Search NASA⌕ Search

SEARCH · Search NASA

Results for “INDEPENDENT VARIABLE”

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
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Comments on the accuracy of Baker-Nunn observations

Many factors influence the accuracy with which the satellite positions may be derived from Baker-Nunn observations. Some of these factors are more important than others. In an accuracy study of satellite tracking methods there are invariably two distinct aspects to be investigated: the accuracy with which the satellite position can be referred to the reference system used - the stellar framework in the case of the optical observations, and the accuracy of the instant of observation. It is generally desirable to keep time as an independent variable so that any uncertainty in measuring the time of observation will be reflected in the positional accuracy.

Lambeck, K.↗
NASA NTRS1972

An evaluation of string theory for the prediction of dynamic tire properties using scale model aircraft tires

The string theory was evaluated for predicting lateral tire dynamic properties as obtained from scaled model tests. The experimental data and string theory predictions are in generally good agreement using lateral stiffness and relaxation length values obtained from the static or slowly rolling tire. The results indicate that lateral forces and self-aligning torques are linearly proportional to tire lateral stiffness and to the amplitude of either steer or lateral displacement. In addition, the results show that the ratio of input excitation frequency to road speed is the proper independent variable by which frequency should be measured.

Clark, S. K.↗
NASA NTRS1972

Development of equilibrium air computer programs suitable for numerical computation using time-dependent or shock-capturing methods

Computer programs were developed which compute the thermodynamic properties of equilibrium air for use in either the time-dependent or shock-capturing computational methods. For the time-dependent method, tne NASA-ARC RGAS computer program was modified to allow internal energy and density to be used as the independent variables. In addition, simplified-curve fits for p = p(e,rho), a = a(e,rho), and T = T(p,rho) were devised to reduce computer time. For the shock-capturing method a simplified curve fit for h = h(p,rho) was made. These approximate curve fits may be particularly useful when employed on advanced computers such as the Illiac 4 or the CDC Star since they avoid the cumbersome table-lookup feature of the RGAS program.

Tannehill, J. C.↗
NASA NTRS1971

Comments on the continuity of distribution functions obtained by superposition.

Assuming that Y is a nonnegative random variable independent of the differential process X(t), attention is given to the question of whether or not the superposition X(Y) can have a continuous probability distribution. If the process has continuous distributions, then the superposition is continuous if and only if P/Y = 0/ = 0. If the process has discontinuous distributions and no trend, then no superposition can have continuous distribution. If the process has discontinuous distributions and nonzero trend, then the superposition onto a random epoch has continuous distribution if and only if Y has continuous distribution.

Huff, B. W.↗
NASA NTRS1971

A systematic exposition of the conservation equations for blast waves.

In order to provide a rational background for the analysis of experimental observations of blast wave phenomena, the conservation equations governing their nonsteady flow field are formulated in a general manner, without the usual restrictions imposed by an equation of state, and with proper account taken, by means of source terms, of other effects which, besides the inertial terms that conventionally dominate these equations, can affect the flow. Taking advantage of the fact that a blast wave can be generally considered as a spatially one-dimensional flow field whose nonsteady behavior can be regarded, consequently, as a function of just two independent variables, two generalized blast wave coordinates are introduced, one associated with the front of the blast wave and the other with its flow field. The conservation equations are accordingly transformed into this coordinate system, acquiring thereby a comprehensive character, in that they refer then to any frame of reference, being applicable, in particular, to problems involving either space or time profiles of the gas-dynamic parameters in the Eulerian system, or time profiles in the Lagrangian system.

Oppenheim, A. K.↗
NASA NTRS1972

Correlation of irradiation data using activation fluences and irradiation temperature.

A new method of correlating radiation damage data is tested using actual measured data taken from the open literature. This method, the activation fluence method, was found to be as accurate as other contemporary models with which it was compared. The new method also has several advantages over the other methods. The method employs a new entity, the activation fluence (time-integrated specific activation rate), as the independent variables in a regression model. Temperature at which the irradiation takes place is also a variable. Although the method was tested for a specific type of damage (change in nil-ductility transition temperature for A302-B steel) it has no inherent restrictions and is limited only by the imagination of the user.

Lynch, J. H.↗
NASA NTRS1973

Highly loaded multi-stage fan drive turbine-cascade test program

Test results are presented for 19 cascades involving five plain and two tandem blade sections. High camber and/or negative reaction is associated with six of the sections. Exit Mach numbers range up to slightly above sonic. Cascade efficiency, exit flow angle and static pressure, and blade surface pressure data are reported with incidence angle, Mach number, solidity, and relative position of the tandem blades as independent variables.

Cherry, D. G.↗
NASA NTRS1973

Water quality parameter measurement using spectral signatures

Regression analysis is applied to the problem of measuring water quality parameters from remote sensing spectral signature data. The equations necessary to perform regression analysis are presented and methods of testing the strength and reliability of a regression are described. An efficient algorithm for selecting an optimal subset of the independent variables available for a regression is also presented.

White, P. E.↗
NASA NTRS1973

Research on the sonic boom problem. Part 1: Second-order solutions for the flow field around slender bodies in supersonic flow for sonic boom analysis

A second-order theory for supersonic flow past slender bodies is presented. Through the introduction of characteristic coordinates as independent variables and the expansion procedure proposed by Lin and Oswatitsch, a uniformly valid solution is obtained for the whole flow field in the axisymmetric case and for far field in the general three-dimensional case. For distances far from the body the theory is an extension of Whitham's first-order solution and for the domain close to the body it is a modification of Van Dyke's second-order solution in the axisymmetric case. From the theory useful formulas relating flow deflections to the Whitham F-function are derived, which permits one to determine the sonic boom strength from wind tunnel measurements fairly close to the body.

