Search NASA⌕ Search

SEARCH · Search NASA

Results for “Linear”

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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Red and photographic infrared linear combinations for monitoring vegetation

The relationships between various linear combinations of red and photographic infrared radiances and vegetation parameters are investigated. In situ spectrometers are used to measure the relationships between linear combinations of red and IR radiances, their ratios and square roots, and biomass, leaf water content and chlorophyll content of a grass canopy in June, September and October. Regression analysis shows red-IR combinations to be more significant than green-red combinations. The IR/red ratio, the square root of the IR/red ratio, the vegetation index (IR-red difference divided by their sum) and the transformed vegetation index (the square root of the vegetation index + 0.5) are found to be sensitive to the amount of photosynthetically active vegetation. The accumulation of dead vegetation over the year is found to have a linearizing effect on the various vegetation measures.

Tucker, C. J.↗
NASA NTRS1979

Acceleration of linear and logarithmic convergence

Eleven different methods for accelerating convergence of sequences and series have been tested and compared on a wide range of test problems, including both linearly and logarithmically convergent series, monotone and alternating series. All but one of these methods are already in the literature, and they include both linear and nonlinear methods. The only methods found to accelerate convergence across the board were the u and v transforms of Levin and the theta algorithm of Brezinski. The paper gives detailed comparisons of all the tested methods on the basis of number of correct digits in the answer as a function of number of terms of the series used. A theorem of Germain-Bonne states that methods of a certain form which are exact on geometric series will accelerate linear convergence. The theorem applies to theta sub 2, and we have extended it to apply to Levin's transforms. No corresponding theorem is known for logarithmic convergence, but u, v, and theta are exact on certain large classes of logarithmic series, and all tested methods lacking this property failed to accelerate some logarithmically convergent series.

Smith, D. A.↗
NASA NTRS1979

Linearization of the boundary-layer equations of the minimum time-to-climb problem

Ardema (1974) has formally linearized the two-point boundary value problem arising from a general optimal control problem, and has reviewed the known stability properties of such a linear system. In the present paper, Ardema's results are applied to the minimum time-to-climb problem. The linearized zeroth-order boundary layer equations of the problem are derived and solved.

Ardema, M. D.↗
NASA NTRS1979

Application of supersonic linear theory and hypersonic impact methods to three nonslender hypersonic airplane concepts at Mach numbers from 1.10 to 2.86

Aerodynamic predictions from supersonic linear theory and hypersonic impact theory were compared with experimental data for three hypersonic research airplane concepts over a Mach number range from 1.10 to 2.86. The linear theory gave good lift prediction and fair to good pitching-moment prediction over the Mach number (M) range. The tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone/tangent-wedge method gave the least accurate prediction of lift and pitching moment. The zero-lift drag was overestimated, especially for M less than 2.0. The linear theory drag prediction was generally poor, with areas of good agreement only for M less than or equal to 1.2. For M more than or equal to 2.), the tangent-cone method predicted the zero-lift drag most accurately.

Pittman, J. L.↗
NASA NTRS1979

Linear feature selection with applications

Several ways in which feature selection techniques were used in LACIE are discussed. In all cases, the methods require some a priori information and assumptions; in most, the classification procedure (Bayes optimal) was chosen in advance. The transformations used for dimensionality reduction are linear, that is, the variables in feature space are always linear combinations of the original measurements. Several numerically tractable criteria developed for LACIE, which provide information about the probability of misclassification, are discussed. Recent results on linear feature selection techniques are included. Their use in LACIE is discussed. Related open questions are mentioned.

Decell, H. P., Jr.↗
NASA NTRS1978

Characterization of acoustic disturbances in linearly sheared flows

The equation describing the plane wave propagation, the stability, or the rectangular duct mode characteristics in a compressible inviscid linearly sheared parallel, but otherwise homogeneous flow, is shown to be reducible to Whittaker's equation. The resulting solutions, which are real, viewed as functions of two variables, depend on a parameter and an argument, the values of which have precise physical meanings depending on the problem. The exact solutions in terms of Whittaker functions are used to obtain a number of known results of plane wave propagation and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). The usefulness of the exact solutions is then discussed in connection with the problems of plane wave propagation and the stability of a finite thickness layer with a linear velocity profile.

