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NASA NTRS1973

The development of accurate and efficient methods of numerical quadrature

Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.

Feagin, T.↗

NASA NTRS1972

The transmission of sonic boom signals into rooms through open windows.

This paper is the second of two companion papers. In the first paper, expressions for the acoustic field generated inside a room with an open window due to incoming transient or periodic signals have been presented. In this paper, the technique has been applied to the specific example of an N-wave type signal. Detailed mathematical analysis is followed by its approximate version and numerical computation. Results of controlled experiments, using simulated sonic booms, have been compared with theoretical predictions.

Vaidya, P. G.↗

NASA NTRS1974

Long-duration life tests of slip ring capsule assemblies for inertial guidance platforms

Eight slip ring capsules, each having 80 or 100 circuits, were operated for time periods ranging from 14,300 hours to 24,700 hours. The test mode simulated the motion of gimbal axes of the Saturn inertial guidance the platform in an organic free nitrogen environment. Computer-compiled noise data (approximately 45,000 recordings) were graphed as a function of test time and position within the capsules and as extreme probability distributions. Greater than ninety-nine percent of the noise measurements for the capsules with sufficient lubrication were less than 10 milliohms. Capsules with glass dielectrics did not perform significantly differently than those with filled epoxy dielectrics. The initial wear mode of prow formation was followed by rider wear. After 10 to the 8th power wipes, ring wear depth did not exceed the surface finish and the radial rider wear depth was less than 13 microns.

Cole, S. R.↗

NASA NTRS1973

Developing a technology base in planetary entry aerothermodynamics

The long-range objectives of the entry technology program are to insure that an adequate technology base for a great variety of mission options exists. Consideration has been given to the entry of vehicles into the atmospheres of all the planets with the exception of Pluto. The experimental facilities for the studies are discussed, giving attention to shock tubes, the planetary entry radiation facility, ballistic ranges, the expansion tube, and arc jet facilities. Flight experiments are considered along with computational analyses and engineering approximations.

Olstad, W. B.↗

NASA NTRS1973

Optimal control of a variable spin speed CMG system for space vehicles

Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

Liu, T. C.↗

NASA NTRS1974

The radiative effect of aerosols in the earth's atmosphere

A modified two-flux approximation is employed to compute the transfer of radiation in a finite, inhomogeneous, turbid atmosphere. A perturbation technique is developed to allow the treatment of nongray gaseous absorption with multiple scattering. The perturbation method, which employs a backscatter factor as a parameter, can be used with anisotropic particle scattering as well as Rayleigh scattering. This method is used to study the effect of aerosols on radiative solar heating and infrared cooling as well as the radiative-convective temperature distribution in the earth's atmosphere. It is found that the effect of aerosols in the infrared cannot be neglected; while in the visible, the effect can be of the same order as that due to absorption by water vapor. For a high surface albedo (greater than 0.30) heating of the earth-atmosphere system results due to the presence of aerosols. The aerosols also reduce the amount of convection needed to maintain a stable atmosphere. For the case of a dense haze a temperature inversion is found to exist close to the ground.

Wang, W.-C.↗

NASA NTRS1974

A comparison of numerical solutions of the advective equation

Second- and third-order finite-difference methods recently applied to problems in high-speed fluid flow are applied to the model advection equation cast in conservative form. The differencing methods considered use forward time differencing with both centered and preferential space differences employed in the predictor-corrector sequences. The free parameter required for stability in the third-order method is adjusted to cause the solution to be either minimum dispersive or minimum dissipative in nature. Results indicate that the third-order method using minimum dispersion is the most accurate method tested. Computer time requirements are approximately twice those needed for second-order techniques.

Anderson, D.↗

NASA NTRS1975

Numerical nonlinear inelastic analysis of stiffened shells of revolution. Volume 3: Engineer's program manual for STARS-2P digital computer program

Engineering programming information is presented for the STARS-2P (shell theory automated for rotational structures-2P (plasticity)) digital computer program, and FORTRAN 4 was used in writing the various subroutines. The execution of this program requires the use of thirteen temporary storage units. The program was initially written and debugged on the IBM 370-165 computer and converted to the UNIVAC 1108 computer, where it utilizes approximately 60,000 words of core. Only basic FORTRAN library routines are required by the program: sine, cosine, absolute value, and square root.

Svalbonas, V.↗

NASA NTRS1977

Spectral analysis of a high-velocity meteor

A spectrogram of a fast optical meteor was reduced and analyzed, and 60 features were identified in the spectrum. Air and ionized elements in this meteor radiate throughout the spectrum from 3000 A to 6800 A. A mass of 9 mg and an effective radiation temperature of approximately 5700 K were computed for the meteor. Weight ratios of Ca:Fe, and Mg:Fe, and Na:Fe were computed. A plasma particle velocity distribution for meteors was derived, and the average collision speed obtained from this distribution was compared with the relative collision speed of a Fe-N2 gas mixture at 5700 K.

