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NASA NTRS1991

An information theory of image gathering

Shannon's mathematical theory of communication is extended to image gathering. Expressions are obtained for the total information that is received with a single image-gathering channel and with parallel channels. It is concluded that the aliased signal components carry information even though these components interfere with the within-passband components in conventional image gathering and restoration, thereby degrading the fidelity and visual quality of the restored image. An examination of the expression for minimum mean-square-error, or Wiener-matrix, restoration from parallel image-gathering channels reveals a method for unscrambling the within-passband and aliased signal components to restore spatial frequencies beyond the sampling passband out to the spatial frequency response cutoff of the optical aperture.

Fales, Carl L.↗
NASA NTRS1991

Modeling of Jupiter's millimeter wave emission utilizing laboratory measurements of ammonia (NH3) opacity

The techniques used to make laboratory measurements of the millimeter wave opacity from gaseous ammonia under simulated Jovian conditions are described. The results are applied to a radiative transfer model, which is used to compute Jupiter's millimeter wavelength emission. The absorptivity of gaseous NH3 is measured to reduce one of the largest uncertainties in modeling Jupiter's millimeter wave emission. Several other millimeter wave opacity sources are examined. New expressions are given for computing the absorptivity of NH3, H2O, cloud condensates, and pressure-induced absorption. Jupiter's reliable millimeter wavelength observations are compared with synthetic emission spectra which utilize these new absorption expressions.

Joiner, Joanna↗
NASA NTRS1991

On the symbolic manipulation and code generation for elasto-plastic material matrices

A computerized procedure for symbolic manipulations and FORTRAN code generation of an elasto-plastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.

Chang, T. Y.↗
NASA NTRS1991

The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR.

Flanagan, M. J.↗
NASA NTRS1991

Space charge enhanced plasma gradient effects on satellite electric field measurements

It has been recognized that plasma gradients can cause error in magnetospheric electric field measurements made by double probes. Space charge enhanced Plasma Gradient Induced Error (PGIE) is discussed in general terms, presenting the results of a laboratory experiment designed to demonstrate this error, and deriving a simple expression that quantifies this error. Experimental conditions were not identical to magnetospheric conditions, although efforts were made to insure the relevant physics applied to both cases. The experimental data demonstrate some of the possible errors in electric field measurements made by strongly emitting probes due to space charge effects in the presence of plasma gradients. Probe errors in space and laboratory conditions are discussed, as well as experimental error. In the final section, theoretical aspects are examined and an expression is derived for the maximum steady state space charge enhanced PGIE taken by two identical current biased probes.

Diebold, Dan↗
NASA NTRS1992

High speed transport cruise drag

This report provides scaling laws for the cruise aerodynamics of high speed transport wings based on the results of Navier-Stokes computations. Expressions for the various drag components are found, together with the corresponding values (L/D)(sub m) for various values of the geometric parameter s/l which allow for simple optimization of the wing configurations with respect to the span. It is found that linear theory expressions can be used for this purpose provided the coefficients of these experiments for C(sub D) and (L/D)(sub m) are available using Navier-Stokes results.

Roberts, Leonard↗
NASA NTRS1992

Sensitivity analysis of dynamic aeroelastic responses

This paper summarizes ongoing research on the sensitivity analysis of dynamic aeroelastic response of wings. Two approaches are being used to express the unsteady aerodynamic loads: (1) the frequency-domain approach, and (2) the state-space approach. The frequency-domain approach is demonstrated on a three-dimensional box wing and the state-space domain approach is demonstrated on a simple two-dimensional sectional model. Three different methods are used to find the sensitivities: (1) a purely finite difference approach, (2) a semi-analytical approach in which an analytical expression is used for calculating the sensitivity of an eigenvalue of the complex valued aeroelastic matrix, however, the derivatives of the components of the matrix are obtained using finite difference, and (3) a semi-analytic approach that differs from (2) in the sense that the sensitivity of the aerodynamic matrix is now obtained analytically. A good agreement is seen between the three sets of results. For the two-dimensional sectional model the results for the sensitivities of the flutter speed with respect to the various parameters are obtained.

Kapania, Rakesh K.↗
NASA NTRS1992

Stiffness and strength tailoring in uniform space-filling truss structures

A deterministic procedure for tailoring the continuum stiffness and strength of uniform space-filling truss structures, through the appropriate selection of truss geometry and member sizes (flexural stiffness, axial stiffness, and length), is presented. The trusses considered herein are generated by uniform replication of a characteristic truss cell. The repeating cells are categorized by one of a set of possible geometric symmetry groups derived using crystallographic techniques. The elastic symmetry associated with each geometric symmetry group is identified to help select an appropriate truss geometry for a given application. Stiffness and strength tailoring of a given truss geometry is enabled through explicit expressions relating the continuum stiffnesses and failure stresses of the truss to the stiffnesses and failure loads of its members. These expressions are derived using an existing equivalent continuum analysis technique and a newly developed analytical failure theory for trusses. Several examples are presented to illustrate the application of these techniques and to demonstrate the usefulness of the information gained from this analysis.

