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NASA NTRS1993

Venus - Global gravity and topography

A new gravity field determination that has been produced combines both the Pioneer Venus Orbiter (PVO) and the Magellan Doppler radio data. Comparisonsbetween this estimate, a spherical harmonic model of degree and order 21, and previous models show that significant improvements have been made. Results are displayed as gravity contours overlaying a topographic map. We also calculate a new spherical harmonic model of topography based on Magellan altimetry, with PVO altimetry included where gaps exist in the Magellan data. This model is also of degree and order 21, so in conjunction with the gravity model, Bouguer and isostatic anomaly maps can be produced. These results are very consistent with previous results, but reveal more spatial resolution in the higher latitudes.

Mcnamee, J. B.↗

NASA NTRS1979

Unsteady pressures on a NACA 64A010 airfoil - Experimental and theoretical results

Transonic testing of an NACA 64A010 airfoil at the Ohio State University Aero-Astro Research Laboratory is described, and results of fixed angle of attack and pitch oscillation experiments are discussed. The operating range was Mach 0.20 to 1.07 with available total pressures of 140,000 N/m2 to 620,000 N/m2. The airfoil model was mounted on roller bearings installed in the solid sidewalls of the tunnel test section. The equipment included transducers to measure unsteady pressures, and static pressure taps obtaining steady-state data. The data gathered at Mach 0.8 gave an indication of the influence of the natural shock instability and shock-induced flow separation on the unsteady pressures, with the location of the peak disturbance level shifting forward in the comparison of 0 to 2 deg pitch angle data. The oscillating airfoil data is examined in terms of harmonic content and the in-phase and out-of-phase components. It is concluded that the experimental data has good qualitative comparison with methods accounting for shock interaction.

Davis, J. A.↗

NASA NTRS1994

Venus spherical harmonic gravity model to degree and order 60

The Magellan and Pioneer Venus Orbiter radiometric tracking data sets have been combined to produce a 60th degree and order spherical harmonic gravity field. The Magellan data include the high-precision X-band gravity tracking from September 1992 to May 1993 and post-aerobraking data up to January 5, 1994. Gravity models are presented from the application of Kaula's power rule for Venus and an alternative a priori method using surface accelerations. Results are given as vertical gravity acceleration at the reference surface, geoid, vertical Bouguer, and vertical isostatic maps with errors for the vertical gravity and geoid maps included. Correlation of the gravity with topography for the different models is also discussed.

Konopliv, Alex S.↗

NASA NTRS1985

The magnetic field at the core-mantle boundary

Models of the geomagnetic field are, in general, produced from a least-squares fit of the coefficients in a truncated spherical harmonic expansion to the available data. Downward continuation of such models to the core-mantle boundary (CMB) is an unstable process: the results are found to be critically dependent on the choice of truncation level. Modern techniques allow this fundamental difficulty to be circumvented. The method of stochastic inversion is applied to modeling the geomagnetic field. Prior information is introduced by requiring that the spectrum of spherical harmonic coefficients to fall-off in a particular manner which is consistent with the Ohmic heating in the core having a finite lower bound. This results in models with finite errors in the radial field at the CMB. Curves of zero radial field can then be determined and integrals of the radial field over patches on the CMB bounded by these null-flux curves calculated. With the assumption of negligible magnetic diffusion in the core; frozen-flux hypothesis, these integrals are time-invariant.

Bloxham, J.↗

NASA NTRS1987

Atlas of wide-field-of-view outgoing longwave radiation derived from Nimbus 6 Earth radiation budget data set, July 1975 to June 1978

An atlas of monthly mean outgoing longwave radiation global contour maps and associated spherical harmonic coefficients is presented. The atlas contains 36 months of continuous data from July 1975 to June 1978. The data were derived from the first Earth radiation budget experiment, which was flown on the Nimbus-6 Sun-synchronous satellite in 1975. Only the wide-field-of-view longwave measurements are cataloged in this atlas. The contour maps along with the associated sets of spherical harmonic coefficients form a valuable data set for studying different aspects of our changing climate over monthly, annual, and interannual scales in the time domain, and over regional, zonal, and global scales in the spatial domain.

