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NASA NTRS1986

Circuit transients due to negative bias arcs-II

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

Metz, R. N.↗
NASA NTRS2017

On High-Order Upwind Methods for Advection

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom 𝐾 per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2𝐾−1, which is higher than the expected order of 𝐾.

high-order methods↗
NASA NTRS1996

Measurements of Ocean Features With AIRSAR

Here we discuss an indirect approach for measuring ocean features from synthetic aperture radar (SAR) imagery. The approach is based on the refraction of swell that can be seen in the SAR imagery. Locally, swell refraction is due only to changes in bathymetry and surface current shear and it is easy to separate these two effects. It has been shown that linear energetic shears can be detected and measured from high resolution images of the ocean. A simple approach to measuring surface velocity and shear is to divide the imagery into smaller segments where the shear in each segment is approximately linear. The known linear algorithm would then be applied to each segment and the velocity/shear distribution can then be determined by assembling the segments with linear shear into an estimate of the actual shear/velocity distribution.

Sheres, David↗
NASA NTRS1988

Error assessments of widely-used orbit error approximations in satellite altimetry

From simulations, the orbit error can be assumed to be a slowly varying sine wave with a predominant wavelength comparable to the Earth's circumference. Thus, one can derive analytically the error committed in representing the orbit error along a segment of the satellite ground track by a bias; by a bias and tilt (linear approximation); or by a bias, tilt, and curvature (quadratic approximation). The result clearly agrees with what is obvious intuitively, i.e., (1) the fit is better with more parameters, and (2) as the length of the segment increases, the approximation gets worse. But more importantly, it provides a quantitative basis to evaluate the accuracy of past results and, in the future, to select the best approximation according to the required precision and the efficiency of various approximations.

Tai, Chang-Kou↗
NASA NTRS1993

Asteroid orbit determination using Bayesian probabilities

Bayesian a priori and a posteriori probability densities are employed to determine asteroid orbital elements from optical astrometric observations. For near-earth asteroids and Jupiter Trojans, the two-body approximation can yield grossly erroneous uncertainty estimates because of the scattering effect of close planetary encounters or prolonged weak planetary perturbations. For main-belt asteroids, the two-body approximation works efficiently, from which it is inferred that, although the ephemeris must be computed from an integrated orbit, only approximate partial derivatives are needed to attain sufficient accuracy in predicting ephemeris uncertainties. The semimajor and semiminor axes of the 2D 1-sigma sky-plane uncertainty ellipse during the years 1993 to 2005 in the many-body and two-body linear approximations are shown.

Muinonen, Karri↗
NASA NTRS1994

Fractionated martian atmosphere in the nakhlites?

Considerable evidence points to a martian origin of the shergottite-nakhlite-chassignite (SNC) meteorites. Noble gas isotopic compositions have been measured in most SNC meteorites. The Xe-129/Xe-132 vs. Kr-84/Xe-132 ratios in Chassigny, most shergottites, and lithology C of EETA 79001 define a linear array. This array is thought to be a mixing line between martian mantle and martian atmosphere. One of the SNC meteorites, Nakhla, contains a leachable component that has an elevated Xe-129/Xe-132 ratio relative to its Kr-84/Xe-132 ratio when compared to this approximately linear array. The leachable component probably consists in part of iddingsite, an alteration product produced by interaction of olivine with aqueous fluid at temperatures lower than 150 C. The elevated Xe isotopic ratio may represent a distinct reservoir in the martian crust or mantle. More plausibly, it is elementally fractionated martian atmosphere. Formation of sediments fractionates the noble gases in the correct direction. The range of sediment/atmosphere fractionation factors is consistent with the elevated Xe-129/Xe-132 component in Nakhla being contained in iddingsite, a low temperature weathering product. The crystallization age of Nakhla is 1.3 Ga. Its low-shock state suggests that it was ejected from near the surface of Mars. As liquid water is required for the formation of iddingsite, these observations provide further evidence for the near surface existence of aqueous fluids on Mars more recently than 1.3 Ga.

