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At least 1,315 records · Page 73

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NASA NTRS1966

Numerical integration of periodic orbits in the elliptic restricted three-body problem

The problem of finding periodic orbits in the circular restricted three-body problem has been very extensively studied in celestial mechanics. It is well known that continuous families of periodic orbits exist, for which the period varies in a continuous way. However, all the applications which are found in the solar system correspond to cases with non-zero eccentricities, and the elliptic restricted three-body problem is thus a better approximation than the circular one. For instance, for the motion of a satellite in the Earth-Moon system, as a first approximation, we may assume that the Moon moves around the Earth in circular motion; but as a much better approximation, we can also assume that the Moon moves in an elliptic orbit around the Earth.

NUMERICAL INTEGRATION↗

NASA NTRS1972

Liquid-phase mixing of bipropellant doublets

Experimental results of unlike doublet mixing are correlated with an analytically derived equation predicting fluid cavitation. The correlation relates the minimum orifice pressure drop required to initiate cavitation, with the system back pressure, cold flow simulant vapor pressure, and the orifice flow discharge and contraction coefficients. Stream flow instabilities are also visually correlated with the onset of cavitation and orifice discharge coefficient measurements. The influence of cavitation on the characteristic phenomenon of hydraulic flip is observed for both circular and noncircular shaped orifices. For certain intermediate orifice lengths, some noncircular shapes are shown to produce more fully developed flows (shorter recovery lengths) and therefore a more cohesive jet, which in turn yields slightly higher cold flow mixing uniformities than circular shaped orifices of equal absolute length. The particular noncircular shaped elements evaluated are shown to be more sensitive to liquid stream misimpingement than the corresponding circular orifices.

Hoehn, F. W.↗

NASA NTRS1973

Systematic two-dimensional cascade tests. Volume 4: Cascade test data

The data pertaining to the performance characteristics of hydrofoils are presented. The hydrofoils are: (1) double circular arc, (2) multiple circular arc, and (3) slotted doubled circular arc. The experimental data are organized into a systematic presentation format and provided with scale factors and reference values for interpretation. The data include local pressure distributions upstream and downstream of the cascade test section, continuous records from flow angle and total pressure surveys, hydrofoil local pressure distributions, and cavitation data.

Murrin, T. A.↗

NASA NTRS1973

Noise tests of a model engine-over-the-wing STOL configuration using a multijet nozzle with deflector

Noise data were obtained with a small scale model stationary STOL configuration that used an eight lobe mixer nozzle with deflector mounted above a 32-cm-chord wing section. The factors varied to determine their effect upon the noise were wing flap angle, nozzle shape, nozzle location, deflector configuration, and jet velocity. The noise from the mixer nozzle model was compared to the noise from a model using a circular nozzle of the same area. The mixer nozzle model was quieter at the low to middle frequencies, while the circular nozzle was quieter at high frequencies. The perceived noise level (PNL) was calculated for an aircraft 10 times larger than the model. The PNL at 500 feet for the mixer nozzle turned out to be within 1 db of the PNL for the circular nozzle. For some configurations at highly directional broadband noise, which could be eliminated by changes in nozzle and/or deflector location, occurred below the wing.

Olsen, W. A.↗

NASA NTRS1974

Acoustic theory of axisymmetric multisectioned ducts

Equations are developed for the acoustic field in a duct system which is made up of a number of connected circular and annular ducts. These equations are suitable for finding the acoustic field inside of and radiated from an aircraft turbofan engine. Acoustic modes are used as generalized coordinates in order to develop a set of matrix equations for the acoustic field. Equations for these modes are given for circular and annular ducts with uniform flow. Modal source equations are derived for point acoustic sources. General equations for mode transmission and reflection are developed and detailed equations are derived for ducts with multiple sections of acoustic treatment and for ducts with circumferential splitter rings. The general theory is applied to the special case of a uniform area circular duct with multisection liners and it is shown that the mode reflection effects are proportional to differences of the acoustic admittances of adjacent liners. A numerical example is given which shows that multisection liners may provide greater noise suppression than uniform liners.