Bess, T. Dale↗

NASA NTRS2011

Weekly Solutions of Time-Variable Gravity from 1993 to 2010

The GRACE mission has been highly successful in determining the time-variable gravity field of the Earth, producing monthly or even more frequent solutions (cf. 10-day) solutions using both spherical harmonics and mascons. However the GRACE time series only commences in 2002 - 2003 and a gap of several years may occur in the series before a GRACE follow-on satellite is launched. Satellites tracked by SLR and DORIS have also been used to study time variations in the Earth's gravitational field. These include (most recently) the solutions of Cox and Chao (2002), Cheng et al. (2004, 2007) and Lemoine et al. (2007). In this paper we discuss the development of a new time series of low degree spherical harmonic fields based on the available SLR, DORIS and GPS data. We develop simultaneous solutions for both the geocenter and the low degree harmonics up to 5x5. The solutions integrate data from SLR geodetic satellites (e.g., Lageos1, Lageos2, Starlette, Stella, Ajisai, Larets, Westpac), altimetry satellites (TOPEX/Poseidon, Envisat, Jason-1, Jason-2), and satellites tracked solely by DORIS (e.g. SPOT2-5). We discuss some pertinent aspects of the satellite-specific modeling. We include altimeter crossovers in the weekly solutions where feasible and time permits. The resulting geocenter time series is compared with geophysical model predictions and other independently-derived solutions. Over the GRACE time period the fidelity and consistency with the GRACE solutions are presented.

Lemoine, F.↗

NASA NTRS2003

Noninterference Systems Developed for Measuring and Monitoring Rotor Blade Vibrations

In the noninterference measurement of blade vibrations, a laser light beam is transmitted to the rotor blade tips through a single optical fiber, and the reflected light from the blade tips is collected by a receiving fiber-optic bundle and conducted to a photodetector. Transmitting and receiving fibers are integrated in an optical probe that is enclosed in a metal tube which also houses a miniature lens that focuses light on the blade tips. Vibratory blade amplitudes can be deduced from the measurement of the instantaneous time of arrival of the blades and the knowledge of the rotor speed. The in-house noninterference blade-vibration measurement system was developed in response to requirements to monitor blade vibrations in several tests where conventional strain gauges could not be installed or where there was a need to back up strain gauges should critical gauges fail during the test. These types of measurements are also performed in the aircraft engine industry using proprietary in-house technology. Two methods of measurement were developed for vibrations that are synchronous with a rotor shaft. One method requires only one sensor; however, it is necessary to continuously record the data while the rotor is being swept through the resonance. In the other method, typically four sensors are employed and the vibratory amplitude is deduced from the data by performing a least square fit to a harmonic function. This method does not require continuous recording of data through the resonance and, therefore, is better suited for monitoring. The single-probe method was tested in the Carl facility at the Wright- Patterson Air Force Base, and the multiple-probe method was tested in NASA Glenn Research Center's Spin Rig facility, which uses permanent magnets to excite synchronous vibrations. Representative results from this test are illustrated in the bar chart. Nonsynchronous vibrations were measured online during testing of the Quiet High Speed Fan in Glenn s 9- by 15-Foot Low-Speed Wind Tunnel. Three sensors were employed, enabling a reconstruction of the vibratory patterns at the leading and trailing edges at the tip span, as well as a determination of vibratory amplitudes for every blade.

Kurkov, Anatole P.↗

NASA NTRS2004

Temporal Characterization of Aircraft Noise Sources

Current aircraft source noise prediction tools yield time-independent frequency spectra as functions of directivity angle. Realistic evaluation and human assessment of aircraft fly-over noise require the temporal characteristics of the noise signature. The purpose of the current study is to analyze empirical data from broadband jet and tonal fan noise sources and to provide the temporal information required for prediction-based synthesis. Noise sources included a one-tenth-scale engine exhaust nozzle and a one-fifth scale scale turbofan engine. A methodology was developed to characterize the low frequency fluctuations employing the Short Time Fourier Transform in a MATLAB computing environment. It was shown that a trade-off is necessary between frequency and time resolution in the acoustic spectrogram. The procedure requires careful evaluation and selection of the data analysis parameters, including the data sampling frequency, Fourier Transform window size, associated time period and frequency resolution, and time period window overlap. Low frequency fluctuations were applied to the synthesis of broadband noise with the resulting records sounding virtually indistinguishable from the measured data in initial subjective evaluations. Amplitude fluctuations of blade passage frequency (BPF) harmonics were successfully characterized for conditions equivalent to take-off and approach. Data demonstrated that the fifth harmonic of the BPF varied more in frequency than the BPF itself and exhibited larger amplitude fluctuations over the duration of the time record. Frequency fluctuations were found to be not perceptible in the current characterization of tonal components.

Grosveld, Ferdinand W.↗

NASA NTRS1981

Report of MAGSAT project by Survey of India

Magsat data fo quiet days for the period 4.11.79, 17.11.79 to 24.11.79, which pertains to 44 passes, was screened to exclude the the period of exclude the period of maximum diurnal variation. The results of this screening process is a data set that has the effect, (or at least the major part of the effect), of the external field removed from it. Such a data set is the basis for further analysis which is in hand. The data set is now being reduced to horizontal plane. The mathematical techniques uses a finite harmonic series representation of the three dimensional data, combined with least squares approach for the solution of coefficients. A computer programme was developed to reduce satellite data to a common elevation.

