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At least 1,189 records · Page 66

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NASA NTRS1977

Application of LANDSAT to the surveillance of lake eutrophication in the Great Lakes basin

The author has identified the following significant results. A step-by-step procedure for establishing and monitoring the trophic status of inland lakes with the use of LANDSAT data, surface sampling, laboratory analysis, and aerial observations were demonstrated. The biomass was related to chlorophyll-a concentrations, water clarity, and trophic state. A procedure was developed for using surface sampling, LANDSAT data, and linear regression equations to produce a color-coded image of large lakes showing the distribution and concentrations of water quality parameters, causing eutrophication as well as parameters which indicate its effects. Cover categories readily derived from LANDSAT were those for which loading rates were available and were known to have major effects on the quality and quantity of runoff and lake eutrophication. Urban, barren land, cropland, grassland, forest, wetlands, and water were included.

Rogers, R. H.↗

NASA NTRS1977

Production of a water quality map of Saginaw Bay by computer processing of LANDSAT-2 data

Surface truth and LANDSAT measurements collected July 31, 1975, for Saginaw Bay were used to demonstrate a technique for producing a color coded water quality map. On this map, color was used as a code to quantify five discrete ranges in the following water quality parameters: (1) temperature, (2) Secchi depth, (3) chloride, (4) conductivity, (5) total Kjeldahl nitrogen, (6) total phosphorous, (7)chlorophyll a, (8) total solids and (9) suspended solids. The LANDSAT and water quality relationship was established through the use of a set of linear regression equations where the water quality parameters are the dependent variables and LANDSAT measurements are the independent variables. Although the procedure is scene and surface truth dependent, it provides both a basis for extrapolating water quality parameters from point samples to unsampled areas and a synoptic view of water mass boundaries over the 3000 sq. km bay area made from one day's ship data that is superior, in many ways, to the traditional machine contoured maps made from three day's ship data.

Mckeon, J. B.↗

NASA NTRS1977

Boundary-value problem of configurations with compressible free vortex flow

A self-consistent version of the compressible boundary-value problem for configurations with leading-edge vortex separation is formulated, based on the assumption that the compressible flow field is controlled by the linearized potential equation. The stream surface boundary condition and the zero pressure jump condition of the compressible free vortex flows are analyzed; application of the Goethert rule permits the compressible nonlinear boundary-value problem for the subsonic flow domain to be transformed into an equivalent nonlinear incompressible problem. The compressibility corrections developed are used in numerical calculations of subsonic leading-edge vortex flows about planar wing geometries. The sample calculations, employing an inviscid flow model in which the wing and vortex sheets are represented by piecewise continuous quadratic doublet sheet distributions, are applicable to high subsonic Mach numbers.

Brune, G. W.↗

NASA NTRS1977

Unsteady flow in a supersonic cascade with strong in-passage shocks

Linearized theory is used to study the unsteady flow in a supersonic cascade with in-passage shock waves. We use the Wiener-Hopf technique to obtain a closed-form analytical solution for the supersonic region. To obtain a solution for the rotational flow in the subsonic region we must solve an infinite set of linear algebraic equations. The analysis shows that it is possible to correlate quantitatively the oscillatory shock motion with the Kutta condition at the trailing edges of the blades. This feature allows us to account for the effect of shock motion on the stability of the cascade. Unlike the theory for a completely supersonic flow, the present study predicts the occurrence of supersonic bending flutter. It therefore provides a possible explanation for the bending flutter that has recently been detected in aircraft-engine compressors at higher blade loadings.

Goldstein, M. E.↗

NASA NTRS1979

An analytical technique for predicting the characteristics of a flexible wing equipped with an active flutter-suppression system and comparison with wind-tunnel data

An analytical technique for predicting the performance of an active flutter-suppression system is presented. This technique is based on the use of an interpolating function to approximate the unsteady aerodynamics. The resulting equations are formulated in terms of linear, ordinary differential equations with constant coefficients. This technique is then applied to an aeroelastic model wing equipped with an active flutter-suppression system. Comparisons between wind-tunnel data and analysis are presented for the wing both with and without active flutter suppression. Results indicate that the wing flutter characteristics without flutter suppression can be predicted very well but that a more adequate model of wind-tunnel turbulence is required when the active flutter-suppression system is used.