Harvey, G. A.↗

NASA NTRS1977

Effects of stream-associated fluctuations upon the radial variation of average solar wind parameters

A numerical MHD model in both spherically symmetric time-dependent and corotating equatorial flow approximations is used to compute the effects of nonlinear fluctuations due to solar wind streams upon radial gradients of average solar wind parameters. Significant effects of correlations between fluctuations on the gradients of azimuthal magnetic field, radial velocity, density, and azimuthal velocity are found. It is found that nonlinear fluctuations are a significant effect in determining the radial gradients of the solar wind at distances as small as 0.2 AU; at distances greater than 1 AU, nonlinear fluctuations dominate the behavior of the radial gradients.

Goldstein, B. E.↗

NASA NTRS1980

The quasi-vortex-lattice method for wings with edge vortex separation

The aerodynamic characteristics of wings with leading-edge vortex separation were predicted using a method based on a flow model with free vortex elements which are allowed to merge into a concentrated core. The calculated pressure distribution is more accurate than that predicted by methods with discrete vortex filaments alone. In addition, the computer time is reduced approximately by half.

Pao, J. L.↗

NASA NTRS1980

Numerical simulation of supersonic inlets using a three-dimensional viscous flow analysis

A three dimensional fully viscous computer analysis was evaluated to determine its usefulness in the design of supersonic inlets. This procedure takes advantage of physical approximations to limit the high computer time and storage associated with complete Navier-Stokes solutions. Computed results are presented for a Mach 3.0 supersonic inlet with bleed and a Mach 7.4 hypersonic inlet. Good agreement was obtained between theory and data for both inlets. Results of a mesh sensitivity study are also shown.

Anderson, B. H.↗

NASA NTRS1980

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.

Bainum, P. M.↗

NASA NTRS1981

Kinetic theory of relativistic plasmas

The thermalization of particle kinetic motion by binary collisions is considered for a plasma with a Boltzmann constant-temperature product approximately equal to 10 to 100 times the product of the electron mass with the square of the speed of light. At this temperature, the principal mechanism for relaxation of electron motion is via radiationless electron-electron collisions (Moller scattering). Ions are nonrelativistic, but are energetic enough so that their Coulomb scattering can be treated in the Born approximation. Relaxation times are computed and Boltzmann-equation Fokker-Planck operators are derived for the various binary-collision processes. The expression for the rate of kinetic energy exchange between electron and ion gases is derived for the case where the gases are at different temperatures.

Gould, R. J.↗

NASA NTRS1981

Algorithm for fuel conservative horizontal capture trajectories

A real time algorithm for computing constant altitude fuel-conservative approach trajectories for aircraft is described. The characteristics of the trajectory computed were chosen to approximate the extremal trajectories obtained from the optimal control solution to the problem and showed a fuel difference of only 0.5 to 2 percent for the real time algorithm in favor of the extremals. The trajectories may start at any initial position, heading, and speed and end at any other final position, heading, and speed. They consist of straight lines and a series of circular arcs of varying radius to approximate constant bank-angle decelerating turns. Throttle control is maximum thrust, nominal thrust, or zero thrust. Bank-angle control is either zero or aproximately 30 deg.

Neuman, F.↗

NASA NTRS1981

Incorporating spatial context into statistical classification of multidimensional image data

Compound decision theory is employed to develop a general statistical model for classifying image data using spatial context. The classification algorithm developed from this model exploits the tendency of certain ground-cover classes to occur more frequently in some spatial contexts than in others. A key input to this contextural classifier is a quantitative characterization of this tendency: the context function. Several methods for estimating the context function are explored, and two complementary methods are recommended. The contextural classifier is shown to produce substantial improvements in classification accuracy compared to the accuracy produced by a non-contextural uniform-priors maximum likelihood classifier when these methods of estimating the context function are used. An approximate algorithm, which cuts computational requirements by over one-half, is presented. The search for an optimal implementation is furthered by an exploration of the relative merits of using spectral classes or information classes for classification and/or context function estimation.

Bauer, M. E.↗

NASA NTRS1982

Recent developments in thermal radiation system analyzer (Trasys)

Changes in the thermal radiation analyzer system (TRASYS) computer program are discussed. New capabilities were added while keeping intact the same data input structure. An overview of the program structure and general capabilities is given. Where appropriate, assessments are made of new features. The application of TRASYS peripheral programs and the importance they have in developing a totally integrated thermal analysis system are discussed. Form factor computations times were reduced approximately 40 percent, and the longer flux runs were reduced 50 percent when shadow tables were used.

Vogt, R. A.↗

NASA NTRS1983

Numerical methods for stiff systems of two-point boundary value problems

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Flaherty, J. E.↗