Theory of statistical analysis of data distributed over a sphere.
Theory of statistical analysis of data distributed over sphere
GEOPHYSICS↗
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Information content of the Mariner Mars 1971 radio tracking data
Covariance analysis of Mars gravity harmonics, ephemeris and radiation pressure from Mariner 1971 range and Doppler radio tracking data
Lorell, J.↗
Recent results on the mass, gravitational field and moments of inertia of the moon.
Use of Doppler tracking data from the Lunar Orbiter series of spacecraft in an analysis of the spherical harmonic coefficients of the lunar gravitational field through thirteenth degree and order. The value obtained for the mass of the moon, GM = 4902.84 cu km/sec/sec, is in good agreement with previous results and with results obtained by alternate procedures. Acceleration contour plots, derived from the gravitational coefficients, show correlations with surface features on the near side of the moon, but are of questionable validity for the far side because of the lack of direct tracking data on the far side. Based on the most recent gravitational field data, the current estimate for the polar moment of inertia of the moon is C/Ma squared = 0.4019 super + 0.004 sub - 0.002. This value indicates that the interior of the moon can be homogeneous, but some results presented strongly suggest that the moon is differentiated, with an excess of mass in the direction toward the earth.
Michael, W. H., Jr.↗
Influence of exit impedance on finite difference solutions of transient acoustic mode propagation in ducts
The time-dependent governing acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard-wall duct without flow and with spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the steady solutions of the acoustic field. The transient method did not converge to the steady-state solution for cutoff acoustic duct modes. This has implications as to its use in a variable-area duct, where modes may become cutoff in the smal-area portion of the duct. For single cutoff mode propagation the steady-state impedance boundary condition produced acoustic reflections during the initial transient that caused finite instabilities in the numerical calculations. The stability problem is resolved by reformulating the exit boundary condition. Example calculations show good agreement with exact analytical and numerical results for forcing frequencies above, below, and nearly at the cutoff frequency.
Baumeister, K. J.↗
Dependence of the spectrum of Pc 3-4 pulsations on the interplanetary magnetic field
Dependence of the power spectrum of Pc 3-4 magnetic pulsations observed at the ATS 6 geosynchronous satellite on the interplanetary magnetic field (IMF) has been studied. Pulsation events that were observed near noon and exhibited harmonic structure are chosen for analysis. Further selected are pulsation events with identical fundamental frequency to study dependence of the power of pulsations at different harmonic bands on the IMF. A weak negative correlation is observed between the IMF cone angle theta-XB and the power of pulsations in the frequency range 20-70 mHz. Also, a positive correlation between the intensity of the IMF B(IMF) and the power of pulsations at 50-70 mHz is found. This B(IMF) control is present at all ranges of the cone angle. A comparison is conducted of this observation with the frequency of bow shock associated upstream waves predicted from a model of wave generation by a cyclotron resonance of ions reflected at the bow shock. The predicted frequency depends on the IMF as B(IMF) (cos theta-XB)-squared. Although this relation gives a proportionality between the frequency and B(IMF) qualitatively consistent with the observation, it does not explain the most obvious IMF control of the spectrum of the pulsations.
Takahashi, K.↗
Added noise due to the effect of an upstream wake on a propeller
An analytical/computational study has been conducted to predict the effect of an upstream wing or pylon on the noise of an operating propeller. The wing trailing edge was placed at variable distances (0.1 and 0.3 chord) upstream of a scaled model propeller (SR-2). The wake was modeled using a similarity formulation. The instantaneous pressure distribution on the propeller blades during the passage through the wake was formulated in terms of a time-dependent variation of each blade section's angle of attack and in terms of the shed vortices from the blade trailing edge. It was found that the final expressions for the unsteady loads considerably altered the radiated noise pattern. Predicted noise for various observer positions, rotational speeds, and propeller/pylon distances were computed and are presented in terms of the pressure time history, harmonics of the Fourier analysis, and overall sound pressure levels (OASPL). The addition of the tangential stress due to skin friction was found to have a damping effect on the acoustic pressure time history and the resulting spectrum of the generated noise. It is shown that the positioning of a pylon upstream of a propeller indeed increases the overall noise.
