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NASA NTRS1979

The equatorial total electron content and shape factor

The diurnal variations of electron content and shape factor observed at an equatorial station during sunspot minimum are shown to be consistent with the electron density profiles observed at Jicamarca during sunspot minimum. The rapid increase in electron content and the shape factor at sunrise results from the EUV production of ionization in the E and F regions. Day-to-day variations in daytime electron content are observed to be quite small at the equator. The evening decrease in the shape factor results from an upward drift of the F region at sunset and the evening decay of the E and bottomside F regions. The nighttime peak or plateau in the shape factor is produced by the slow downward drift of the electron density profile. The deep predawn dip in the shape factor is caused by the main peak of the F layer reaching low altitudes where high loss rates cause a large reduction in ionization below 300 km and very flat electron density profile.

Donnelly, R. F.↗

NASA NTRS1980

The shape and stability of rotating liquid drops

Equilibrium shapes and stability of rotating drops held together by surface tension are found by computer-aided analysis that uses expansions in finite-element basis functions. Shapes are calculated as extrema of appropriate energies. Stability and relative stability are determined from curvatures of the energy surface in the neighborhood of the extremum. Families of axisymmetric, two-, three-, and four-lobed drop shapes are traced systematically. Bifurcation and turning points are located and the principle of exchange of stabilities is tested. The axisymmetric shapes are stable at low rotation rates but lose stability at the bifurcation to two-lobed shapes. Two-lobed drops isolated with constant angular momentum are stable. The results bear on experiments designed to further those of Plateau (1863).

Brown, R. A.↗

NASA NTRS1981

Calculation of the room-temperature shapes of unsymmetric laminates

A theory explaining the characteristics of the cured shapes of unsymmetric laminates is presented. The theory is based on an extension of classical lamination theory which accounts for geometric nonlinearities. A Rayleigh-Ritz approach to minimizing the total potential energy is used to obtain quantitative information regarding the room temperature shapes of square T300/5208 (0(2)/90(2))T and (0(4)/90(4))T graphite-epoxy laminates. It is shown that, depending on the thickness of the laminate and the length of the side the square, the saddle shape configuration is actually unstable. For values of length and thickness that render the saddle shape unstable, it is shown that two stable cylindrical shapes exist. The predictions of the theory are compared with existing experimental data.

Hyer, M. W.↗

NASA NTRS1982

Cauchy integral method for two-dimensional solidification interface shapes

A method is developed to determine the shape of steady state solidification interfaces formed when liquid above its freezing point circulates over a cold surface. The solidification interface, which is at uniform temperature, will form in a shape such that the non-uniform energy convected to it is locally balanced by conduction into the solid. The interface shape is of interest relative to the crystal structure formed during solidification; regulating the crystal structure has application in casting naturally strengthened metallic composites. The results also pertain to phase-change energy storage devices, where the solidified configuration and overall heat transfer are needed. The analysis uses a conformal mapping technique to relate the desired interface coordinates to the components of the temperature gradient at the interface. These components are unknown because the interface shape is unknown. A Cauchy integral formulation provides a second relation involving the components, and a simultaneous solution yields the interface shape.

Siegel, R.↗

NASA NTRS1983

Elevated temperature behavior of superplastically formed/weld-brazed titanium compression panels having advanced shaped stiffeners

The 316 C (600 F) buckling behavior of superplastically formed/weld-brazed titanium compression panels having advanced shaped stiffeners was investigated. Fabrication of the advanced shaped stiffeners was made possible by the increased formability afforded by the superplasticity characteristics of the titanium alloy Ti-6Al-4V. Stiffeners having the configurations of a conventional hat, a beaded web, a modified beaded web, a ribbed web, and a stepped web were investigated. The data from the panel tests include load-shortening curves, local buckling strengths, and failure loads. The superplastic formed/weld-brazed panels with the ribbed web and stepped web stiffeners developed 25 and 27 percent higher buckling strengths at 316 C (600 F) than panels with conventionally shaped stiffeners. The buckling load reductions for panels tested at 316 C (600 F), compared with panels tested at room temperature, were in agreement with predictions based on titanium material property data. The advantage that higher buckling loads can be readily achieved by superplastically forming of advanced stiffener shapes was demonstrated. Application of these advanced stiffener shapes offers the potential to achieve substantial weight savings in aerospace vehicles.