Zorumski, W. E.↗

NASA NTRS1973

Geodesic synchrotron radiation

This paper presents the results and methods of computing the high-frequency radiation emitted by freely falling particles moving in circular geodesic orbits in a spherically symmetric gravitational field. The high-frequency radiation, to which the methods of this paper apply, is the principal part of radiated energy only in the case of a particle moving in a highly relativistic, and therefore unstable, circular geodesic. The geodesic synchrotron radiation emitted in this case shows excitation of high-frequency harmonics and a narrow angular distribution. A Green's-function solution of the scalar wave equation is obtained using WKB methods. For application to relativistic circular orbits, a parabolic WKB approximation is required and yields solutions in terms of parabolic cylinder functions.

Breuer, R. A.↗

NASA NTRS1973

Some physical parameters of micrometeoroids

Detailed morphological parameters (depth/diameter ratio, circularity index) of microcraters in the 0.2 to 100 micron diameter range were obtained via SEM techniques for three lunar glass surfaces. The depth/diameter ratios are typically 0.5 to 0.8 with a range of 0.3 to 1.3. The circularity index varies from 0.4 to 1.0 with a pronounced maximum at 0.7 to 0.9. These parameters are compared with microcraters produced in the laboratory via electrostatic particle accelerators. The following conclusions are drawn: The great majority of observed crater depths are compatible with micrometeoroid densities of 2 to 4 g/cu cm; crater depths are incompatible for projectile densities less than 1 g/cu cm and greater than 7 g/cu cm. The circularity index of microcrater pits indicates rather equidimensional, if not spherical, projectiles. Needles, platelets and other highly irregular shapes can be excluded. Less than 5% of all craters observed may offer different conclusions.

Brownlee, D. E.↗

NASA NTRS1974

Some examples of exact and approximate solutions in small particle scattering - A progress report

The formulation of basic equations from which the scattering of radiation by a localized variation in a medium is discussed. These equations are developed in both the differential and the integral form. Primary interest is in the scattering of electromagnetic waves for which the solution of the vector wave equation with appropriate boundary conditions must be considered. Scalar scattering by an infinite homogeneous isotropic circular cylinder, and scattering of electromagnetic waves by infinite circular cylinders are treated, and the case of the finite circular cylinder is considered. A procedure is given for obtaining angular scattering distributions from spheroids.

Greenberg, J. M.↗

NASA NTRS1974

Experimental and theoretical investigation of a slotted noise shield model for wind tunnel walls

Tests at Mach 6 and 8 have been conducted on a model of a wind tunnel sound radiation shield which consists of interchangeable circular and wedge-shaped longitudinal rods with gaps between the rods for boundary layer removal. In view of the large effective sweep angle of the circular rods with respect to the local flow, the boundary layer behavior was surprisingly well represented by swept cylinder theory. Laminar flow was maintained up to a maximum local unit Reynolds number of 8 million per foot which would presumably be independent of model length for a given rod diameter by analogy with results on swept cylinders. Reduction in wind-tunnel sound levels within the shielded region of the circular rod model were about 90% of the maximum possible reduction for an ideal shield.

Harvey, W. D.↗

NASA NTRS1974

An interdisciplinary analysis of multispectral satellite data for selected cover types in the Colorado mountains, using automatic data processing techniques

The author has identified the following significant results. In the San Juan Mountains there exists a group of structural and topographic features which suggest a common origin. The relative positions of the San Juan Depression with the Silverton and Lake City Calderas indicate they are possibly on the edge of a large circular feature. Comparison with the 1:250,000 scale Durango Geologic Map reveals a series of radial and arcuate faults concentric with the major circular feature. Such a fracture pattern implies that the circular feature may represent the extent of a major domal uplift in the area. The uplift was very likely due to the sub-crustal emplacement of the parent magma of the San Juan volcanics and intrusives. The broad doming led to the formation of a zone of tensional ring fractures which acted as conduits of release for the magma and the eventual development of the various calderas. The ring fracturing was probably incomplete with hinging occurring in the southern and southwestern portions of the dome accounting for the lack of development of caldera structures in that portion of the area.

Hoffer, R. M.↗

NASA NTRS1974

Lunar mascons - Another model and its implications

A mascon model is proposed in which the mass excess of the mare basalts in the circular maria is supported isostatically by mass deficits at depth. The model predicts the observed positive gravity anomalies surrounded by negative ring anomalies and explains the absence of gravity anomalies over the irregular maria. The model implies that mare basalts were derived by partial melting of a source region at depth due to pressure relief resulting from the excavation of the circular mare basins, and that the crystalline residuum in the source region is of lower density than the original source rock. The trace element enrichment and near cotectic character of Apollo 11 and 12 lavas reported by some investigators may be caused by extensive magma fractionation enroute from an origin in the circular maria to the final, distant emplacement sites.