Lake, Mark S.↗
NASA NTRS1992

Mechanically verified hardware implementing an 8-bit parallel IO Byzantine agreement processor

Consider a network of four processors that use the Oral Messages (Byzantine Generals) Algorithm of Pease, Shostak, and Lamport to achieve agreement in the presence of faults. Bevier and Young have published a functional description of a single processor that, when interconnected appropriately with three identical others, implements this network under the assumption that the four processors step in synchrony. By formalizing the original Pease, et al work, Bevier and Young mechanically proved that such a network achieves fault tolerance. We develop, formalize, and discuss a hardware design that has been mechanically proven to implement their processor. In particular, we formally define mapping functions from the abstract state space of the Bevier-Young processor to a concrete state space of a hardware module and state a theorem that expresses the claim that the hardware correctly implements the processor. We briefly discuss the Brock-Hunt Formal Hardware Description Language which permits designs both to be proved correct with the Boyer-Moore theorem prover and to be expressed in a commercially supported hardware description language for additional electrical analysis and layout. We briefly describe our implementation.

Moore, J. Strother↗
NASA NTRS1992

Effect of atmospheric extinction on laser rangefinder performance at 1.54 and 0.6 microns

Extinction of laser rangefinder (LRF) pulses by the atmosphere depends on the wavelength, weather conditions, and aerosol concentration along the optical path. In the IR, extinction is due to absorption by molecular constituents and scattering and absorption by aerosols. The total atmospheric extinction alpha(lambda) is the sum of the molecular and aerosol contributions, alpha(sub m)(lambda)and Alpha(sub a)(lambda). We present simple expressions for alpha(sub m)(lambda) and alpha(sub a)(lambda) for two LRF sources: Er:glass and CO2 which operate at 1.54 and 10.6 microns, respectively. The expressions are based on accepted models of atmospheric aerosols and molecular extinction and give an estimate of alpha(lambda) as a function of standard meteorological parameters, assuming horizontal beam propagation. Signal-to-noise ratios of LRF returns, measured from a reference target under different weather conditions are compared to predictions based on the estimate of alpha(lambda).

Hutt, D. L.↗
NASA NTRS1992

High-frequency techniques for RCS prediction of plate geometries

Given here are hard polarization diffraction coefficients for the special case of a wedge that is coated with a lossy dielectric on one face and is perfectly conducting on the other face. Expressions for plane-wave incidence, far-field observation; for cylindrical-wave incidence, far-field observation; and for plane-wave incidence, near-field observation are presented for regular diffractions. In addition, terms for surface-wave and surface-wave transition fields are presented. These expressions are derived from the Uniform Theory of Diffraction (UTD) coefficients for a generalized impedance wedge and are simplified for rapid calculation for the case of one perfectly conducting face. Results from a first-order model for a coated, rectangular plate are examined; and potential problems in extending this modeling approach to more complicated coated structures are identified.

Balanis, Constantine A.↗
NASA NTRS1991

Optimum data analysis procedures for Titan 4 and Space Shuttle payload acoustic measurements during lift-off

Analytical expressions have been derived to describe the mean square error in the estimation of the maximum rms value computed from a step-wise (or running) time average of a nonstationary random signal. These analytical expressions have been applied to the problem of selecting the optimum averaging times that will minimize the total mean square errors in estimates of the maximum sound pressure levels measured inside the Titan IV payload fairing (PLF) and the Space Shuttle payload bay (PLB) during lift-off. Based on evaluations of typical Titan IV and Space Shuttle launch data, it has been determined that the optimum averaging times for computing the maximum levels are (1) T (sub o) = 1.14 sec for the maximum overall level, and T(sub oi) = 4.88 f (sub i) (exp -0.2) sec for the maximum 1/3 octave band levels inside the Titan IV PLF, and (2) T (sub o) = 1.65 sec for the maximum overall level, and T (sub oi) = 7.10 f (sub i) (exp -0.2) sec for the maximum 1/3 octave band levels inside the Space Shuttle PLB, where f (sub i) is the 1/3 octave band center frequency. However, the results for both vehicles indicate that the total rms error in the maximum level estimates will be within 25 percent the minimum error for all averaging times within plus or minus 50 percent of the optimum averaging time, so a precise selection of the exact optimum averaging time is not critical. Based on these results, linear averaging times (T) are recommended for computing the maximum sound pressure level during lift-off.