Royster, D. M.↗

NASA NTRS1983

Growth and stability of interacting surface flaws of arbitrary shape

Growth regimes of interacting surface flaws of arbitrary shape are analyzed with the aid of the body force method, and the stability of the process is assessed on the basis of the variation of the load during the growth. It is shown that irregularly shaped flaws are often associated with very high stress intensity factors locally, which tend to change as the flaws grow into more regular shapes. Several examples of various flaw shapes are worked out for illustration, and it is shown that a simple formula seems to provide an accurate estimate of the maximum stress intensity factor for surface flaws of various shapes, which are not very slender. The formula involves the overall maximum tension, as well as the area of the projection of the flaw on the plane normal to the maximum tension.

Murakami, Y.↗

NASA NTRS1984

Measurements of local convective heat transfer coefficients on ice accretion shapes

The thin-skin heat rate technique was used to determine local convective heat transfer coefficients for four representative ice accretion shapes. The shapes represented three stages of glaze ice formation and one rime ice formation; the ice models had varying degrees of surface roughness. In general, convective heat transfer was higher in regions where the model's surfaces were convex and lower in regions where the surfaces were concave. The effect of roughness was different for the glaze and rime ice shapes. On the glaze ice shapes, roughness increased the maximum Nu by 80 percent, but the other Nu values were virtually unchanged. On the rime ice shape, the Nu numbers near the stagnation point were unchanged. The maximum Nu value increased by 45 percent, and the Nu number downstream of the peak increased by approximately 150 percent.

Arimilli, R. V.↗

NASA NTRS1984

Static shape determination and control for large space structures. I - The flexible beam. II - A large space antenna

A method for determining and controlling the shape of large, continuous space structures by means of discrete or pointwise observations and control devices is presented. The general linear boundary value problem satisfied by a one-dimensional shape function is defined, and the existence of solutions is studied. The static shape control problems for one-dimensional systems with and without rigid body modes and the static shape estimation problem are presented and solved. Eigenfunction expansions are presented which provide approximations to the algorithm terms when the associated Green's function is not known. An integral operator approach is applied to the multidimensional static problem, and the results are illustrated with a finite element model of the disk of a large space antenna which assumes no rigid body modes. It is shown that the shape control algorithm must be modified for systems with rigid body modes.

Weeks, C. J.↗

NASA NTRS1972

Line shape parameters for HCl and HF in a CO2 atmosphere.

Results of high-resolution (0.1 cm/cm) on several CO2-broadened lines in the fundamentals of HCl35 and HCl37. Line intensities, half-widths, and shapes were determined at room temperature. Half-widths in HCl-CO2 collisions were computed for several temperatures, employing Anderson's (1949) theory. The measured shapes of HCl lines broadened by CO2 are described by a semiempirical super-Lorentzian shape. The curve-of-growth for this line shape is derived in terms of a function similar to the Ladenburgh-Reiche function. Absorption between R(0) and P(1) is affected by the appearance of several pressure-induced Q-branch lines, at the pressures from 1 to 10 atm used in the present study.

Varanasi, P.↗

NASA NTRS1972

Planimetric shapes of lunar rilles, part Q

Selected Apollo 16 photographs of lunar rilles have been analyzed with a new technique that includes a finite Fourier analysis. Preliminary results suggest that it will be possible to classify rilles quantitatively by their planimetric shape. Shapes of possible terrestrial analogs for lunar rilles also can be compared to the shapes of lunar rilles by using this new technique. Preliminary results also suggest that the new technique may be useful for demonstrating structural control of shape of lunar rilles.

Oberbeck, V. R.↗

NASA NTRS1973

Part 1: The stability of equilibrium shapes of elastic systems

The stability of equilibrium shapes of elastic systems is examined. Stability loss in the case of similar equilibrium shapes, the disappearance of stable equilibrium shapes, and the disappearance of any forms of equilibrium are discussed. The error made by Euler in analyzing stability loss is pointed out, and Mises' truss is used as an example of stability loss in the case of similar equilibrium shapes.

Panovko, Y. G.↗

NASA NTRS1974

A parametric study of effect of forebody shape on flow angularity at Mach 8

Flow angularity and static pressure measurements have been made on the lower surface of nine forebody models that simulate the bottom forward surface of a hypersonic aircraft. Measurements were made in an area of the forebody that represents the location of an inlet of a scramjet engine. A parametric variation of the forebody surface investigated the effect of: (1) spanwise curvature; (2) longitudinal curvature; and (3) planform shape on both flow angularity and static pressure distribution. Results of each of the three parametric variations of geometry were compared to those for the same flat delta forebody. Spanwise curvature results showed that a concave shape and the flat delta had the lowest flow angularity and lowest rate of increase in flow angularity with angle of attack. Longitudinal curvature results showed a convex surface to give the better flow at the higher angles of attack. The better of the two planform shapes tested was a convex elliptical shape. Limited flow field calculations were made at angles of attack using a three dimensional, method-of-characteristics program. In general, at all angles of attack there was agreement between data and theory.