Sawhney, J. L.↗

NASA NTRS1987

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.

Thobe, Glenn E.↗

NASA NTRS1975

A flight investigation of oscillating air forces: Equipment and technique

The equipment and techniques are described which are to be used in a project aimed at measuring oscillating air forces and dynamic aeroelastic response of a swept wing airplane at high subsonic speeds. Electro-hydraulic inertia type shakers installed in the wing tips will excite various elastic airplane modes while the related oscillating chordwise pressures at two spanwise wing stations and the wing mode shapes are recorded on magnetic tape. The data reduction technique, following the principle of a wattmeter harmonic analyzer employed by Bratt, Wight, and Tilly, utilizes magnetic tape and high speed electronic multipliers to record directly the real and imaginary components of oscillatory data signals relative to a simple harmonic reference signal. Through an extension of this technique an automatic flight-flutter-test data analyzer is suggested in which vector plots of mechanical admittance or impedance would be plotted during the flight test.

Reed, W. H., III↗

NASA NTRS1975

A determination of the lunar moment of inertia

An estimate of the second zonal coefficient of the spherical-harmonic representation of the lunar gravitational field has been obtained from an analysis of particular orbital-element variations of the Explorer 35 and Explorer 49 spacecraft. Data from these spacecraft were used because the orbital configurations resulted in variations of the longitude of periapse and node which were, to first order, dependent only on the even zonal harmonics. The data time span for each satellite was extremely long: 2138 days for Explorer 35 and 230 days for Explorer 49. The value of the harmonic coefficient is determined and used to obtain a value of the lunar moment of inertia.

Gapcynski, J. P.↗

NASA NTRS1993

Spectral study of Venus global topography and geoid from Magellan and PVO data

An analysis of newly available global harmonic models for topography and geoid on Venus was conducted. It was found that the power spectral density for Venus topography has a power law dependence on wave-number characteristic of Brown Noise, similar to what is found for the Earth. However, the Venus topography spectrum presents a rollover at lower degree (l = 3) than is observed for the Earth spectrum and has smaller amplitudes than that of the Earth's. The Venus geoid also obeys a power law relationship, at least for small values of l, but with a smaller slope and more power (for l greater than 3) than the Earth geoid.

Kucinskas, A. B.↗

NASA NTRS1976

The Jovian magnetosphere and magnetopause

The characteristics of the planet Jupiter's inner magnetosphere are examined, taking into account the Pioneer 10 and 11 magnetometer data. Data on the reliability of spherical harmonic expansions are presented in a table. The properties of the Jovian magnetosheath and magnetopause are described. Bow shock and magnetopause crossings were securely identified in plasma data and were usually identified in plasma data and were usually identifiable in the magnetometer data. Explanations for the large number of observed crossings are discussed. It is pointed out that in the case of the outer magnetosphere the observed field strength is nearly an order of magnitude larger than would be expected from Jupiter's dipole moment. The distinguishing characteristics of the magnetic field in the middle magnetosphere are also considered.

Davis, L., Jr.↗

NASA NTRS1994

On determining the spectrum of primordial inhomogeneity from the COBE DMR sky maps: Method

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the Galactic plane data from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications.

Gorski, Krzysztof M.↗

NASA NTRS1972

Apollo 15 laser altimeter, part D

The laser altimeter, consisting of a Q switched ruby laser, transmitting optics, counting timer, receiving optics, and a photomultiplier is described. Harmonic analysis of the mission data is also presented.

Robertson, F. L.↗

NASA NTRS1972

The geopotential at synchronous-orbit altitudes

The earth's gravity potential at synchronous orbit satellite altitudes is studied by analyzing the small effects of the resonant harmonic of gravity in tracking data from eight satellites during 21 distinct drift-free arcs. Results show: (1) absolute accuracy of second degree resonant geopotential coefficients better than three percent and coefficients through fourth degree better than 15 percent; (2) positions of equilibrium points for geostationary satellites better than 1/2 degree; and (3) accuracy in predicting orbits for 24-hour satellites better than 1 degree for periods greater than 2 years.

Wagner, C. A.↗

NASA NTRS1980

Far-field radiation of aft turbofan noise

Approximate expressions were developed for the noise radiation from the aft duct. The results of approximate aft radiation equation compare favorably to more exact Wiener-Hopf radiation results. Refraction as well as convective effects in the multiple flow streams is considered. The peak in the radiation pattern, which occurs nearly at engine sideline, is composed of modes with relatively large cut-off ratios. This implies that aft fan radiation will be inherently more difficult to suppress that the fan inlet noise. The theoretical multimodal radiation pattern is compared to experimental data for the first two harmonics of blade passage frequency for three full scale fans at two speeds. The agreement between theory and experiment is quite good.

Rice, E. J.↗