Abel, I.↗

NASA NTRS1979

A two-dimensional thermal analysis of a new high-performance tubular solar collector

The first of two articles are presented which describe and analyze the thermal performance of a vacuum tube solar collector. The assumptions and mathematical modeling are presented. The problem is reduced to the formulation of two simultaneous linear differential equations characterizing the collector thermal behavior. After applying the boundary conditions, a general solution is obtained which is found similar to the general Hottel, Whillier and Bliss form but with a complex flow factor.

Lansing, F. L.↗

NASA NTRS1979

Numerical methods for problems involving the Drazin inverse

The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.

Meyer, C. D., Jr.↗

NASA NTRS1979

Connection and validation of narrow-band delta VLBI phase observations

Narrow-band differential very long baseline interferometry required phase connections between consecutive scans. An efficient computer aided scheme for this purpose is presented. This scheme is an iteration process alternating between a grand fit on many scans and integer quantization of the phase shift cycles to be assigned to the scans. Only linear simultaneous equations of a few unknowns need to be solved. A simulation analysis indicates that faultless phase connection can be expected when there is no localized systematic noise. When systematic noise of moderate level exists, the possible incorrect phase connection can be detected and connected for by comparing the connected phases from the two alternating observations, after removing the residual diurnal effects.

Wu, S. C.↗

NASA NTRS1979

A high order accurate numerical solution algorithm for turbulent boundary layer flow

A fourth-order accurate numerical solution algorithm is derived using finite element interpolation theory for the non-linear parabolic equations governing turbulent boundary layer flow including a two-equation turbulence closure model. The results of carefully controlled numerical experiments firmly quantize for the first time performance differences between finite element and finite difference solution methodology for this type of equation. The developed algorithm takes advantage of the apparent semi-analytical formulational procedure, in establishment of a single, retarded-evaluation Jacobian matrix iterative solution algorithm. Numerical results document performance of solution economy features in terms of computer requirements and solution accuracy. The developed algorithm should find wide application in aerodynamics analysis.

Soliman, M. O.↗

NASA NTRS1979

Decoupling control of a long flexible beam in orbit

The paper presents a method of control for large flexible systems using state variable feedback, with a long flexible beam given as an example. These feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping and (2) by applying the linear regulator problem to the individual modal coordinates separately. It is shown that the linear control law thus obtained are then evaluated by numerical integration of the non-linear system equations. Also included are results showing the effects (control spillover) on the uncontrolled modes when the number of controllers is less than the number of modes, and the effects of inaccurate knowledge of the control influence coefficients which lead to errors in the calculated feedback gains.

Reddy, A. S. S. R.↗

NASA NTRS1979

Utility of a finite element solution algorithm for initial-value problems

The Galerkin criterion within a finite element Weighted Residuals formulation is employed to establish an implicit solution algorithm for an initial-value partial differential equation. Numerical solutions of a transient parabolic and a hyperbolic equation, obtained using linear, quadratic and two cubic finite element basis functions, are employed to quantize accuracy and confirm and refine theoretical convergence rate estimates. The linear basis algorithm for the hyperbolic equation displays excellent accuracy on a coarse computational grid and a high-order convergence rate with discretization refinement. Good accuracy and a strong convergence rate in surface flux are determined for a nonhomogeneous Neumann boundary constraint applied to a parabolic equation. The results amply demonstrate the impact of the nondiagonal finite element initial-value matrix structure on solution accuracy and/or convergence rate.

Baker, A. J.↗

NASA NTRS1979

Investigations on the hierarchy of reference frames in geodesy and geodynamics

Problems related to reference directions were investigated. Space and time variant angular parameters are illustrated in hierarchic structures or towers. Using least squares techniques, model towers of triads are presented which allow the formation of linear observation equations. Translational and rotational degrees of freedom (origin and orientation) are discussed along with and the notion of length and scale degrees of freedom. According to the notion of scale parallelism, scale factors with respect to a unit length are given. Three-dimensional geodesy was constructed from the set of three base vectors (gravity, earth-rotation and the ecliptic normal vector). Space and time variations are given with respect to a polar and singular value decomposition or in terms of changes in translation, rotation, deformation (shear, dilatation or angular and scale distortions).

