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NASA NTRS1980

On the equivalence between semiempirical fracture analyses and R-curves

The relationship between the R-curves and semiempirical fracture analyses (SEFA) is investigated theoretically using a hypothetical material. Equivalent R-curves (ERC) are developed for real materials using data from the literature. It is shown that for each SEFA there is an ERC whose magnitude and shape are determined by the SEFA formulation and its empirical parameters. The ERC is equivalent in that it predicts exactly the same relationship between the fracture stress and the initial crack length (residual strength) as the SEFA. If the effective R-curve is unique, then the various empirical parameters cannot be constant, and vice versa. However, for one of the SEFA examined, Newman's SEFA, parameter variations are small enough to be within the range of normal data scatter for real materials.

Orange, T. W.↗

NASA NTRS1981

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.

Von Frese, R. R. B.↗

NASA NTRS1980

Explosive materials equivalency, test methods and evaluation

Attention is given to concepts of explosive equivalency of energetic materials based on specific airblast parameters. A description is provided of a wide bandwidth high accuracy instrumentation system which has been used extensively in obtaining pressure time profiles of energetic materials. The object of the considered test method is to determine the maximum output from the detonation of explosive materials in terms of airblast overpressure and positive impulse. The measured pressure and impulse values are compared with known characteristics of hemispherical TNT data to determine the equivalency of the test material in relation to TNT. An investigation shows that meaningful comparisons between various explosives and a standard reference material such as TNT should be based upon the same parameters. The tests should be conducted under the same conditions.

Koger, D. M.↗

NASA NTRS1982

Basis for equivalent fluence concept in space solar cells

The equivalent fluence concept is defined, and its use and potential problems are noted. Silicon and GaAs solar cells are compared in a radiation environment. The analysis indicates that valid equivalent fluence values may be easier to obtain in GaAs than in silicon.

Meulenberg, A.↗

NASA NTRS1983

The equivalence of three techniques for estimating ground reflectance from LANDSAT digital count data

The equivalence of three separate investigations that related LANDSAT digital count (DC) to ground measured reflectance (R) was demonstrated. One investigator related DC data to the cosZ, where Z is the solar zenith angle, for surfaces of constant R. The second investigator corrected the DC data to the solar zenith angle of 39 degrees before relating to surface R. Both of these investigators used LANDSAT 1 and 2 data from overpass dates 1972 through 1977. A third investigator calculated the relation between DC and R based on atmospheric radiative transfer theory. The equation coefficients obtained from these three investigators for all four LANDSAT MSS bands were shown to be equivalent although differences in ground reflectance measurement procedures have created coefficient variations among the three investigations. These relations should be useful for testing atmospheric radiative transfer theory.

Richardson, A. J.↗

NASA NTRS1983

The role of the equivalent blackbody temperature in the study of Atlantic Ocean tropical cyclones

Satellite measured equivalent blackbody temperatures of Atlantic Ocean tropical cyclones are used to investigate their role in describing the convection and cloud patterns of the storms and in predicting wind intensity. The high temporal resolution of the equivalent blackbody temperature measurements afforded with the geosynchronous satellite provided sequential quantitative measurements of the tropical cyclone which reveal a diurnal pattern of convection at the inner core during the early developmental stage; a diurnal pattern of cloudiness in the storm's outer circulation throughout the life cycle; a semidiurnal pattern of cloudiness in the environmental atmosphere surrounding the storms during the weak storm stage; an outward modulating atmospheric wave originating at the inner core; and long term convective bursts at the inner core prior to wind intensification.

Steranka, J.↗

NASA NTRS1983

Equivalent-circuit consideration of dual-gate MESFETs at high frequency

The simplified high-frequency equivalent circuit of a dual-gate FET is described. It is shown that the input impedance is similar to that of a single-gate FET but the output resistance and capacitance (parallel equivalent circuit) are higher. The output resistance and the transconductance decrease as frequency increases. The unilateral gain of a dual-gate FET rolls off 12 dB/octave.

