Spherical harmonic analyses for the spheroidal earth, ii
Spherical harmonic analysis of earth magnetic field
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Evaluation and Analysis of F-16XL Wind Tunnel Data From Static and Dynamic Tests
A series of wind tunnel tests were conducted in the NASA Langley Research Center as part of an ongoing effort to develop and test mathematical models for aircraft rigid-body aerodynamics in nonlinear unsteady flight regimes. Analysis of measurement accuracy, especially for nonlinear dynamic systems that may exhibit complicated behaviors, is an essential component of this ongoing effort. In this report, tools for harmonic analysis of dynamic data and assessing measurement accuracy are presented. A linear aerodynamic model is assumed that is appropriate for conventional forced-oscillation experiments, although more general models can be used with these tools. Application of the tools to experimental data is demonstrated and results indicate the levels of uncertainty in output measurements that can arise from experimental setup, calibration procedures, mechanical limitations, and input errors.
Kim, Sungwan↗
Evaluation and Analysis of F-16XL Wind Tunnel Data from Dynamic Tests
A series of wind tunnel tests were conducted in the NASA Langley Research Center as part of an ongoing effort to develop and test mathematical models for aircraft rigid-body aerodynamics in nonlinear unsteady flight regimes. Analysis of measurement accuracy, especially for nonlinear dynamic systems that may exhibit complicated behaviors, is an essential component of this ongoing effort. In this paper, tools for harmonic analysis of dynamic data and assessing measurement accuracy are presented. A linear aerodynamic model is assumed that is appropriate for conventional forced-oscillation experiments, although more general models can be used with these tools. Application of the tools to experimental data is demonstrated and results indicate the levels of uncertainty in output measurements that can arise from experimental setup, calibration procedures, mechanical limitations, and input errors.
Kim, Sungwan↗
Seasonal and interannual variations in total ozone revealed by the Nimbus-4 backscattered ultraviolet experiment
The first two years of Backscattered Ultraviolet (BUV) ozone data from the Nimbus-4 spacecraft were reprocessed. The seasonal variations of total ozone for the period April 1970 to April 1972 are described using daily zonal means to 10 deg latitude zones and a time-latitude cross section. In addition, the BUV data are compared with analyzed Dobson data and with IRIS data also obtained from the Nimbus-4 spacecraft. A harmonic analysis was performed on the daily zonal means. Amplitudes, days of peaks, and percentage of variance were computed for annual and semi-annual waves and for higher harmonics of an annual period for the two years. Asymmetries are found in the annual waves in the two hemispheres, with a subtle interannual difference which may be due to changes in the general circulation. A significant semi-annual component is detected in the tropics for the first year, which appears to result from influences of the annual waves in the two hemispheres.
Hilsenrath, E.↗
Seasonal variations of total ozone revealed by the Nimbus-4 BUV data set
Backscattered ultraviolet (BUV) data from the Nimbus-4 spacecraft for the period 1970-1977 have been processed to a refined level. The seasonal and interannual variations of total ozone are examined on a global scale, using daily zonal means of 10 deg latitude bands and a time-latitude cross section. A harmonic analysis was performed on the daily zonal means and the amplitude, days of peak ozone values, and percentage of variance were computed for the annual, semiannual and higer harmonics for several years and each year. A clear quasi-biennial oscillation (QBO) was revealed from the tropics to midlatitudes after removing the mean annual wave. Asymmetries in the annual wave in the two hemispheres found earlier for the period 1970-1972 persist through the entire observation period. Interannual variations appear to be the result of the QBO of ozone from low to midlatitudes. Asymmetries in the QBO amplitude phase, and period were also detected in the two hemispheres.
Hilsenrath, E.↗
High resolution mapping of the magnetic field of the solar corona
The mapping of the current-free magnetic field of the solar corona and the reliability of the spherical harmonic analysis of the photospheric magnetic field pattern are improved by data with much greater dynamic range and spatial resolution than previously available and a new algorithm which permits spherical harmonic expansion to a much higher value of the principal index. Coronal field maps can be drawn for local regions, for just the open field lines, and for various spatial resolutions on a global scale.