Takallu, M. A.↗
Stability analysis of large space structure control systems with delayed input
Large space structural systems, due to their inherent flexibility and low mass to area ratio, are represented by large dimensional mathematical models. For implementation of the control laws for such systems a finite amount of time is required to evaluate the control signals; and this time delay may cause instability in the closed loop control system that was previously designed without taking the input delay into consideration. The stability analysis of a simple harmonic oscillator representing the equation of a single mode as a function of delay time is treated analytically and verified numerically. The effect of inherent damping on the delay is also analyzed. The control problem with delayed input is also formulated in the discrete time domain.
Reddy, A. S. S. R.↗
Stability analysis of large space structure control systems with delayed input
Large space structural systems, due to their inherent flexibility and low mass to area ratio, are represented by large dimensional mathematical models. For implementation of the control laws for such systems a finite amount of time is required to evaluate the control signals; and this time delay may cause instability in the closed loop control system that was previously designed without taking the input delay into consideration. The stability analysis of a simple harmonic oscillator representing the equation of a single mode as a function of delay time is analyzed analytically and verified numerically. The effect of inherent damping on the delay is also analyzed. The control problem with delayed input is also formulated in the discrete time domain.
Reddy, A. S. S. R.↗
Equilibrium shape and location of a liquid drop acoustically positioned in a resonant rectangular chamber
The effect of a standing wave field in a rectangular chamber on the shape and location of an acoustically positioned drop or bubble is calculated. The sample deformation and equilibrium position are obtained from an analysis of the spherical harmonic projections of the total surface stress tensor. The method of calculation relies on the assumed condition that the sample is only slightly distorted from a spherical form. The equilibrium location of a levitated drop is combined with a formula introduced by Hasegawa (1979) to calcualte the ka dependence of the radiation force function. The present theory is valid for large as well as small ka values. Calculations in the small ka limit agree with previous theories and experimental results. Examples are presented for nonplane-wave modes as well as plane-wave rectangular modes.
Jackson, H. W.↗
Harmonic Balance Computations of Fan Aeroelastic Stability
A harmonic balance (HB) aeroelastic analysis, which has been recently developed, was used to determine the aeroelastic stability (flutter) characteristics of an experimental fan. To assess the numerical accuracy of this HB aeroelastic analysis, a time-domain aeroelastic analysis was also used to determine the aeroelastic stability characteristics of the same fan. Both of these three-dimensional analysis codes model the unsteady flowfield due to blade vibrations using the Reynolds-averaged Navier-Stokes (RANS) equations. In the HB analysis, the unsteady flow equations are converted to a HB form and solved using a pseudo-time marching method. In the time-domain analysis, the unsteady flow equations are solved using an implicit time-marching approach. Steady and unsteady computations for two vibration modes were carried out at two rotational speeds: 100 percent (design) and 70 percent (part-speed). The steady and unsteady results obtained from the two analysis methods compare well, thus verifying the recently developed HB aeroelastic analysis. Based on the results, the experimental fan was found to have no aeroelastic instability (flutter) at the conditions examined in this study.
Bakhle, Milind A.↗
Piezoelectric Vibration Damping Study for Rotating Composite Fan Blades
Resonant vibrations of aircraft engine blades cause blade fatigue problems in engines, which can lead to thicker and aerodynamically lower performing blade designs, increasing engine weight, fuel burn, and maintenance costs. In order to mitigate undesirable blade vibration levels, active piezoelectric vibration control has been investigated, potentially enabling thinner blade designs for higher performing blades and minimizing blade fatigue problems. While the piezoelectric damping idea has been investigated by other researchers over the years, very little study has been done including rotational effects. The present study attempts to fill this void. The particular objectives of this study were: (a) to develop and analyze a multiphysics piezoelectric finite element composite blade model for harmonic forced vibration response analysis coupled with a tuned RLC circuit for rotating engine blade conditions, (b) to validate a numerical model with experimental test data, and (c) to achieve a cost-effective numerical modeling capability which enables simulation of rotating blades within the NASA Glenn Research Center (GRC) Dynamic Spin Rig Facility. A numerical and experimental study for rotating piezoelectric composite subscale fan blades was performed. It was also proved that the proposed numerical method is feasible and effective when applied to the rotating blade base excitation model. The experimental test and multiphysics finite element modeling technique described in this paper show that piezoelectric vibration damping can significantly reduce vibrations of aircraft engine composite fan blades.
