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The angular dependence of the interaction between two rigid linear rotors is considered, and one of the two expansions in current use is shown to be inappropriate. Interpolation of tabulated radial interactions is also discussed, and numerical tests are presented which demonstrate the accuracy of Lagrange and spline algorithms as a function of the spacing between points.
Finite-element computer program enables analysis of distortions and stresses occurring in components having relative interference. Program restricts itself to simple elements and axisymmetric loading situations. External inertial and thermal loads may be applied in addition to forces arising from interference conditions.
The essential part of numerical solutions of partial differential equations is the representation of gradients and integrals by, respectively, differences between points and summations over points. In order for such numerical representations to be accurate, it is necessary that these points be more closely spaced in regions of large gradients. The need for accurate representation is particularly acute near body surfaces, since the boundary conditions are generally the most influential part of a partial differential equation solution. This is especially true of viscous solutions at high Reynolds number, where very large gradients occur in the boundary layer.
The influence of molecular transport is included in the computation by treating viscous and thermal diffusion terms in the governing partial differential equations as correction terms in the method of characteristics scheme. The development of a production type computer program is reported which is capable of calculating the flow field in a variety of axisymmetric mixed-compression aircraft inlets. The results agreed well with those produced by the two-dimensional method characteristics when axisymmetric flow fields are computed. For three-dimensional flow fields, the results agree well with experimental data except in regions of high viscous interaction and boundary layer removal.
The reported analysis is based on the factored IOS T-matrix. It is shown that line shape measurements may be used over a range of temperatures to evaluate inelastic scattering cross sections. Basic factorization or parameterization relations are derived by considering the wavefunction equations. The parameterization of cross sections is considered, taking into account the differential scattering amplitude and cross section, integral cross sections, phenomenological cross sections for general relaxation processes, and viscosity and diffusion cross sections. Thermal averages and rates are discussed, giving attention to integral cross sections and rates, and general phenomenological cross sections. The results of computational studies are also presented.
Using altimeter data from a single pass, orbital fiting of these data is investigated. The stability problems of this special kind of short are method as well as the problem in the case of a mean Keplerian ellipse are discussed in detail. It is shown that short periodic perturbations can influence the size of the eccentricity of the satellite orbit computed from these data. In this way the desired result, the corrections of d zeta to the geoidal undulations, may be falsified.
A group of 12 highly trained athletes and a group of 12untrained students were subjected to passive changes of position on a tilt table and positive accelerations in a centrifuge. During a 20 min tilt, including two additional respiratory maneuvers, the number of faints and average cardiovascular responses did not differ significantly between the groups. During linear increase of acceleration, the average blackout level was almost identical in both groups. Statistically significant coefficients of product-moment correlation for various relations were obtained. The coefficient of multiple determination computed for the dependence of acceleration tolerance on heart-eye distance and systolic blood pressure at rest allows the explanation of almost 50% of the variation of acceleration tolerance. The maximum oxygen uptake showed the expected significant correlation to the heart rate at rest, but not the acceleration tolerance, or to the cardiovascular responses to tilting.
The implementation of the approximate factorization algorithm and its ability to efficiently and accurately describe transonic flow about an NACA 64A010 airfoil section is examined. The approximate factorization algorithm is developed from the nondimensional, conservative, vectorized Navier-Stokes equations expressed in curvilinear coordinates. Equations of state and transport coefficient relations appropriate to atmospheric air are appended to close the system of partial differential equations. An algebraic turbulence model is also incorporated into the equation set. This algorithm was verified by investigating the flow about an NACA 64A010 airfoil at 0, 2, and 3.5 deg angle of attack for free-stream conditions of 2,000,000 Reynolds number and 0.8 Mach number. Overall results were in good qualitative agreement with wind tunnel data sets. However, while nondimensional times of six were attained, numerical difficulties prevented any case from reaching a true steady state.
An unusual application of the method proposed by Asher (1958) for structural dynamic and modal testing is discussed. Asher's method has the capability, using the admittance matrix and multiple-shaker sinusoidal excitation, of separating structural modes having indefinitely close natural frequencies. The present application uses Asher's method in conjunction with a modern Fourier analyzer system but eliminates the necessity of exciting the test structure simultaneously with several shakers. Evaluation of this approach with numerically simulated data demonstrated its effectiveness; the parameters of two modes having almost identical natural frequencies were accurately identified. Laboratory evaluation of this approach was inconclusive because of poor experimental input data.
A method for constructing a direct functional relation between the computational and physical domains such that boundaries in the computational domain map into boundaries in the physical domain is presented. This method which is called the 'two-boundary technique' is based on generating functions that represent two disconnected boundaries in the physical domain and an independent function which connects one boundary with another to generate grids. The suggested connecting functions are simple linear and cubic parametric polynomials with parameters based on position and derivatives at the disconnected boundaries. The boundaries can be defined by analytical, approximate, and tension spline functions; the grid density in specified regions is controlled by embedding contraction functions in either the boundary representation or the connecting function.
A method of estimating the values of the parameters in the models describing the positions, widths, and intensities of the lines in rotation-vibration bands of gases, without the need for line by line analysis, is described. To illustrate the technique, portions of the 1-0 bands of HCl and CO have been analyzed. The values of up to 27 parameters, their standard deviations, and the correlations between the parameters required to describe the spectra have been obtained.
The hyperbolic scheme is used to efficiently generate smoothly varying grids with good step size control near the body. Although only two dimensional applications are presented, the basic concepts are shown to extend to three dimensions.
It is demonstrated by analyses and by numerical illustrations that any arbitrarily prescribed contour, open or closed, can be mapped conformally onto a simple contour, such as a unit circle, using any arbitrarily prescribed distribution of scale factor of transformation. This flexibility of selecting a scale factor distribution on the contour is not in violation of the well-known Riemann's uniqueness theory for conformal mapping.
Energy distribution of the component stars of the Algol type semidetached binaries were studied by combining IUE low dispersion spectra with optical scans made with the same resolution. In most cases the flux distributions are matched by Kuruz model atmospheres with normal solar composition. Deviations from normal atmospheres which indicate a higher level of activity and interaction in the binaries are examined. Eclipse observations in U Cep and V356 Sgr reveal emission lines of the W serpentis type.
A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.
A modified form of the Lepping - Argentiero single spacecraft, shock normal determination procedure is presented. The modified method incorporates a simple predictor-corrector algorithm which allows a faster convergence rate and the use of average values of the parameters for the starting vector.
A procedure is examined whereby the acoustic model parameters, natural frequencies and mode shapes, in the cavities of transportation vehicles are determined experimentally. The acoustic model shapes are described in terms of the particle motion. The acoustic modal analysis procedure is tailored to existing minicomputer based spectral analysis systems.
The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.