Altschuler, M. D.↗
Elementary Theoretical Forms for the Spatial Power Spectrum of Earth's Crustal Magnetic Field
The magnetic field produced by magnetization in Earth's crust and lithosphere can be distinguished from the field produced by electric currents in Earth's core because the spatial magnetic power spectrum of the crustal field differs from that of the core field. Theoretical forms for the spectrum of the crustal field are derived by treating each magnetic domain in the crust as the point source of a dipole field. The geologic null-hypothesis that such moments are uncorrelated is used to obtain the magnetic spectrum expected from a randomly magnetized, or unstructured, spherical crust of negligible thickness. This simplest spectral form is modified to allow for uniform crustal thickness, ellipsoidality, and the polarization of domains by an periodically reversing, geocentric axial dipole field from Earth's core. Such spectra are intended to describe the background crustal field. Magnetic anomalies due to correlated magnetization within coherent geologic structures may well be superimposed upon this background; yet representing each such anomaly with a single point dipole may lead to similar spectral forms. Results from attempts to fit these forms to observational spectra, determined via spherical harmonic analysis of MAGSAT data, are summarized in terms of amplitude, source depth, and misfit. Each theoretical spectrum reduces to a source factor multiplied by the usual exponential function of spherical harmonic degree n due to geometric attenuation with attitude above the source layer. The source factors always vary with n and are approximately proportional to n(exp 3) for degrees 12 through 120. The theoretical spectra are therefore not directly proportional to an exponential function of spherical harmonic degree n. There is no radius at which these spectra are flat, level, or otherwise independent of n.
Voorhies, C.↗
Rapid correlation analysis in a group of motions and homogeneous scale transforms of the plane (M(2)xR sub +)
A method is proposed for picking out a given image, in a plane, irrespective of translations, rotations, and homogeneous scale transforms of the plane. The correlation integral is calculated, using the method of abstract harmonic analysis. In this case, and also for groups of translations, it is possible to carry out the calculations using the rapid Fourier transform. The latter fact makes it possible to substantially reduce the number of computer operations for calculating the correlation integral, as compared with direct methods.
Tkhabisimov, D. K.↗
Global electromagnetic induction in the moon and planets
Experiments and analyses concerning electromagnetic induction in the moon and other extraterrestrial bodies are summarized. The theory of classical electromagnetic induction in a sphere is first considered, and this treatment is extended to the case of the moon, where poloidal eddy-current response has been found experimentally to dominate other induction modes. Analysis of lunar poloidal induction yields lunar internal electrical conductivity and temperature profiles. Two poloidal-induction analytical techniques are discussed: a transient-response method applied to time-series magnetometer data, and a harmonic-analysis method applied to data numerically Fourier-transformed to the frequency domain, with emphasis on the former technique. Attention is given to complicating effects of the solar wind interaction with both induced poloidal fields and remanent steady fields. The static magnetization field induction mode is described, from which are calculated bulk magnetic permeability profiles. Magnetic field measurements obtained from the moon and from fly-bys of Venus and Mars are studied to determine the feasibility of extending theoretical and experimental induction techniques to other bodies in the solar system.