Min, James B.↗
Drag-Free Control and Drag Force Recovery of Small Satellites
Drag-free satellites provide autonomous precision orbit determination, accurately map the static and time varying components of Earth's mass distribution, aid in our understanding of the fundamental force of gravity, and will ultimately open up a new window to our universe through the detection and observation of gravitational waves. At the heart of this technology is a gravitational reference sensor, which (a) contains and shields a free-floating proof mass from all non-gravitational forces, and (b) precisely measures the position of the test mass inside the sensor. Thus, both test mass and spacecraft follow a pure geodesic in spacetime. By tracking the position of a low Earth orbiting drag-free satellite we can directly determine the detailed shape of geodesics and through analysis, the higher order harmonics of the Earths geopotential. This paper explores two different drag-free control systems on small satellites. The first drag-free control system is a continuously compensated single thruster 3-unit CubeSat with a suspension-free spherical proof-mass. A feedback control system commands the thruster and Attitude and Determination Control System to fly the tender spacecraft with respect to the test mass. The spheres position is sensed with a LED-based differential optical shadow sensor, its electric charge controlled by photoemission using UV LEDs, and the spacecraft position is maintained with respect to the sphere using an ion electrospray propulsion system. This configuration is the most fuel-efficient drag-free system possible today. The second drag-free control system is an electro-statically suspended cubical proof-mass that is operated with a low duty cycle, limiting suspension force noise over brief, known time intervals on a small GRACE-II -like satellite. The readout is performed using a laser interferometer, which is immune to the dynamic range limitations of voltage references. This system eliminates the need for a thruster, enabling drag-free control systems for passive satellites. In both cases, the test mass position, GPS tracking data, and commanded actuation, either thrust or suspension system, can be analyzed to estimate the 3-axis drag forces acting on the satellite. The data produces the most precise maps of upper atmospheric drag forces and with additional information, detailed models that describe the dynamics of the upper atmosphere and its impact on all satellites that orbit the Earth. This paper highlights the history, applications, design, laboratory technology development and highly detailed simulation results of each control system.
Small Satellites↗
Harmonizing Multi-Disciplinary Data for Applied Research: A Comprehensive Analysis of GES DISC Datasets through NLP and TF-IDF Techniques
Data centers distribute data encompassing multiple disciplines, making it necessary to evaluate dataset applicability to applied research. Typically, these datasets are generated by specialized science teams and consist of single-discipline data, such as atmospheric temperature, pressure, and precipitation, leading to unique dataset formats and access services. However, in applied research, the utilization of datasets from multiple disciplines is commonly necessary. The increasing availability of research literature citing Earth Science datasets presents an opportunity to analyze the usage of datasets in multi-disciplinary research. This study proposes a novel approach wherein research publications citing datasets archived at the GES DISC (Goddard Earth Sciences Data and Information Services Center) are collected, and each publication is associated with specific research topics through the application of Natural Language Processing (NLP), using the Term Frequency Inverse Document Frequency (TF-IDF) technique on the publication titles and abstracts. Through this analysis, we gain insights into the distribution of dataset disciplines as they are being used in various applied research areas. This knowledge is essential for the development of dataset tools and services tailored to effectively support applied research studies, as it enhances a data center's comprehension of how datasets from multiple disciplines are integrated into research endeavors.
Infometrics↗
Turbulence of electrostatic electron cyclotron harmonic waves observed by Ogo 5.