Johnson, C. B.↗

NASA NTRS1975

Effects of nacelle shape on drag and weight of a supersonic cruising aircraft

The quantitive relationship of cruise drag and nacelle shape was investigated for a representative advanced supersonic transport configuration. Nacelle shape parameters were systematically varied, and the effects of these variations on wave and friction drag were determined. The effects of changes in vehicle drag, propulsion weight, and specific fuel consumption on vehicle takeoff gross weight were computed. Generally, it was found that nacelle shapes such that the maximum cross-sectional area occurred at or near the nozzle exit resulted in the lowest wave drag. In fact, nacelle shapes were found that produce favorable interference effects (drag reduction) of such magnitude as to nearly offset the friction drag of the nacelle.

Bonner, E.↗

NASA NTRS1976

The effect of cowling shape on the stability characteristics of an airplane, September 1942

Three widely different nose shapes were tested on a fuselage alone and on a complete model in the NACA stability tunnel to investigate the effect of cowling shape on stability characteristics. The results are presented in the form of charts which show the variation in the aerodynamic characteristics with the three nose shapes for the propeller-removed condition over a wide range of angles of attack and yaw. The results indicated that large changes in the cowling shape produced relatively small changes in the aerodynamic characteristics. The effects may be appreciable, however, in the case of an airplane that has marginal stability.

Donlan, C. J.↗

NASA NTRS1976

A generalization of MSK-type signaling based upon input data symbol pulse shaping

Minimum-shift-keying (MSK), which is a special case of continuous phase frequency-shift-keying (CPFSK) with frequency deviation ratio equal to 0.5, is known to be spectrally equivalent to a form of offset quadrature phase-shift-keying (OQPSK) in which the symbol pulse shape is a half-cycle sinusoid rather than the usual rectangular form. Appropriate shaping of the input data symbols allows one to generate an entire class of constant envelope, MSK-type signals, whose spectral properties are in some applications more desirable than those of MSK or OQPSK. The present study derives and presents a set of conditions on the input pulse shaping which in turn describes the class of envelope shapes allowable. The autocorrelation function and power spectral density of this class of signals are then derived, and specific examples are given to illustrate the desirable spectral properties. Such properties are important considerations in system design where interchannel and intersymbol interference degradations must be kept to a minimum.

Simon, M. K.↗

NASA NTRS1977

Shape optimization of pressure gradient microphones

Recently developed finite element computer programs were utilized to investigate the influence of the shape of a body on its scattering field with the aim of determining the optimal shape for a Pressure Gradient Microphone (PGM). Circular cylinders of various aspect ratios were evaluated to choose the length to diameter ratio best suited for a dual element PGM application. Alterations of the basic cylindrical shape by rounding the edges and recessing at the centerline were also studied. It was found that for a + or - 1 db deviation from a linear pressure gradient response, a circular cylinder of aspect ratio near 0.5 was most suitable, yielding a useful upper frequency corresponding to ka = 1.8. The maximum increase in this upper frequency limit obtained through a number of shape alterations was only about 20 percent. An initial experimental evaluation of a single element cylindrical PGM of aspect ratio 0.18 utilizing a piezoresistive type sensor was also performed and is compared to the analytical results.

Norum, T. D.↗

NASA NTRS1977

Fourier analysis of planimetric lunar crater shape - Possible guide to impact history and lunar geology

If the lithology of lunar crust influences impact crater morphology, a method of analysis that is sensitive to small-scale changes in crater shape is required. In the present paper, it is shown that Fourier analysis in closed form can provide detailed information regarding planimetric crater shape. Preliminary analysis of the rim crest outline of 247 nearside lunar craters (larger than 18 km in diam) led to the following information: Imbrian and pre-Imbrian craters are more elongate than younger craters, possibly as a result of widespread crustal deformation early in the moon's history. Crater size does not affect the planimetric shape of craters. Highland craters are less circular than mare craters, probably due to the greater structural and lithologic complexity of the highland crust. Craters comprising each shape family of the eleventh harmonic typically are located in the same general geographic region of the moon.

Eppler, D. T.↗

NASA NTRS1978

Approximate line shapes for hydrogen

Two independent methods are presented for calculating radiative transport within hydrogen lines. In Method 1, a simple equation is proposed for calculating the line shape. In Method 2, the line shape is assumed to be a dispersion profile and an equation is presented for calculating the half half-width. The results obtained for the line shapes and curves of growth by the two approximate methods are compared with similar results using the detailed line shapes by Vidal et al.

Sutton, K.↗