Drake, Michael J.↗
NASA NTRS2017

Comparison of EKF and UKF for Robotic Missions to Mars

The batched Kalman lter works well for a wide variety of orbit determination scenarios but requires linearized approximations to the underlying dynamical system. Furthermore, implementation depends on the computation of partial derivatives for all measurements and parameters used in the lter, a non-trivial task even when analytical derivations are possible. To address these limitations, many extensions and modi - cations to the linear Kalman lter have been proposed over the years since Kalman's initial publication. Our investigation examines two popular variants of the Kalman lter, namely the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), within the context of spacecraft missions to Mars. The EKF relies on the same mathematical basis as the classic version of the lter, however it sequentially updates the linearization as the ltering process is conducted. In contrast, the UKF is built upon the unscented transform which samples the nearby solution space and numerically propagates perturbed trajectories as part of the update / estimation process. We assess the performance of the ltering algorithms under a variety of mission scenarios with the goal of establishing decision criteria for which implementation to use under di ering circumstances.

Ely, Todd↗
NASA NTRS1993

Possible near-IR channels for remote sensing precipitable water vapor from geostationary satellite platforms

Remote sensing of troposheric water vapor profiles from current geostationary weather satellites is made using a few broadband infrared (IR) channels in the 6-13 micron region. Uncertainties greater than 20% exist in derived water vapor values just above the surface from the IR emission measurements. In this paper, we propose three near-IR channels, one within the 0.94-micron water vapor band absorption region, and the other two in nearby atmospheric windows, for remote sensing of precipitable water vapor over land areas, excluding lakes and rivers, during daytime from future geostationary satellite platforms. The physical principles are as follows. The reflectance of most surface targets varies approximately linearly with wavelength near 1 micron. The solar radiation on the sun-surface-sensor ray path is attenuated by atmospheric water vapor. The ratio of the radiance from the absorption channel with the radiances from the two window channels removes the surface reflectance effects and yields approximately the mean atmospheric water vapor transmittance of the absorption channel. The integrated water vapor amount from ground to space can be obtained with a precision of better than 5% from the mean transmittance. Because surface reflectances vary slowly with time, temporal variation of precipitable water vapor can be determined reliably. High spatial resolution, precipitable water vapor images are derived from spectral data collected by the Airborne Visable-Infrared Imaging Spectrometer, which measures solar radiation reflected by the surface in the 0.4-2.5 micron region in 10-nm channels and has a ground instantaneous field of view of 20 m from its platform on an ER-2 aircraft at 20 km. The proposed near-IR reflectance technique would complement the IR emission techniques for remote sensing of water vapor profiles from geostationary satellite platforms, especially in the boundary layer where most of the water vapor is located.

Gao, B.-C.↗
NASA NTRS1996

DCTune Perceptual Optimization of Compressed Dental X-Rays

In current dental practice, x-rays of completed dental work are often sent to the insurer for verification. It is faster and cheaper to transmit instead digital scans of the x-rays. Further economies result if the images are sent in compressed form. DCTune is a technology for optimizing DCT (digital communication technology) quantization matrices to yield maximum perceptual quality for a given bit-rate, or minimum bit-rate for a given perceptual quality. Perceptual optimization of DCT color quantization matrices. In addition, the technology provides a means of setting the perceptual quality of compressed imagery in a systematic way. The purpose of this research was, with respect to dental x-rays, 1) to verify the advantage of DCTune over standard JPEG (Joint Photographic Experts Group), 2) to verify the quality control feature of DCTune, and 3) to discover regularities in the optimized matrices of a set of images. We optimized matrices for a total of 20 images at two resolutions (150 and 300 dpi) and four bit-rates (0.25, 0.5, 0.75, 1.0 bits/pixel), and examined structural regularities in the resulting matrices. We also conducted psychophysical studies (1) to discover the DCTune quality level at which the images became 'visually lossless,' and (2) to rate the relative quality of DCTune and standard JPEG images at various bitrates. Results include: (1) At both resolutions, DCTune quality is a linear function of bit-rate. (2) DCTune quantization matrices for all images at all bitrates and resolutions are modeled well by an inverse Gaussian, with parameters of amplitude and width. (3) As bit-rate is varied, optimal values of both amplitude and width covary in an approximately linear fashion. (4) Both amplitude and width vary in systematic and orderly fashion with either bit-rate or DCTune quality; simple mathematical functions serve to describe these relationships. (5) In going from 150 to 300 dpi, amplitude parameters are substantially lower and widths larger at corresponding bit-rates or qualities. (6) Visually lossless compression occurs at a DCTune quality value of about 1. (7) At 0.25 bits/pixel, comparative ratings give DCTune a substantial advantage over standard JPEG. As visually lossless bit-rates are approached, this advantage of necessity diminishes. We have concluded that DCTune optimized quantization matrices provide better visual quality than standard JPEG. Meaningful quality levels may be specified by means of the DCTune metric. Optimized matrices are very similar across the class of dental x-rays, suggesting the possibility of a 'class-optimal' matrix. DCTune technology appears to provide some value in the context of compressed dental x-rays.

