-junction heteroface GaAs solar cells is used to evaluate the equivalent electron fluence concept especially in the sense of additivity of electron and proton exposure. It is found that spatial dependent factors for low-energy proton exposure results in a dose dependent equivalent fluence ratio so that additivity within the equivalent fluence concept is generally not possible.

Wilson, J. W.↗

NASA NTRS1983

The damage equivalence of electrons, protons, alphas and gamma rays in rad-hard MOS devices

This paper reports on a study of damage equivalence in rad-hard MOS devices with 100,000 rads (SiO2) capability. Damage sensitivities for electrons of 1, 2, 3, 5, and 7 MeV, protons of 1, 3, 7, 22, and 40 MeV, 3.4-MeV alphas, and Co-60 gammas were measured and compared. Results indicated that qualitatively the same charge recombination effects occurred in hard oxide devices for doses of 100,000 rads (SiO2) as in soft oxide parts for doses of 1 to 4 krads (SiO2). Consequently, damage equivalency or non-equivalency depended on radiation type and energy. However, recovery effects, both during and after irradiation, controlled relative damage sensitivity and its dependency on total dose, dose rate, supply bias, gate bias, radiation type, and energy. Correction factors can be derived from these data or from similar tests of other hard oxide type, so as to properly evaluate the combined effects of the total space environment.

Stassinopoulos, E. G.↗

NASA NTRS1984

Equivalence of the generalized Lie-Hori method and the method of averaging

In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence Duffing's equation, the van der Pol equation and the oscillator with quadratic damping problem are solved using each method.

Ahmed, A. H.↗

NASA NTRS1985

Distribution of Snow and Maximum Snow Water Equivalent Obtained by LANDSAT Data and Degree Day Method

Maximum snow water equivalence and snowcover distribution are estimated using several LANDSAT data taken in snowmelting season over a four year period. The test site is Okutadami-gawa Basin located in the central position of Tohoku-Kanto-Chubu District. The year to year normalization for snowmelt volume computation on the snow line is conducted by year to year correction of degree days using the snowcover percentage within the test basin obtained from LANDSAT data. The maximum snow water equivalent map in the test basin is generated based on the normalized snowmelt volume on the snow line extracted from four LANDSAT data taken in a different year. The snowcover distribution on an arbitrary day in snowmelting of 1982 is estimated from the maximum snow water equivalent map. The estimated snowcover is compared with the snowcover area extracted from NOAA-AVHRR data taken on the same day. The applicability of the snow estimation using LANDSAT data is discussed.

Takeda, K.↗

NASA NTRS1984

Equivalent electron fluence for space qualification of shallow junction heteroface GaAs solar cells

It is desirable to perform qualification tests prior to deployment of solar cells in space power applications. Such test procedures are complicated by the complex mixture of differing radiation components in space which are difficult to simulate in ground test facilities. Although it has been shown that an equivalent electron fluence ratio cannot be uniquely defined for monoenergetic proton exposure of GaAs shallow junction cells, an equivalent electron fluence test can be defined for common spectral components of protons found in space. Equivalent electron fluence levels for the geosynchronous environment are presented.

Wilson, J. W.↗

NASA NTRS1985

Extremely metal-deficient red giants. IV - Equivalent widths for 36 halo giants

Further work on a study of 36 metal-poor field red giants is reported. Chemical abundances previously determined were based on model stellar atmosphere analyses of equivalent widths from photographic image-tube echelle spectrograms obtained with with 4-m reflectors at Kitt Peak and Cerro Tololo. A tabulation of the equivalent-width data (a total of 18, 275 equivalent widths) is presented.

Luck, R. E.↗

NASA NTRS1987

Further generalization of an equivalent plate representation for aircraft structural analysis

Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described, allow modeling of wing cross sections having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

Giles, Gary L.↗

NASA NTRS1987

Further generalization of an equivalent plate representation for aircraft structural analysis

Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described in this paper, allow modeling of wing cross section having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

Giles, Gary L.↗

NASA NTRS1989

Equivalent linearization for fatigue life estimates of a nonlinear structure

An analysis is presented of the suitability of the method of equivalent linearization for estimating the fatigue life of a nonlinear structure. Comparisons are made of the fatigue life of a nonlinear plate as predicted using conventional equivalent linearization and three other more accurate methods. The excitation of the plate is assumed to be Gaussian white noise and the plate response is modeled using a single resonant mode. The methods used for comparison consist of numerical simulation, a probabalistic formulation, and a modification of equivalent linearization which avoids the usual assumption that the response process is Gaussian. Remarkably close agreement is obtained between all four methods, even for cases where the response is significantly linear.

Miles, R. N.↗

NASA NTRS1989

Equivalent linearization for fatigue life estimates of a nonlinear structure

An analysis is presented of the suitability of the method of equivalent linearization for estimating the fatigue life of a nonlinear structure. Comparisons are made of the fatigue life of a nonlinear plate as predicted using conventional equivalent linearization and three other more accurate methods. The excitation of the plate is assumed to be Gaussian white noise and the plate response is modeled using a single resonant mode. The methods used for comparison consist of numerical simulation, a probabilistic formulation, and a modification of equivalent linearization which avoids the usual assumption that the response process is Gaussian. Remarkably close agreement is obtained between all four methods, even for cases where the response is significantly linear.

Miles, R. N.↗

NASA NTRS1989

The Stanford equivalence principle program

The Stanford Equivalence Principle Program (Worden, Jr. 1983) is intended to test the uniqueness of free fall to the ultimate possible accuracy. The program is being conducted in two phases: first, a ground-based version of the experiment, which should have a sensitivity to differences in rate of fall of one part in 10(exp 12); followed by an orbital experiment with a sensitivity of one part in 10(exp 17) or better. The ground-based experiment, although a sensitive equivalence principle test in its own right, is being used for technology development for the orbital experiment. A secondary goal of the experiment is a search for exotic forces. The instrument is very well suited for this search, which would be conducted mostly with the ground-based apparatus. The short range predicted for these forces means that forces originating in the Earth would not be detectable in orbit. But detection of Yukawa-type exotic forces from a nearby large satellite (such as Space Station) is feasible, and gives a very sensitive and controllable test for little more effort than the orbiting equivalence principle test itself.

Worden, Paul W., Jr.↗

NASA NTRS1990

Obtaining an equivalent beam

In modeling a complex structure the researcher was faced with a component that would have logical appeal if it were modeled as a beam. The structure was a mast of a robot controlled gantry crane. The structure up to this point already had a large number of degrees of freedom, so the idea of conserving grid points by modeling the mast as a beam was attractive. The researcher decided to make a separate problem of of the mast and model it in three dimensions with plates, then extract the equivalent beam properties by setting up the loading to simulate beam-like deformation and constraints. The results could then be used to represent the mast as a beam in the full model. A comparison was made of properties derived from models of different constraints versus manual calculations. The researcher shows that the three-dimensional model is ineffective in trying to conform to the requirements of an equivalent beam representation. If a full 3-D plate model were used in the complete representation of the crane structure, good results would be obtained. Since the attempt is to economize on the size of the model, a better way to achieve the same results is to use substructuring and condense the mast to equivalent end boundary and intermediate mass points.

Butler, Thomas G.↗