Search NASA⌕ Search

SEARCH · Search NASA

Results for “Linear approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Observations of low-energy ions in the wake of a magnetospheric satellite

Measurements of low-energy ions made by the retarding ion mass spectrometer (RIMS) onboard the Dynamics Explorer 1 (DE 1) satellite are used to study some aspects of 'body-plasma interactions' in the terrestrial plasmasphere. Preliminary results are presented, yielding the degree of H+ and He+ ion depletion in the wake of the satellite in terms of specific and average ion Mach numbers, average ion mass, body size normalized to ionic Debye length, and body potential normalized to ion thermal energy. Some results from the RIMS measurements are compared with relevant results from the Explorer 31 and the Atmosphere Explorer C ionospheric satellites. Wake depletion is found to vary approximately linearly for small bodies (R-sub-Di less than about 12) and exponentially for large bodies (R-sub-Di greater than 50).

Samir, U.↗

Fixed lag smoothers for carrier phase and frequency tracking

The application of fixed lag smoothing algorithms are presented for the problem of estimation of the phase and frequency of a sinusoidal carrier received in the presence of process noise and additive observation noise. A suboptimal structure consists of a phase-locked loop (PLL) followed by a post loop correction to the phase and frequency estimates. When the PLL is operating under a high signal-to-noise ratio, the phase detector is approximately linear, and the smoother equations then correspond to the optimal linear equations for an equivalent linear signal model. The performance of such a smoother can be predicted by the linear filtering theory. However, if the PLL is operating near the threshold region of the signal to noise ratio, the phase detector cannot be assumed to be linear. Then the actual performance of the smoother can significantly differ from that predicted by linear filtering theory. Both the theoretical and simulated performance of such smoothers derived on the basis of various models for the phase of frequency processes are presented.

Kumar, R.↗

Simulation of double layers in a model auroral circuit with nonlinear impedance

A reduced circuit description of the U-shaped potential structure of a discrete auroral arc, consisting of the flank transmission line plus parallel-electric-field region, is used to provide the boundary condition for one-dimensional simulations of the double-layer evolution. The model yields asymptotic scalings of the double-layer potential, as a function of an anomalous transport coefficient alpha and of the perpendicular length scale l(a) of the arc. The arc potential phi(DL) scales approximately linearly with alpha, and for alpha fixed phi (DL) about l(a) to the z power. Using parameters appropriate to the auroral zone acceleration region, potentials of phi (DPL) 10 kV scale to projected ionospheric dimensions of about 1 km, with power flows of the order of magnitude of substorm dissipation rates.

Smith, R. A.↗

Active suppression of an 'apparent shock induced instability'

A control law was designed, using constrained optimization techniques, to suppress an apparent shock induced instability of a sweptback, aeroelastic wing with supercritical airfoil sections. The controller design was based on an approximate linear plant representation obtained using forced response data from a previous entry in the Langley Transonic Dynamics tunnel. During a second tunnel entry, it was found that there was not an instability in the uncontrolled case but there was a region of very low damping (high dynamic response) near a Mach number of 0.92. Controller performance was obtained during the test in near real-time and revealed that the controller attenuated the open-loop response and provided a small but significant amount of damping over a Mach number range from M = 0.70 to M = 0.92.

Adams, William M., Jr.↗

The silicate component of Martian dust

Absorption features in telescopic reflectance spectra of Mars obtained during 1978, and absorption features in Mariner 7 and Mariner 9 spectra, are analyzed which are assigned to structural hydroxyl within a strongly hydrogen-bonded acidic material suggested to be a silicate. Deduced fundamentals indicate that the Si-O(b)-Si bond angle may be approximately linear, and that the estimated Si-O(b) bridge length may be about 1.61 A. Viking compositional data indicate that Mg(2+), rather than Ca(2+) may be the dominant cation in the Martian material. The results suggest that the silicate component of the dust may be an incipient hydrolysis product of olivine-rich ultramafic or mafic material, involving a process that resulted in minimum loss of mobile cations and that maintained the high O/Si ratio of the starting material.