Landahl, M.↗
NASA NTRS1973

Hard cosmic X-ray sources.

A review of the observational status of X-ray sources detected in the 20 to 500 keV range is presented. Of the approximately 115 sources listed in the March 1972 edition of the UHURU 2-6 keV sky survey catalog, about 15 sources have been studied in hard X rays. Most of the data have been obtained from balloons, although the OSO-3, and more recently the OSO-7, have contributed. With the exception of CEN A, the SMC, and possibly M-87, all the sources detected at higher energies are galactic and heavily concentrated in the galactic plane. The Crab Nebula has been measured to about 500 keV in continuous emission and a component at the 33-msec pulsar period comprising about 20% of the total emission has been detected to 10 MeV. Objects such as SCO-1 and CYG-2 are characterized by an exponential spectrum, which varies over a 10-min time scale about a factor of two, and a flatter spectrum extending to above 40 keV which exhibits independent variability.

Peterson, L. E.↗
NASA NTRS1973

Multiple-beam satellite repeater tradeoffs applied to a multifunctional system.

This paper concerns satellite repeater tradeoffs for a multiple-beam, multiple-channel, multiple-connectivity satellite postulated to serve a diversity of domestic U.S. noncommercial requirements, with a substantial portion of the satellite power, weight, and bandwidth dedicated to video distribution and bradcast. The orders-of-magnitude of the requirements are given for the video plus high-rate data traffic category. The designs of two alternative baseline repeater configurations are presented, and estimates of their weight and their prime power consumption are given. These data are the basis for estimating the weight and power consumption of a range of alternative beam coverage, modulation, and channel capacity systems. These estimates are used to illustrate tradeoffs with different performance criteria as the independent variable: number of channels per beam and total number of beam-channels.

Kinal, G. V.↗
NASA NTRS1973

A preliminary sensitivity analysis of the coupled diffusion and chemistry model

The sensitivity of the coupled chemistry/diffusion model's outputs to a wide range of variation of the model's independent variables has been investigated. It is shown that the efficiency with which the now catalytic cycle destroys ambient O3 is extremely sensitive to the amount of NO emitted and to the relative rates of turbulent diffusion and chemical reactions. For representative conditions in the stratosphere, a tenfold variation of either the turbulence intensity or the reaction rate constant or the source strength can vary the efficiency from 1% to 50%. If the duration of Phase 3 is a significant fraction of the total residence time of the plume, then these efficiency variations can alter O3 depletion rates by more than a factor of two. These results, therefore, point toward those variables which must be accurately defined or measured if one is to adequately predict the effect of SST operations on the ambient inventory of O3 in the lower stratosphere.

Hilst, G. R.↗
NASA NTRS1974

Solution of an eigenvalue problem for the Laplace operator on a spherical surface

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Walden, H.↗
NASA NTRS1974

Information content of IRIS spectra

Spectra from the satellite instrument IRIS (infra red interferometer spectrometer) were examined to find the number of independent variables needed to describe these broadband high spectral resolution data. The radiated power in the atmospheric window from 771 to 981/cm was the first parameter chosen for fitting observed spectra. At succeeding levels of analysis the residual variability (observed spectrum - best fit spectrum) in an ensemble of observations was partioned into spectral eigenvectors. The eigenvector describing the largest fraction of this variability was examined for a strong spectral signature; the power in the corresponding spectral band was then used as the next fitting parameter. The measured power in nine spectral intervals, when inserted in the spectral fitting functions, was adequate to describe most spectra to within the noise level of IRIS. Considerations of relative signal strength and scales of atmospheric variability suggest a combination sounder (multichannel-broad field of view) scanner (window channel-small field of view) as an efficient observing instrument.

Price, J. C.↗
NASA NTRS1973

Aircraft Range Optimization Using Singular Perturbations

An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

Oconnor, Joseph Taffe↗
NASA NTRS1973

Applications of the Kustaanheimo-Stieffel transformation of the perturbed two-body problem

The Newtonian differential equations of motion for the two-body problem can be transformed into four linear harmonic-oscillator equations by simultaneously applying the regularization step dt/ds = r and the Kustaanheimo-Stieffel (KS) transformation. The regularization step changes the independent variable from time to a new variable s, and the KS transformation transforms the position and velocity vectors from Cartesian space into a four-dimensional space. A derivation of a uniform, regular solution for the perturbed two-body problem in the four-dimensional space is presented. The variation-of-parameters technique is used to develop expressions for the derivatives of ten elements (which are constants in the unperturbed motion) for the general case that includes both perturbations which can arise from a potential and perturbations which cannot be derived from a potential. This ten-element solution has mixed secular terms that degrade the long-term accuracy during numerical integration. Therefore, to eliminate these terms, the solution is modified by introducing two additional elements.

Bond, V. R.↗
NASA NTRS1974

Computer-assisted design in perceptual-motor skills research

A categorization was made of independent variables previously found to be potent in simple perceptual-motor tasks. A computer was then used to generate hypothetical factorial designs. These were evaluated in terms of literature trends and pragmatic criteria. Potential side-effects of machine-assisted research strategy were discussed.

Rogers, C. A., Jr.↗
NASA NTRS1975

Minimization search method for data inversion

Technique has been developed for determining values of selected subsets of independent variables in mathematical formulations. Required computation time increases with first power of the number of variables. This is in contrast with classical minimization methods for which computational time increases with third power of the number of variables.

Fymat, A. L.↗