Kim, B.↗

NASA NTRS1983

Equivalent source modeling of the core magnetic field using magsat data

Experiments are carried out on fitting the main field using different numbers of equivalent sources arranged in equal area at fixed radii at and inside the core-mantle boundary. In fixing the radius for a given series of runs, the convergence problems that result from the extreme nonlinearity of the problem when dipole positions are allowed to vary are avoided. Results are presented from a comparison between this approach and the standard spherical harmonic approach for modeling the main field in terms of accuracy and computational efficiency. The modeling of the main field with an equivalent dipole representation is found to be comparable to the standard spherical harmonic approach in accuracy. The 32 deg dipole density (42 dipoles) corresponds approximately to an eleventh degree/order spherical harmonic expansion (143 parameters), whereas the 21 dipole density (92 dipoles) corresponds to approximately a seventeenth degree and order expansion (323 parameters). It is pointed out that fixing the dipole positions results in rapid convergence of the dipole solutions for single-epoch models.

Mayhew, M. A.↗

NASA NTRS1985

A preliminary study of a cryogenic equivalence principle experiment on Shuttle

The Weak Equivalence Principle is the hypothesis that all test bodies fall with the same acceleration in the same gravitational field. The current limit on violations of the Weak Equivalence Principle, measured by the ratio of the difference in acceleration of two test masses to their average acceleration, is about 3 parts in one-hundred billion. It is anticipated that this can be improved in a shuttle experiment to a part in one quadrillion. Topics covered include: (1) studies of the shuttle environment, including interference with the experiment, interfacing to the experiment, and possible alternatives; (2) numerical simulations of the proposed experiment, including analytic solutions for special cases of the mass motion and preliminary estimates of sensitivity and time required; (3) error analysis of several noise sources such as thermal distortion, gas and radiation pressure effects, and mechanical distortion; and (4) development and performance tests of a laboratory version of the instrument.

Everitt, C. W. F.↗

NASA NTRS1984

Generalized serial search code acquisition - The equivalent circular state diagram approach

A transform-domain method for deriving the generating function of the acquisition process resulting from an arbitrary serial search strategy is presented. The method relies on equivalent circular state diagrams, uses Mason's formula from flow-graph theory, and employs a minimum number of required parameters. The transform-domain approach is briefly described and the concept of equivalent circular state diagrams is introduced and exploited to derive the generating function and resulting mean acquisition time for three particular cases of interest, the continuous/center Z search, the broken/center Z search, and the expanding window search. An optimization of the latter technique is performed whereby the number of partial windows which minimizes the mean acquisition time is determined. The numerical results satisfy certain intuitive predictions and provide useful design guidelines for such systems.

Polydoros, A.↗

NASA NTRS1985

Cryogenic Equivalence Principle Experiment

The purpose of this project is to test the equivalence of inertial and passive gravitational mass in an Earth-orbiting satellite. A ground-based experiment is now well developed. It consists of comparing the motions of two cylindrical test masses suspended in precision superconducting magnetic bearings and free to move along the horizontal (axis) direction. The masses are made of niobium and lead-plated aluminum. A position detector based on a SQUID magnetometer measures the differential motion between the masses. The periods of the masses are matched by adjustment of the position detector until the system is insensitive to common mode signals, and so that the experiment is less sensitive to seismic vibration. The apparatus is contained in a twelve inch helium dewar suspended in a vibration isolation stand. The stand achieves 30 db isolation from horizontal motions between 0.1 and 60 Hz, by simulating the motion of a 200 meter long pendulum with an air bearing. With this attenuation of seismic noise and a common mode rejection ratio of 10 to the 5th power in the differential mode, the ground based apparatus should have a sensitivity to equivalence principle violations of one part in 10 to the 13th power; the satellite version might have a sensitivity of one part in 10 to the 17th power.

Everitt, C. W. F.↗

NASA NTRS1986

Equivalent plate analysis of aircraft wing box structures with general planform geometry

A new equivalent plate analysis formulation is described which is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. Multiple trapezoidal segments are used to represent such planforms. A Ritz solution technique is used in conjunction with global displacement functions which encompass all the segments. This Ritz solution procedure is implemented efficiently into a computer program so that it can be used by rigorous optimization algorithms for application in early preliminary design. A direct method to interface this structural analysis procedure with aerodynamic programs for use in aeroelastic calculations is described. This equivalent plate analysis procedure is used to calculate the static deflections and stresses and vibration frequencies and modes of an example wing configuration. The numerical results are compared with results from a finite element model of the same configuration to illustrate typical levels of accuracy and computation times resulting from use of this procedure.