Watson, Andrew B.↗
NASA NTRS1977

Extreme ultraviolet spectrograph ATM experiment S082B

The extreme-ultraviolet double-dispersion photographic spectrograph for the Apollo Telescope Mount (ATM) experiment S082B on Skylab is described. Novel features were the use of a predisperser grating with a ruling whose spacing varied approximately linearly with distance for the purpose of increasing the instrument speed by reducing the astigmatism and a photoelectric servosystem to stabilize to 1 sec of arc the solar image at various near-limb positions. The 970-3940-A range was covered in two sections with effective resolving power of approximately 30,000 from 1100 A to 1970 A. The spatial resolution was 2 x 60 solar sec of arc. During the Skylab mission 6400 exposures were made with the instrument pointed by an astronaut at selected and recorded solar positions.

Bartoe, J.-D. F.↗
NASA NTRS1979

Comparison of inlet suppressor data with approximate theory based on cutoff ratio

Inlet suppressor far-field directivity suppression was quantitatively compared with that predicted using an approximate linear design and evaluation method based upon mode cutoff ratio. The experimental data was obtained using a series of cylindrical point-reacting inlet liners on a YF102 engine. The theoretical prediction program is based upon simplified sound propagation concepts derived from exact calculations. These indicate that all of the controlling phenomenon can be approximately correlated with mode cutoff ratio which itself is intimately related to the angles of propagation within the duct. The theory-data comparisons are intended to point out possible deficiencies in the approximate theory which may be corrected. After all theoretical refinements are made, then empirical corrections can be applied.

Rice, E. J.↗
NASA NTRS1994

Age as a diagnostic of stratospheric transport

Estimates of stratospheric age from observations of long-lived trace gases with increasing tropospheric concentrations invoke the implicit assumption that an air parcel has been transported intact from the tropopical tropopause. However, because of rapid and irreversible mixing in the stratosphere, a particular air parcel cannot be identified with one that left the troposphere at some prior time. The parcel contains a mix of air with a range of transit times, and the mean value over this range is the most appropriate definition of age. The measured tracer concentration is also a mean over the parcel, but its value depends both on the transit time distribution and the past history of the tracer in the troposphere. In principle, only if the tropospheric concentration is increasing linearly can the age be directly inferred. We illustrate these points by employing both a one-dimensional diffusive analog of stratospheric transport, and the general circulation model (GCM) of the Goddard Institute for Space Studies (GISS). Within the limits of the GCM, we estimate the time over which tropospheric tracer concentrations must be approximately linear in order to determine stratospheric age unambiguously; the concentration of an exponentially increasing tracer is a function only of age if the growth time constant is greater than about 7 years, which is true for all the chlorofluorocarbons. More rapid source variations (for example, the annual cycle in CO2) have no such direct relationship with age.