Dyal, P.↗
Magnetospheric and ionospheric signals in magnetic observatory monthly means: Electrical conductivity of the deep mantle
First differences of magnetic observatory monthly means for 1963-1982 were analyzed using techniques of spherical harmonics analysis and power spectral analysis. The external source signal is shown to be primarily zonal in geomagnetic coordinates. Prominent peaks are present in the power spectrum at frequencies of 1.0 cycle/yr and 2.0 cycles/yr. The annual signal is largest on the degree 2 external zonal spherical harmonic, while the semiannual signal is largest on the degree 1 and degree 3 external zonal spherical harmonics. The presence of the semiannual signal on odd-degree spherical harmonics and of the annual signal on even-degree spherical harmonics was predicted from symmetry considerations and the annual cycle of solar inclination. These signals are all modulated by the sunspot frequency and its harmonics. The degree 1 term is believed to be due mainly to magnetopause and ring currents while the degree 2 and degree 3 terms are believed to be due mainly to ionospheric currents. The degree 1 external zonal harmonic has a continuous spectrum in addition to the semiannual spectral peak. A corresponding degree 1 internal term is due to electromagnetic induction. The degree 1 continuous spectrum is useful for study of the electrical conductivity of the deep mantle. A global geomagnetic response function consistent with a mantle conductivity of about 10 S/m at the core-mantle boundary has been derived.
Mcleod, Malcolm G.↗
Analysis of Wind Tunnel Lateral Oscillatory Data of the F-16XL Aircraft
Static and dynamic wind tunnel tests were performed on an 18% scale model of the F-16XL aircraft. These tests were performed over a wide range of angles of attack and sideslip with oscillation amplitudes from 5 deg. to 30 deg. and reduced frequencies from 0.073 to 0.269. Harmonic analysis was used to estimate Fourier coefficients and in-phase and out-of-phase components. For frequency dependent data from rolling oscillations, a two-step regression method was used to obtain unsteady models (indicial functions), and derivatives due to sideslip angle, roll rate and yaw rate from in-phase and out-of-phase components. Frequency dependence was found for angles of attack between 20 deg. and 50 deg. Reduced values of coefficient of determination and increased values of fit error were found for angles of attack between 35 deg. and 45 deg. An attempt to estimate model parameters from yaw oscillations failed, probably due to the low number of test cases at different frequencies.
Klein, Vladislav↗
Electromagnetic deep-probing (100-1000 kms) of the Earth's interior from artificial satellites: Constraints on the regional emplacement of crustal resources
A spherical harmonic analysis program is being tested which takes magnetic data in universal time from a set of arbitrarily space observatories and calculates a value for the instantaneous magnetic field at any point on the globe. The calculation is done as a least mean-squares value fit to a set of spherical harmonics up to any desired order. The program accepts as a set of input the orbit position of a satellite coordinates it with ground-based magnetic data for a given time. The output is a predicted time series for the magnetic field on the Earth's surface at the (r, theta) position directly under the hypothetically orbiting satellite for the duration of the time period of the input data set. By tracking the surface magnetic field beneath the satellite, narrow-band averages crosspowers between the spatially coordinated satellite and the ground-based data sets are computed. These crosspowers are used to calculate field transfer coefficients with minimum noise distortion. The application of this technique to calculating the vector response function W is discussed.
Hermance, J. F.↗
Tidal Prediction
Tides are the most predictable of oceanographic phenomena, due both to the simplicity and predictability of the astronomical forcing and to the near linearity of the ocean's dynamical response. In the classical and simplest scenario, tidal prediction is based on harmonic analysis of past measurements at a fixed location. Limits to predictability arise because isolated astronomical spectral lines are broadened into "cusps" of incoherent energy, for example through interactions with non-tidal flows. Tidal prediction at locations without past measurements has historically been a major challenge, but, owing to near-global observations of modern satellite altimeters, the empirical harmonic approach now yields reasonably accurate predictions throughout most of the open ocean. Advances in numerical modeling and data assimilation allow these predictions to be refined (especially in shallow seas where observations remain insufficient to directly constrain tidal wave structure) and extended to include tidal currents. We review recent progress in the development of global and regional-scale tidal prediction capabilities, summarize accuracy of available charts, and briefly consider outstanding issues. Satellite altimetry has also helped unravel the global tidal energy budget and has clarified the role of internal tides as a sink of tidal energy. We summarize these results, and then turn to the challenging problem of predicting internal tides. To the extent that low modes remain coherent with the surface tide, elevations can be directly mapped. We review current efforts in this direction, which are already producing charts with predictive capability. However, internal tides (especially higher modes) interact much more strongly with lower-frequency ocean flows, so a significant fraction of this tidal signal is intermittent and incoherent. We close with a brief review of ongoing efforts to model global tides in combination with wind-forced ocean motions.