Piersol, Allan G.↗
NASA NTRS1992

Ballistic limit regression analysis for Space Station Freedom meteoroid and space debris protection system

Relationships defining the ballistic limit of Space Station Freedom's (SSF) dual wall protection systems have been determined. These functions were regressed from empirical data found in Marshall Space Flight Center's (MSFC) Hypervelocity Impact Testing Summary (HITS) for the velocity range between three and seven kilometers per second. A stepwise linear least squares regression was used to determine the coefficients of several expressions that define a ballistic limit surface. Using statistical significance indicators and graphical comparisons to other limit curves, a final set of expressions is recommended for potential use in Probability of No Critical Flaw (PNCF) calculations for Space Station. The three equations listed below represent the mean curves for normal, 45 degree, and 65 degree obliquity ballistic limits, respectively, for a dual wall protection system consisting of a thin 6061-T6 aluminum bumper spaced 4.0 inches from a .125 inches thick 2219-T87 rear wall with multiple layer thermal insulation installed between the two walls. Normal obliquity is d(sub c) = 1.0514 v(exp 0.2983 t(sub 1)(exp 0.5228). Forty-five degree obliquity is d(sub c) = 0.8591 v(exp 0.0428) t(sub 1)(exp 0.2063). Sixty-five degree obliquity is d(sub c) = 0.2824 v(exp 0.1986) t(sub 1)(exp -0.3874). Plots of these curves are provided. A sensitivity study on the effects of using these new equations in the probability of no critical flaw analysis indicated a negligible increase in the performance of the dual wall protection system for SSF over the current baseline. The magnitude of the increase was 0.17 percent over 25 years on the MB-7 configuration run with the Bumper II program code.

Jolly, William H.↗
NASA NTRS1991

A constitutive relation for the viscous flow of an oriented fiber assembly

A constitutive relation for an equivalent, homogeneous fluid is developed for the anisotropic viscous flow of an oriented assembly of discontinuous fibers suspended in a viscous fluid. The anisotropic viscous compliance matrix can be expressed in terms of three constants by assuming the equivalent fluid to be incompressible and the microstructure to have axial symmetry (transversely isotropic). By means of a micromechanics analysis, the three terms of the constitutive relation are expressed in terms of the viscosity of the matrix fluid, the fiber aspect ratio, and the fiber volume fraction. A comparison of the viscosity terms reveals that the elongational viscosity in the fiber direction varies as the square of the fiber aspect ratio and a complex function of the fiber volume fraction. Furthermore, the ratio of the axial elongational viscosity to the transverse elongational viscosity and both axial and transverse shear viscosities was shown to be 10 exp 4 - 10 exp 6 for fiber aspect ratio of 100-1000, except at extreme values of the fiber volume fraction.

Pipes, R. B.↗
NASA NTRS1992

Optimization and analysis of large chemical kinetic mechanisms using the solution mapping method - Combustion of methane

A method of systematic optimization, solution mapping, as applied to a large-scale dynamic model is presented. The basis of the technique is parameterization of model responses in terms of model parameters by simple algebraic expressions. These expressions are obtained by computer experiments arranged in a factorial design. The developed parameterized responses are then used in a joint multiparameter multidata-set optimization. A brief review of the mathematical background of the technique is given. The concept of active parameters is discussed. The technique is applied to determine an optimum set of parameters for a methane combustion mechanism. Five independent responses - comprising ignition delay times, pre-ignition methyl radical concentration profiles, and laminar premixed flame velocities - were optimized with respect to thirteen reaction rate parameters. The numerical predictions of the optimized model are compared to those computed with several recent literature mechanisms. The utility of the solution mapping technique in situations where the optimum is not unique is also demonstrated.

Frenklach, Michael↗
NASA NTRS1992

Nonequilibrium algebraic turbulence modeling considerations for transonic airfoils and wings

The nonequilibrium algebraic turbulence model of Johnson and King has been applied successfully to both airfoils and wings. However, in wing applications a different expression for the outer 'equilibrium' eddy viscosity has been used because of apparent difficulties in determining the boundary-layer thickness. It is shown in this paper, that this expression does not give eddy viscosity levels for two-dimensional flows that are consistent with Clauser's correlation for equilibrium turbulent boundary layers. And as a consequence, results in inferior predictions when used in airfoil calculations. The objective of this paper is to develop a formulation applicable to wing flows which reduces to the proper form in the two-dimensional case. This necessitates, in part, finding a better way of estimating the boundary-layer thickness from the computed flowfield.

Johnson, D. A.↗
NASA NTRS1991

On optimal infinite impulse response edge detection filters

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Sarkar, Sudeep↗