Hall, Timothy M.↗
NASA NTRS1986

Linearly polarized magnetic fluctuations at comet Giacobini-Zinner

The fully electromagnetic linear Vlasov dispersion equation for instabilities in a homogeneous, magnetized plasma is solved. Parameters appropriate to conditions observed during the ICE encounter with comet Giacobini-Zinner are used to study the polarization of electromagnetic instabilities driven by the relative streaming of two ion components. If the ion/ion relative drift is near the Alfven speed, the associated long-wavelength modes may be approximately linearly polarized at relatively small angles of propagation with respect to the magnetic field. The relatively inhomogeneous plasma background of the comet may impose such oblique propagation, so that this result provides an alternate explanation to the observations of linearly polarized waves near the comet.

Gary, S. Peter↗
NASA NTRS1973

Some optimal considerations in attitude control systems

The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.

Boland, J. S., III↗
NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗
NASA NTRS1996

Vibration Control in Turbomachinery Using Active Magnetic Journal Bearings

The effective use of active magnetic bearings for vibration control in turbomachinery depends on an understanding of the forces available from a magnetic bearing actuator. The purpose of this project was to characterize the forces as functions shaft position. Both numerical and experimental studies were done to determine the characteristics of the forces exerted on a stationary shaft by a magnetic bearing actuator. The numerical studies were based on finite element computations and included both linear and nonlinear magnetization functions. Measurements of the force versus position of a nonrotating shaft were made using two separate measurement rigs, one based on strain gage measurement of forces, the other based on deflections of a calibrated beam. The general trends of the measured principal forces agree with the predictions of the theory while the magnitudes of forces are somewhat smaller than those predicted. Other aspects of theory are not confirmed by the measurements. The measured forces in the normal direction are larger than those predicted by theory when the rotor has a normal eccentricity. Over the ranges of position examined, the data indicate an approximately linear relationship between the normal eccentricity of the shaft and the ratio of normal to principal force. The constant of proportionality seems to be larger at lower currents, but for all cases examined its value is between 0.14 and 0.17. The nonlinear theory predicts the existence of normal forces, but has not predicted such a large constant of proportionality for the ratio. The type of coupling illustrated by these measurements would not tend to cause whirl, because the coupling coefficients have the same sign, unlike the case of a fluid film bearing, where the normal stiffness coefficients often have opposite signs. They might, however, tend to cause other self-excited behavior. This possibility must be considered when designing magnetic bearings for flexible rotor applications, such as gas turbines and other turbomachinery.

Knight, Josiah D.↗
NASA NTRS2003

Mapping Soil pH Buffering Capacity of Selected Fields

Soil pH buffering capacity, since it varies spatially within crop production fields, may be used to define sampling zones to assess lime requirement, or for modeling changes in soil pH when acid forming fertilizers or manures are added to a field. Our objective was to develop a procedure to map this soil property. One hundred thirty six soil samples (0 to 15 cm depth) from three Georgia Coastal Plain fields were titrated with calcium hydroxide to characterize differences in pH buffering capacity of the soils. Since the relationship between soil pH and added calcium hydroxide was approximately linear for all samples up to pH 6.5, the slope values of these linear relationships for all soils were regressed on the organic C and clay contents of the 136 soil samples using multiple linear regression. The equation that fit the data best was b (slope of pH vs. lime added) = 0.00029 - 0.00003 * % clay + 0.00135 * % O/C, r(exp 2) = 0.68. This equation was applied within geographic information system (GIS) software to create maps of soil pH buffering capacity for the three fields. When the mapped values of the pH buffering capacity were compared with measured values for a total of 18 locations in the three fields, there was good general agreement. A regression of directly measured pH buffering capacities on mapped pH buffering capacities at the field locations for these samples gave an r(exp 2) of 0.88 with a slope of 1.04 for a group of soils that varied approximately tenfold in their pH buffering capacities.

Weaver, A. R.↗
NASA NTRS2013

Inclusion of Linearized Moist Physics in Nasa's Goddard Earth Observing System Data Assimilation Tools

Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa-Schubert (RAS) convection scheme has been developed and tested in NASA's Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture.

Convection↗