Giles, G. L.↗

NASA NTRS1986

Representation of the vaporization behavior of turbulent polydisperse sprays by equivalent monodisperse sprays

The concept of using an equivalent monodisperse spray to represent the vaporization behavior of polydisperse sprays has been examined by numerically solving two turbulent vaporizing sprays. One involves the injection of Freon-11 in a still environment, whereas the other is a methanol spray in a still but hot environment. The use of three different mean sizes, namely, Sauter mean diameter, volume median diameter, and surface-area mean diameter, has been investigated. Results indicate a good degree of correlation between the polydisperse spray and its equivalent monodisperse sprays represented by the volume median diameter and the Sauter mean diameter, the former giving slightly better results. The surface-area mean diameter does not provide as good a correlation as the other two mean diameters.

Aggarwal, S. K.↗

NASA NTRS1986

Optimum structural sizing of conventional cantilever and joined wing configurations using equivalent beam models

The present paper describes an approach for the optimum sizing of single and joined wing structures that is based on representing the built-up finite element model of the structure by an equivalent beam model. The low order beam model is computationally more efficient in an environment that requires repetitive analysis of several trial designs. The design procedure is implemented in a computer program that requires geometry and loading data typically available from an aerodynamic synthesis program, to create the finite element model of the lifting surface and an equivalent beam model. A fully stressed design procedure is used to obtain rapid estimates of the optimum structural weight for the beam model for a given geometry, and a qualitative description of the material distribution over the wing structure. The synthesis procedure is demonstrated for representative single wing and joined wing structures.

Hajela, P.↗

NASA NTRS1987

Representation of the vaporization behavior of turbulent polydisperse sprays by 'equivalent' monodisperse sprays

Aggarwal, S. K.↗

NASA NTRS1986

On testing of functionally equivalent components of fault-tolerant software

Six functionally equivalent programs were tested with specification based random and extremal/special value (ESV) test cases. Statement and branch coverage were used to measure and compare the attained testing effectiveness. It was observed that both measures reached a nearly steady state value after 25 to 75 random test cases. Coverage saturation curves appear to follow an exponential growth model. However, the steady state values for branch coverage of different components, but the same input cases, differed by as much as 22 percent. The effect is the result of the differences in the detailed structure of the components. Improvement in coverage provided by the random test data, after the ESV cases were executed, was only about 1 percent. Results indicate that extensive random testing can be a process of diminishing returns, and that in the FTS context functional ('black box') testing can provide a very uneven execution coverage of the functionally equivalent software, and therefore should be supplemented by structure based testing.

Vouk, Mladen A.↗

NASA NTRS1988

Galactic interstellar abundance surveys with IUE. II - The equivalent widths and column densities

This paper continues a survey of interstellar densities, abundances, and cloud structure in the Galaxy, using the International Ultraviolet Explorer (IUE) satellite. Equivalent widths of 18 ultraviolet resonance transitions are presented and column densities for Si II, Mn II, Fe II, S II, and Zn II toward 261 early-type stars are derived. These equivalent widths and column densities agree within the stated errors of earlier Copernicus, BUSS, or IUE surveys of Mn II, Fe II, S II, and Zn II for 45 stars in common. The column densities are derived from single-component curves of growth with a common b-value based on that of Fe II and Si II.

Van Steenberg, Michael E.↗

NASA NTRS1990

Reliability of equivalent sphere model in blood-forming organ dose estimation

The radiation dose equivalents to blood-forming organs (BFO's) of the astronauts at the Martian surface due to major solar flare events are calculated using the detailed body geometry of Langley and Billings. The solar flare spectra of February 1956, November 1960, and August 1972 events are employed instead of the idealized Webber form. The detailed geometry results are compared with those based on the 5-cm sphere model which was used often in the past to approximate BFO dose or dose equivalent. Larger discrepancies are found for the later two events possibly due to the lower numbers of highly penetrating protons. It is concluded that the 5-cm sphere model is not suitable for quantitative use in connection with future NASA deep-space, long-duration mission shield design studies.

Shinn, Judy L.↗