Harmonic Constants↗
Conical Euler simulation and active suppression of delta wing rocking motion
A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.
Lee, Elizabeth M.↗
Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies
The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest
Modeling↗
Analysis of Wind Tunnel Longitudinal Static and Oscillatory Data of the F-16XL Aircraft
Static and oscillatory wind tunnel data are presented for a 10-percent-scale model of an F-16XL aircraft. Static data include the effect of angle of attack, sideslip angle, and control surface deflections on aerodynamic coefficients. Dynamic data from small-amplitude oscillatory tests are presented at nominal values of angle of attack between 20 and 60 degrees. Model oscillations were performed at five frequencies from 0.6 to 2.9 Hz and one amplitude of 5 degrees. A simple harmonic analysis of the oscillatory data provided Fourier coefficients associated with the in-phase and out-of-phase components of the aerodynamic coefficients. A strong dependence of the oscillatory data on frequency led to the development of models with unsteady terms in the form of indicial functions. Two models expressing the variation of the in-phase and out-of-phase components with angle of attack and frequency were proposed and their parameters estimated from measured data.
Klein, Vladislav↗
WRATS Integrated Data Acquisition System
The Wing and Rotor Aeroelastic Test System (WRATS) data acquisition system (DAS) is a 64-channel data acquisition display and analysis system specifically designed for use with the WRATS 1/5-scale V-22 tiltrotor model of the Bell Osprey. It is the primary data acquisition system for experimental aeroelastic testing of the WRATS model for the purpose of characterizing the aeromechanical and aeroelastic stability of prototype tiltrotor configurations. The WRATS DAS was also used during aeroelastic testing of Bell Helicopter Textron s Quad-Tiltrotor (QTR) design concept, a test which received international attention. The LabVIEW-based design is portable and capable of powering and conditioning over 64 channels of dynamic data at sampling rates up to 1,000 Hz. The system includes a 60-second circular data archive, an integrated model swashplate excitation system, a moving block damping application for calculation of whirl flutter mode subcritical damping, a loads and safety monitor, a pilot-control console display, data analysis capabilities, and instrumentation calibration functions. Three networked computers running custom-designed LabVIEW software acquire data through National Instruments data acquisition hardware. The aeroelastic model (see figure) was tested with the DAS at two facilities at NASA Langley, the Transonic Dynamics Tunnel (TDT) and the Rotorcraft Hover Test Facility (RHTF). Because of the need for seamless transition between testing at these facilities, DAS is portable. The software is capable of harmonic analysis of periodic time history data, Fast Fourier Transform calculations, power spectral density calculations, and on-line calibration of test instrumentation. DAS has a circular buffer archive to ensure critical data is not lost in event of model failure/incident, as well as a sample-and-hold capability for phase-correct time history data.
Piatak, David J.↗
Engineering studies related to geodetic and oceanographic remote sensing using short pulse techniques
For the Skylab S-193 radar altimeter, data processing flow charts and identification of calibration requirements and problem areas for defined S-193 altimeter experiments are presented. An analysis and simulation of the relationship between one particular S-193 measurement and the parameter of interest for determining the sea surface scattering cross-section are considered. For the GEOS-C radar altimeter, results are presented for system analyses pertaining to signal-to-noise ratio, pulse compression threshold behavior, altimeter measurement variance characteristics, desirability of onboard averaging, tracker bandwidth considerations, and statistical character of the altimeter data in relation to harmonic analysis properties of the geodetic signal.
Miller, L. S.↗