Koutsoyannis, S. P.↗
NASA NTRS1980

Combined linear theory/impact theory method for analysis and design of high speed configurations

Pressure distributions on a wing body at Mach 4.63 are calculated. The combined theory is shown to give improved predictions over either linear theory or impact theory alone. The combined theory is also applied in the inverse design mode to calculate optimum camber slopes at Mach 4.63. Comparisons with optimum camber slopes obtained from unmodified linear theory show large differences. Analysis of the results indicate that the combined theory correctly predicts the effect of thickness on the loading distributions at high Mach numbers, and that finite thickness wings optimized at high Mach numbers using unmodified linear theory will not achieve the minimum drag characteristics for which they are designed.

Brooke, D.↗
NASA NTRS1979

Self-motion magnitude estimation during linear oscillation - Changes with head orientation and following fatigue

Two types of experiments concerning the estimated magnitude of self-motion during exposure to linear oscillation on a parallel swing are described in this paper. Experiment I examined changes in magnitude estimation as a function of variation of the subject's head orientation, and Experiments II a, II b, and II c assessed changes in magnitude estimation performance following exposure to sustained, 'intense' linear oscillation (fatigue-inducting stimulation). The subjects' performance was summarized employing Stevens' power law R = k x S to the nth, where R is perceived self-motion magnitude, k is a constant, S is amplitude of linear oscillation, and n is an exponent). The results of Experiment I indicated that the exponents, n, for the magnitude estimation functions varied with head orientation and were greatest when the head was oriented 135 deg off the vertical. In Experiments II a-c, the magnitude estimation function exponents were increased following fatigue. Both types of experiments suggest ways in which the vestibular system's contribution to a spatial orientation perceptual system may vary. This variability may be a contributing factor to the development of pilot/astronaut disorientation and may also be implicated in the occurrence of motion sickness.

Parker, D. E.↗
NASA NTRS1980

Characterization of acoustic disturbances in linearly sheared flows

Inviscid fluctuations in a compressible linearly sheared, but otherwise homogeneous, parallel two-dimensional flow are considered. The equation describing the plane wave propagation (PWP), the stability, or the rectangular duct mode characteristics in such a flow is shown to be reducible to Whittaker's equation. The exact solutions are applied to problems of PWP and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). With respect to the PWP it is shown that the shear layer possesses no resonances and no Brewster angles, while with regard to the problem of the stability of a finite thickness shear layer with a linear velocity profile, it is shown that the thin layer is unstable to long wavelength disturbances for all Mach numbers.

Koutsoyannis, S. P.↗
NASA NTRS1978

Numerical derivation of linear perturbation model from nonlinear real-time vehicle simulations - A means of validation and increased credibility

A numerical technique has been developed which generates linear perturbation models from nonlinear real-time aircraft vehicle simulations at Langley Research Center. The technique is very general and can be applied to simulations of any system described by nonlinear differential equations. Linear models about various trim conditions have been obtained from simulations of the Boeing 737, Northrop F5-E, Cessna 180, Sikorsky CH-54, and NASA/Army Rotor Systems Research Aircraft (RSRA). One use of the derived linear models is as a validation and verification tool for the nonlinear simulation.

Dieudonne, J. E.↗
NASA NTRS1980

Linear analysis of poststall gyrations

The poststall gyrations of a high-performance aircraft are investigated by approximating the equations of motion with a linear mathematical model. Equilibrium poststall spin conditions are determined, which are not limited to small angles or spin rates and are used as reference conditions about which the linear model is developed. As a result, complete coupling between lateral and longitudinal motions is retained. Three aerodynamic models are evaluated using this linear analysis. These models include pure rotary derivatives obtained from VPI&SU stability tunnel, forced-oscillation data obtained from NASA tests, and a combination of the two which separates the unsteady and pure rotary derivatives. Results indicate that this last model gives better predictions of aircraft motion during poststall gyrations at high angles of attack and large sideslip angles. Comparisons are made with full-scale flight test results.

