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NASA NTRS1981

A semi-analytic approach to the self-induced motion of vortex sheets

The rolling-up of the trailing vortex sheet produced by a wing of finite span is calculated as a series expansion in time. For a vorticity distribution corresponding to a wing with cusped tips, the shape of the sheet is found by summing the series using Pade approximants. The sheet remains analytic for some time but ultimately develops an exponential spiral at the tips. The centroid of vorticity is conserved to high accuracy.

Schwartz, L. W.↗

NASA NTRS1982

Analytical model of jet shielding

An analytical model of the shielding of a stationary point noise source by a cylindrical jet is developed. The directivity function is derived which estimates the normalized sound pressure level at a far field receiver. The shielding model is compared to experimental data for a point noise source impinging on an unheated air jet and on a simulated hot air jet. The model compares favorably to measured shielding at receiver locations away from the jet axis. The trend of the estimated shielding diverges from the measured data as the jet axis is approached. Refinement of the model is discussed.

Gerhold, C. H.↗

NASA NTRS1982

An analytical technique for the analysis of airplane spin entry and recovery

The dynamic equations of motion for a spinning airplane are simplified to facilitate the analysis of spin entry and recovery maneuvers. Solutions of a nonlinear, first order equation for spin rate enable calculation of spin entry and recovery times and control required for recovery. The analysis is applied to a light airplane for which both aerodynamic data, rotory balance wind tunnel tests, and spin flight test data have been obtained. A comparison of predicted and actual transient spin responses is made which supports the validity of the analytical approach taken but which also illustrates the difficulty in obtaining accurate aerodynamic data for spinning airplanes. Certain normalized parameters of the reduced state spin equation suggest criteria for assessing the transient spin characteristics of light airplanes.

Taylor, L. W., Jr.↗

NASA NTRS1981

Analytic approximations to the modon dispersion relation

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Boyd, J. P.↗

NASA NTRS1982

Analytical model accuracy requirements for structural dynamic systems

A test/analysis correlation criterion for the analytical model accuracy requirement has been developed. It is based on the principle of equal errors from the model inaccuracy and the uncertainties of dynamic environments. The forcing functions are idealized to establish the base for uncertainty definition and the maximum allowable errors from these uncertainties are obtained. Then the model accuracy requirement is established by comparing the responses due to the model errors to those due to the forcing function uncertainties.

Chen, J.-C.↗

NASA NTRS1981

Analytical calculation of thickness versus diameter requirements of silicon solar cells

It may be more cost-effective to produce larger diameter silicon Cz solar cells. However, greater thickness is anticipated to be necessary for larger diameter wafers to withstand wafering, cell processing and handling. No material standard for these dimensional requirements is practical or cost-effective for cell manufacturers. The equations relating wafer thickness and diameter were derived by using fracture mechanics analysis. An analytical model was used as a guideline to estimate thickness versus diameter requirements of silicon solar cells in terms of fracture mechanics parameters.

Chen, C. P.↗

NASA NTRS1982

Analytical study of vortex flaps on highly swept delta wings

This paper highlights some current results from ongoing analytical studies of vortex flaps on highly swept delta wings. A brief discussion of the vortex flow analysis tools is given along with comparisons of the theories to vortex flap force and pressure data. Theoretical trends in surface pressure distribution for both angle-of-attack variation and flap deflection are correctly predicted by Free Vortex Sheet theory. Also shown are some interesting calculations for attached-flow and vortex-flow flap hinge moments that indicate flaps utilizing vortex flow may generate less hinge moment than attached flow flaps. Finally, trailing-edge flap effects on leading-edge flap thrust potential are investigated and theory-experiment comparisons made.

Frink, N. T.↗

NASA NTRS1982

An analytic approach to two-fixed-impulse transfers between Keplerian orbits

Solutions are obtained for the two-impulse transfer of a vehicle between arbitrary inclined orbits in an inverse-square force field with the restriction that the magnitude of each of the two impulses has a fixed preassigned value. The two magnitudes need not be equal. The equations for the conservation of angular momentum and energy are augmented by the Laplace integral; these equations establish linear relationships between several of the variables. This set of linear equations and one of two quadratic equations constitute the analytically tractable part of the solution. The remaining part, consisting of finding the zeros (if they exist) of a single trigonometric function of one variable, is solved using numerical methods. Explicit lower bounds on each of the magnitudes of the two impulses are obtained by requiring the solution be real. Graphical results are presented to illustrate the solution.

Jezewski, D. J.↗

NASA NTRS1982

The structure and evolution of galacto-detonation waves - Some analytic results in sequential star formation models of spiral galaxies

Waves of star formation in a uniform, differentially rotating disk galaxy are treated analytically as a propagating detonation wave front. It is shown, that if single solitary waves could be excited, they would evolve asymptotically to one of two stable spiral forms, each of which rotates with a fixed pattern speed. Simple numerical solutions confirm these results. However, the pattern of waves that develop naturally from an initially localized disturbance is more complex and dies out within a few rotation periods. These results suggest a conclusive observational test for deciding whether sequential star formation is an important determinant of spiral structure in some class of galaxies.

Cowie, L. L.↗

NASA NTRS1981

An analytical approach to photovoltaic encapsulation system design

This paper describes a set of analytical methods which have been developed to enable quantitative analysis of encapsulation system designs for terrestrial photovoltaic modules. Design factors determined most important include: encapsulant thickness and modules, emissivity of module surface, ribs on substrate modulus, and AR.