Grafarend, E. W.↗

NASA NTRS1979

MSFC solar activity predictions for satellite orbital lifetime estimation

The procedure to predict solar activity indexes for use in upper atmosphere density models is given together with an example of the performance. The prediction procedure employs a least square linear regression model to generate the predicted smoothed vinculum R sub 13 and geomagnetic vinculum A sub p(13) values. Linear regression equations are then employed to compute corresponding vinculum F sub 10.7(13) solar flux values from the predicted vinculum R sub 13 values. The output is issued principally for satellite orbital lifetime estimations.

Fuler, H. C.↗

NASA NTRS1980

A general panel method for the analysis and design of arbitrary configurations in incompressible flows

A method for solving the linear integral equations of incompressible potential flow in three dimensions is presented. Both analysis (Neumann) and design (Dirichlet) boundary conditions are treated in a unified approach to the general flow problem. The method is an influence coefficient scheme which employs source and doublet panels as boundary surfaces. Curved panels possessing singularity strengths, which vary as polynomials are used, and all influence coefficients are derived in closed form. These and other features combine to produce an efficient scheme which is not only versatile but eminently suited to the practical realities of a user-oriented environment. A wide variety of numerical results demonstrating the method is presented.

Johnson, F. T.↗

NASA NTRS1978

Steady state spurious errors in shock-capturing numerical schemes

The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows.

Karlsen, L. K.↗

NASA NTRS1979

Elastic lithosphere thickness on the moon from mare tectonic features - A formal inversion

The thickness (T) of the lunar elastic lithosphere at the time (3.6 to 3.8 billion years ago) of the earliest preserved basalt flows in circular mare basins can be estimated by inverting the observed locations of extensional tectonic features in and surrounding the maria. In performing the inversion, the lithosphere is modeled as an elastic shell with a liquid interior, and the basalt load for each mare is approximated by a set of concentric cylinders. To permit solving the forward problem of placing radial limits on the positions of the rilles around a given mare, an additional parameter F, the ratio of the radial stress at the radial limits to the maximum radial stress, is introduced. T and F are chosen to give the best weighted-squares fit of the radial limits to the observations, and are used as the initial values in a linearized matrix inversion to check the resolution and estimate errors. The application of the procedure to three maria with prominent extensional features, Humorum, Orientale, and Serenitatis, gives values of T from about 40 + or - 10 to 50 + or - 10 km, and in each case the linearized matrix equation has an exact inverse.

Comer, R. P.↗

NASA NTRS1979

An analysis of interface crack in adhesively bonded lap shear joints

This paper presents an analytical study of interface crack problems in adhesively bonded lap shear joints. A convenient and accurate method of analysis is developed on the basis of conservation laws in elasticity and of the fundamental relationships in fracture mechanics of interface crack problems. The problem is eventually reduced to a system of linear algebraic equations of mixed-mode stress intensity factor solutions. One of the salient features of the present approach is that the interface crack-tip stress intensity solutions can be determined accurately and directly by the information extracted from the far field. Solutions of the interface crack problems in lap shear joints have been obtained for the cases of various adhesive/adherend material systems and geometric configurations of the crack and the joint. Of particular interest is the evaluation of the mixed-mode stress intensity factors and the associated energy release rates. They are determined explicitly to illustrate the fundamental nature of the joint fracture problem.

Wang, S. S.↗

NASA NTRS1980

A collection of formulas for calculation of rotating blade noise - Compact and noncompact source results

A unified approach is used to derive many of the current formulations for calculation of discrete frequency noise for helicopter rotors and propellers. Both compact and noncompact source formulations are derived. The compact formulations are obtained as the limit of noncompact source results. In particular, the linearized acoustic equations by Hawkings and Lowson, Farassat, Hanson, Woan and Gregorek, Succi, and Jou are derived in this paper. An interesting thickness noise formula by Isom and its recent extension to the near field by Ffowcs Williams are also presented. The paper includes some comparisons of measured and calculated acoustic pressure signatures and spectra for an advanced propeller. The theoretical results are obtained using a computer program developed by the author and P. A. Nystrom.

Farassat, F.↗