Huguenin, R. L.↗

Exosat observations of 4U/MXB 1636-53 - On the relation between the amount of accreted fuel and the strength of an X-ray burst

During Exosat observations of 4U/MXB 1636-53 in August 1985, three bursts were observed in 6 h and 24 bursts in 79 h of uninterrupted observation. The burst times, burst fluences, peak burst fluxes, burst rise times, decay times, burst intervals, mean persistent fluxes, and the product of the latter two are listed, analyzed, and discussed. The implications of the results for thermonuclear flash models are examined. A model which fits the data well involves bursts which suffer from nuclear energy losses due to stable hydrogen burning between bursts. Thus, the percentage of 'lost' energy increases with increasing burst intervals. For individual bursts, however, there are significant deviations from the approximate linear relationship.

Lewin, W. H. G.↗

Minimum weight design of rectangular and tapered helicopter rotor blades with frequency constraints

The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to autorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.

Chattopadhyay, Aditi↗

Optimum filters and smoothers design for carrier phase and frequency tracking

The report presents the application of fixed lag smoothing algorithms to the problem of estimation of the phase and frequency of a sinusoidal carrier received in the presence of process noise and additive observation noise. A suboptimal structure consists of a phase-locked loop (PLL) followed by post-loop correction to the phase and frequency estimates. When the PLL is operating under high signal-to-noise ratio, the phase detector is approximately linear, and the smoother equations then correspond to the optimal linear equations for an equivalent linear signal model. The performance of such a smoother can be predicted by linear filtering theory. However, if the PLL is operating near the threshold region of the signal-to-noise ratio, the phase detector cannot be assumed to be linear. Then the actual performance of the smoother can significantly differ from that predicted by linear theory. In this report we present both the theoretical and simulated performance of such smoothers derived on the basis of various models for the phase and frequency processes.

Kumar, Rajendra↗

An experimental and theoretical study of the ice accretion process during artificial and natural icing conditions

Real-time measurements of ice growth during artificial and natural icing conditions were conducted using an ultrasonic pulse-echo technique. This technique allows ice thickness to be measured with an accuracy of + or - 0.5 mm; in addition, the ultrasonic signal characteristics may be used to detect the presence of liquid on the ice surface and hence discern wet and dry ice growth behavior. Ice growth was measured on the stagnation line of a cylinder exposed to artificial icing conditions in the NASA Lewis Icing Research Tunnel (IRT), and similarly for a cylinder exposed in flight to natural icing conditions. Ice thickness was observed to increase approximately linearly with exposure time during the initial icing period. The ice accretion rate was found to vary with cloud temperature during wet ice growth, and liquid runback from the stagnation region was inferred. A steady-state energy balance model for the icing surface was used to compare heat transfer characteristics for IRT and natural icing conditions. Ultrasonic measurements of wet and dry ice growth observed in the IRT and in flight were compared with icing regimes predicted by a series of heat transfer coefficients. The heat transfer magnitude was generally inferred to be higher for the IRT than for the natural icing conditions encountered in flight. An apparent variation in the heat transfer magnitude was also observed for flights conducted through different natural icing-cloud formations.

Kirby, Mark S.↗

Minimum weight design of rotorcraft blades with multiple frequency and stress constraints

Minimum weight designs of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies are studied. Constraints are imposed on the minimum value of the blade autorotational inertia to ensure sufficient rotary inertia to autorotate in case of engine failure and on stresses to guard against structural failure due to blade centrifugal forces. Design variables include blade taper ratio, dimensions of the box beam located inside the airfoil and magnitudes of nonstructural weights. The program CAMRAD is used for the blade modal analysis; the program CONMIN is used for the optimization. A linear approximation involving Taylor series expansion is used to reduce the analysis effort. The procedure contains a sensitivity analysis consisting of analytical derivatives for objective function and constraints on autorotational inertia and stresses. Central finite difference derivatives are used for frequency constraints. Optimal designs are obtained for both rectangular and tapered blades. Using this method, it is possible to design a rotor blade with reduced weight, when compared to a baseline blade, while satisfying all the imposed design requirements.

Chattopadhyay, Aditi↗

Calibration of high-temperature, fiber-optic, microbend, pressure transducers

The microbend pressure transducer was evaluated on the basis of a series of specified tests to determine the pressure, temperature, overpressure, and vibration response. The response was found to be approximately linear with a pressure in the range of -690 to + 690 kPa. The transducer exhibited high sensitivity to diaphragm deflection and rapid response to pressure changes and was insensitive to vibration for frequencies of 50 to 2500 Hz. The microbend transducer test data showed acceptable sensitivity and stability as a function of temperature and pressure to be used as the basis for a compensatable transducer.