Hreha, M. A.↗
NASA NTRS1982

Linear-Algebra Programs

The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

Lawson, C. L.↗
NASA NTRS1981

Linear and nonlinear aspects of snow albedo feedbacks in atmospheric models

Namias' hypothesis, that anomalous snowcover on the eastern side of the North American continent can generate an anomalous east coast low pressure system and an anomalous inland high pressure system, is consistent with the time-averaged anomalous response from a nonlinear, primitive equation channel model with an idealized, flat land-sea arrangement. An attempt to understand and describe this anomalous response in the nonlinear model as a linear response to anomalous diabatic heating was largely unsuccessful, primarily because the anomalous eddy fluxes were also important. This unsuccessful attempt to describe the nonlinear model's time averages by linear theory then motivated several comparisons between linear and nonlinear severely truncated quasi-geostrophic models. It was also found in these models that the eddy fluxes were extremely important for forcing or dissipating the stationary eddies.

Roads, J. O.↗
NASA NTRS1981

State-variable analysis of non-linear circuits with a desk computer

State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.

Cohen, E.↗
NASA NTRS1981

Linear polarization of light by two wheat canopies measured at many view angles

The linear polarization and reflection of visible light by wheat as a function of sun-view directions, crop development stage, and wavelength were examined. Two-hundred spectra were taken continuously in wave-lengths from 0.45 to 0.72 Micron in 33 view directions using an Exotech model 20C spectroradiometer six meters above two wheat canopies in the boot and fully headed maturity stages. The analysis results show that the amount of linearly polarized light from the wheat canopies is greatest in the blue spectral region and decreases gradually with increasing wavelength. The results also show that the linearly polarized light from the canopies is generally greatest in the azimuth direction of the Sun and tends toward zero as the view direction tends toward the direction of the hot spot or anti-solar point. It is demonstrated that the single, angle of incidence of sunlight on the leaf, explains almost all of the variation of the amount of polarized light with Sun-view direction.

Bauer, M. E.↗
NASA NTRS1982

Linear decentralized systems with special structure

Certain fundamental structures associated with linear systems having internal symmetries are outlined. It is shown that the theory of finite-dimensional algebras and their representations are closely related to such systems. It is also demonstrated that certain problems in the decentralized control of symmetric systems are equivalent to long-standing problems of linear systems theory. Even though the structure imposed arose in considering the problems of twin-lift helicopters, any large system composed of several identical intercoupled control systems can be modeled by a linear system that satisfies the constraints imposed. Internal symmetry can be exploited to yield new system-theoretic invariants and a better understanding of the way in which the underlying structure affects overall system performance.

Martin, C. F.↗
NASA NTRS1982

The use of linearized-aerodynamics and vortex-flow methods in aircraft design /invited paper/

This paper deals with selected linearized-aerodynamic and vortex-flow methods as applied to aircraft design problems at high subsonic speeds. In particular, the NASA Vortex Lattice and Modified Multhopp methods are the linearized techniques employed, and the suction analogy is used to provide estimates associated with vortex-flow aerodynamics. Many examples are given as to how researchers at Langley have used these methods to design the high subsonic, wing-mean-camber shapes for various configurations such as a supersonic transport, high-aspect-ratio transport, trapezoidal fighter wing, strake wing, tandem wing, joined wing, delta wing, and slender cranked wing. Many of these have been built, tested, and have had their data compared with theory. In addition, a technique for defining efficiently performing strake planforms for use in strake-wing combinations is discussed, and further improvements in wing design are outlined. The latter may be obtained by using higher-ordered linear panel methods as well as nonlinear-transonic methods.

Lamar, J. E.↗
NASA NTRS1982

On the linearity of the SWP camera of the international ultraviolet explorer /IUE/ - A correction algorithm

An algorithm is presented for correcting IUE low resolution spectral images obtained with the SWP camera for some of the non-linearity effects reported by Bohlin et al. (1980). The non-linearity problem, which affects SWP images processed at Goddard Space Flight Center in the period May 22, 1978 to July 7, 1979 and at VILSPA in the period June 14, 1978 to August 6, 1979, was essentially due to the use of an Intensity Transfer Function (ITF) that erroneously included a blank image in the 20 percent exposure level. The correction algorithm described here was adopted by the three IUE Agencies in November 1979 as being suitable for most IUE users. It has the advantages to be applicable to any kind of low resolution SWP spectra, to introduce errors which are usually less than the intrinsic photometric errors, and to be of simple application. The results obtained by applying the method to a representative set of spectra of both point and extended sources are reported. In addition, a new evaluation of linearity and reproducibility of the SWP spectral data is provided, based on the improved ITF.

Holm, A.↗