Analysis of VLF emissions that have been observed near 3/2, 5/2, and 7/2 f sub H by Ogo 5 in the magnetosphere (f sub H is the electron cyclotron frequency) in the light of the mechanism used for the diffuse plasma resonance f sub Dn observed by Alouette 2 and Isis 1. The VLF emission is considered to be generated by nonlinear coupling mechanisms in certain portions of the observation as the f sub Dn is enhanced by its association with nonlinear wave-particle interaction of the electrostatic electron cyclotron harmonic wave, including the instability due to the nonlinear inverse Landau damping mechanism in the turbulence. The difference between the two observations is in the excitation mechanism of the turbulence; the turbulence in the plasma trough detected by Ogo 5 is due to natural origins, whereas the ionospheric topside sounder makes the plasma wave turbulence artificially by submitting strong stimulation pulses. Electron density values in the plasma trough are deduced by applying the f sub Dn-f sub N/f sub H relationship obtained from the Alouette 2 experiment as well as by applying the condition for the wave-particle nonlinear interactions. The electron density values reveal good agreement with the ion density values observed simultaneously by the highly sensitive ion mass spectrometer.
Oya, H.↗
Zonal harmonic model of Saturn's magnetic field from Voyager 1 and 2 observations
An analysis of the magnetic field of Saturn is presented which takes into account both the Voyager 1 and 2 vector magnetic field observations. The analysis is based on the traditional spherical harmonic expansion of a scale potential to derive the magnetic field within 8 Saturn radii. A third-order zonal harmonic model fitted to Voyager 1 and 2 observations is found to be capable of predicting the magnetic field characteristics at one encounter based on those observed at another, unlike models including dipole and quadrupole terms only. The third-order model is noted to lead to significantly enhanced polar surface field intensities with respect to dipole models, and probably represents the axisymmetric part of a complex dynamo field.
Connerney, J. E. P.↗
Bayesian Treatment of Prospective LISA Parameter Estimation for Massive Black Hole Mergers
A full understanding of LISA (Laser Interferometer Space Antenna)'s science capability will require accurate models of incident waveform signals and the instrumental response. While Fisher matrix analysis is useful for some estimates, a full Bayesian treatment is needed for important cases at the limit of LISA's capability. We will apply fast analysis algorithms enabling accurate treatment with EOB (effective-one-body) waveforms and the full-featured LISA response to study the significance of higher spherical harmonics and mergers in LISA analysis.
Baker, John G.↗
A deformation analysis of flat flexible gear and its equation of original curved surfaces
The equation of the original curved surface of end harmonic gearing is determined by displacement analysis of flat flexible gear. The displacement analysis is also used to calculate the strength and rigidity of the gear. The latter is regarded as a circular plate with two concentrated loads, since its torsional rigidity is much larger than its bending rigidity. Small-deflection theory of thin plates is used to solve for the displacement of any point in the middle plane of the gear. New expressions are given for radial and tangential displacements of the middle plane under asymmetrical loading. A digital computer is used to obtain numerical values for the displacements.
Yunwen, S.↗
Winter bulge and diurnal variations in hydrogen inferred from AE-C composition measurements
The atomic hydrogen distribution at 250 km during December 1974 solstice was inferred, considering charge exchange equilibrium, from Atmosphere Explorer-C measurements of n(H(+)), n(O(+) and N(O). An empirical model, derived from the observations by least suqare analysis in terms of spherical harmonics, has the following characteristics: (1) n(H) increases by as much as a factor of two between the summer and winter hemispheres, (2) the n(H) diurnal variation is largest at the equator and (3) the diurnal variation is larger in the winter hemisphere than in the summer. Similar analysis of the gas temperature derived from n(N2) measurements reveals that all n(H) and Tg spherical harmonic coefficients are anticorrelated. Both the diurnal and latitudinal (annual) n(H) and Tg amplitudes are in substantial agreement with the zero flux condition, in which exospheric flow dominates the hydrogen distribution. The observed diurnal phase lag of n(H) with respect to Tg is about one hour, agreeing with theory.
Brinton, H. C.↗