Garcia, A., III↗

NASA NTRS1982

Analytical and experimental investigation of stator endwall contouring in a small axial-flow turbine. 1: Stator performance

Three stator configurations were studied to determine the effect of stator outer endwall contouring on stator performance. One configuration was a cylindrical stator design. One contoured stator configuration had an S-shaped outer endwall, the other had a conical-convergent outer endwall. The experimental investigation consisted of annular surveys of stator exit total pressure and flow angle for each stator configuration over a range of stator pressure ratio. Radial variations in stator loss and aftermixed flow conditions were obtained when these data were compared with the analytical results to assess the validity of the analysis, good agreement was found.

Haas, J. E.↗

NASA NTRS1982

Gas turbine rotor/case structural response to rotating stall: Experimental documentation and analytical approach

The forcing functions and structural responses characterizing gas turbine rotor/case system vibration due to rotating stall in an axial flow compressor are described. Two data sets with fundamentally different response characteristics are presented; one is supersynchronous and the other subsynchronous. Conventional beam element rotor dynamics analysis is shown to be severely limited in its ability to predict these responses. A new analytical approach, which significantly increases structural response predictive capability for these phenomena, is briefly discussed.

Haley, P. J.↗

NASA NTRS1983

Analytical and experimental study of a standing torus with normal loads

Finite element analysis is applied to study the large deflection and stress of a thin-walled pressurized torus loaded by normal contact with a plane. Experimentally determined stresses are compared to those resulting from finite element analysis at various meridional and circumferential coordinates of the torus, including the footprint area. Circumferential strains compare favorably while meridional strains are higher in the finite element analysis, probably due to slippage of the boundary at the rim. The STAGS finite element computer program was used. The purpose of the study was to evaluate the various program options for structural loading, for material modeling, for stress analysis, and for grid refinement. The experimental model, a thin-walled rubber tube mounted on a steel cylindrical rim, provided measured results to compare with various analytical trade-offs. It was found that there was almost no difference in predicted deflections or stress distributions between linear and nonlinear material description. However, the difference between linear analysis and that of geometric nonlinearities utilizing incremental loading was marked.

Mack, M. J., Jr.↗

NASA NTRS1983

Analytic determinations of single-folding optical potentials

A simple analytic method for calculating nucleon-nucleus optical potentials using a single folding of a Gaussian two body interaction with an arbitrary nuclear distribution is presented. When applied to proton-lead elastic scattering, the predicted real part of the Woods-Saxon potential is in substantial agreement with the experimentally determined phenomenological potential, although there are no adjustable parameters. In addition, the volume integrals of both real potentials are nearly identical.

Townsend, L. W.↗

NASA NTRS1983

New test techniques and analytical procedures for understanding the behavior of advanced propellers

Analytical procedures and experimental techniques were developed to improve the capability to design advanced high speed propellers. Some results from the propeller lifting line and lifting surface aerodynamic analysis codes are compared with propeller force data, probe data and laser velocimeter data. In general, the code comparisons with data indicate good qualitative agreement. A rotating propeller force balance demonstrated good accuracy and reduced test time by 50 percent. Results from three propeller flow visualization techniques are shown which illustrate some of the physical phenomena occurring on these propellers.

Stefko, G. L.↗

NASA NTRS1982

Two-dimensional convolute integers for analytical instrumentation

As new analytical instruments and techniques emerge with increased dimensionality, a corresponding need is seen for data processing logic which can appropriately address the data. Two-dimensional measurements reveal enhanced unknown mixture analysis capability as a result of the greater spectral information content over two one-dimensional methods taken separately. It is noted that two-dimensional convolute integers are merely an extension of the work by Savitzky and Golay (1964). It is shown that these low-pass, high-pass and band-pass digital filters are truly two-dimensional and that they can be applied in a manner identical with their one-dimensional counterpart, that is, a weighted nearest-neighbor, moving average with zero phase shifting, convoluted integer (universal number) weighting coefficients.

Edwards, T. R.↗

NASA NTRS1982

An analytic solution to the classical two-body problem with drag

An analytic solution to the two-body problem with a specific drag model is obtained. The model treats drag as a force proportional to the vector velocity and inversely proportional to the square of the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time-of-flight is expressed as a quadrature in the 'true anomaly'.

Mittleman, D.↗

NASA NTRS1983

An analytical comparison of two wing structures for Mach 5 cruise airplanes

Mach 5 cruise research conducted by NASA is related to aerodynamics, propulsion, and structures. The study of structures includes the propulsion system, fuselage, and wings. Various studies have shown that the achievement of adequate range is largely dependent on a low structural mass fraction. The present investigation is concerned with a study of two wing structure configurations for Mach 5 aircraft. An uprated version (Ti-6242 replacing B-120 titanium) of the YF-12/SR-71 wing structure is considered. The B-120 titanium structure represents the current art of high speed aircraft wing structures. The YF-12 wing structure was designed about 20 years ago when the analytical methods for calculating thermal stresses were limited. The second wing structural configuration studied in the present investigation also used Ti-6242 materials but replaced the corrugated-beaded panels with diffusion bonded honeycomb-core sandwich panels, and replaced the z-stiffened shear webs with sine-wave stiffened shear webs.

Taylor, A. H.↗