Berthold, J. W.↗

New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Wen, John T.↗

Response to soil moisture of spectral indexes derived from bidirectional reflectance in Thematic Mapper wavebands

Laboratory reflectance measurements of 10 soils were used to determine the relationship between soil moisture and three spectral indices: the TM5/7 ratio and the Wetness(R) and Brightness(R) features of the reflectance factor TM Tasseled Cap transformation. Response of the indices to dry mass water percentage was approximately linear for individual soils, except for Wetness(R) and Brightness(R) at high moisture content. Soil differences in the slopes of the Wetness(R)- and Brightness(R)-moisture content relationships were almost entirely eliminated by expressing water content as the percentage of water retained at 0.1 bar (10 kPa) tension (relative water content). The resultant soil lines were offset from one another by the differences in dry soil index value. Slope of the TM5/7 response was not completely normalized by expressing moisture status as relative water content, because slope appeared to vary with dry soil ratio value. Sensitivity to the effects of illumination angle was negligible for the TM5/7 ratio, somewhat greater for Wetness(R) and greatest for Brightness(R).

Musick, H. Brad↗

Minimum weight design of rectangular and tapered helicopter rotor blades with frequency constraints

The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to aurorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.

Chattopadhyay, Aditi↗

Dynamic-Range Compression For Infrared Imagery

Photorefractive crystals covering detectors prevent saturation. To make full use of information in image, desirable to compress dynamic range of input intensity to within region of approximately linear response of detector. Dynamic-range compression exhibited by measurements of attenuation in photorefractive GaAs. Effective dynamic-range-compressor plate, film, or coating reduces apparent contrast of scene imaged on detector plane to within dynamic range of detectors; original image contrast or intensity data recovered subsequently in electronic image processing because range-compression function and inverse known.

Cheng, Li-Jen↗

The near-infrared polarization and color of Comet Halley: What can we learn about the grains

The near infrared polarization and JHK colors of light scattered by dust grains in comet Halley were measured over a wide range in phase angle and heliocentric distance. Colors were redder than solar with no statistically significant variation with phase angle, heliocentric distance, or pre- and post-perihelion. This suggests that the grain population did not change drastically over time and that the data may be combined and modeled. However, short term variations in visible polarization and dust albedo were seen in Halley. Also, near infrared colors became systematically bluer after the observations were completed. The near infrared colors of Halley fall in the range of those of other comets. The near infrared polarization is similar to the visible polarization of Halley and other comets in showing a negative branch at small phase angles and an approximately linear rise toward positive values at larger phase angles. Mie theory calculations and a size distribution based on spacecraft data were used to model the near infrared polarization and color of comet Halley. Numerous lines of evidence point to the presence of dark, absorbing, probably carbonaceous materials in comets.

Brooke, Timothy Y.↗

Ignition characteristics of the iron-based alloy UNS S66286 in pressurized oxygen

The development of ignition and combustion in pressurized oxygen atmospheres was studied for the iron based alloy UNS S66286. Ignition of the alloy was achieved by heating the top surface of a cylindrical specimen with a continuous-wave CO2 laser. Two heating procedures were used. In the first, laser power was adjusted to maintain an approximately linear increase in surface temperature. In the second, laser power was periodically increased until autoheating (self-heating) was established. It was found that the alloy would autoheat to destruction from temperatures below the solidus temperature. In addition endothermic events occurred as the alloy was heated, many at reproducible temperatures. Many endothermic events occurred prior to abrupt increases in surface temperature and appeared to accelerate the rate of increase in specimen temperature to rates greater than what would be expected from increased temperature alone. It is suggested that the source of these endotherms may increase the oxidation rate of the alloy. Ignition parameters are defined and the temperatures at which these parameters occur are given for the oxygen pressure range of 1.72 to 13.8 MPa (25 to 2000 psia).

Bransford, James W.↗

Simple robust control laws for robot manipulators. Part 2: Adaptive case

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

Bayard, D. S.↗