Kunze, A. W. G.↗

NASA NTRS1974

On the origin of mascons and moonquakes

Hypotheses are proposed for the origin of mascons and moonquakes. It is noted that a horizontal transfer of magma is required to explain the mascons and that a basin which can fill with lava to a depth of about 20 km is necessary before mascon formation is possible. It is shown that hydrostatic equilibrium theories can account for the excess filling of lava in circular maria and that mascons will result when this process occurs in the presence of a thick rigid lithosphere. It is postulated that a cylindrical fault system extends through the lithosphere and surrounds the circular maria. In this case, the release of potential energy through the fault system would be adequate to explain moonquakes, their properties, and the clustering of the locations of lunar transient events around the circular maria.

Runcorn, S. K.↗

NASA NTRS1975

Earth resources evaluation for New Mexico by LANDSAT-2

The author has identified the following significant results. The Middle Rio Grande project has not yet progressed to the point where mineral exploration sites can be chosen; however, there does appear to be some correlation between the known structure and mineral deposits and the LANDSAT lineament map. A circular feature identified in the southern Magdalena Mountains on LANDSAT-1 imagery agrees well with the location of a newly proposed caldron complex. Several recognized and unrecognized circular features were identified on imagery of the Mogollon-Datil volcanic field. A check of aeromagnetic maps for New Mexico found that the circular features on the LANDSAT imagery showed up as areas of generally high magnetic intensity.

Linden, K. V.↗

NASA NTRS1975

Research on recognition of the geologic framework of porphyry copper deposits on ERTS-1 imagery

The author has identified the following significant results. Many new linear and circular features were found. These features prompted novel tectonic classification and analysis especially in the Ray and Ely areas. Tectonic analyses of the Ok Tedi, Tanacross, and Silvertone areas follow conventional interpretations. Circular features are mapped in many cases and are interpreted as exposed or covered intrusive centers. The small circular features reported in the Ok Tedi test area are valid and useful correlations with tertiary intrusion and volcanism in this remote part of New Guinea. Several major faults of regional dimensions, such as the Denali fault in Alaska and the Colorado mineral belt structures in Colorado are detected in the imagery. Many more faults and regional structures are found in the imagery than exist on present maps.

Wilson, J. C.↗

NASA NTRS1975

Small-scale imagery: A useful tool for mapping geological features in the Texas Gulf Coastal plain

A sample of satellite imagery includes photographs and multispectral scanner imagery from the Apollo, LANDSAT, and Skylab spacecraft over an area west of Houston, Texas. Large circular features and lineaments can readily be mapped. One of the circular features identified by drainage, vegetation, and soil-tone anomalies, occurs in Fort Bend County, Texas, and covers an area about 25 miles in diameter. Another circular feature lies to the north, immediately west of Houston, and is about 15 miles in diameter. These features represent the surface expression of deeply-buried positive structures. It is recommended that regional geological studies begin with photointerpretations of high-altitude aircraft and synoptic space imagery, space imagery provides the synoptic view of rapid evaluation of large-scale features, and, at enlarged scales, the resolution required for detailed study of selected areas of structures.

Amsbury, D. L.↗

NASA NTRS1976

A fuselage/tank structure study for actively cooled hypersonic cruise vehicles, summary

A detailed analytical study was made to investigate the effects of fuselage cross section (circular and elliptical) and the structural arrangement (integral and nonintegral tanks) on aircraft performance. The vehicle was a 200 passenger, liquid hydrogen fueled Mach 6 transport designed to meet a range goal of 9.26 Mn (5000 NM). A variety of trade studies were conducted in the area of configuration arrangement, structural design, and active cooling design in order to maximize the performance of each of three point design aircraft: (1) circular wing-body with nonintegral tanks, (2) circular wing-body with integral tanks and (3) elliptical blended wing-body with integral tanks. Aircraft range and weight were used as the basis for comparison. The resulting design and performance characteristics show that the blended body integral tank aircraft weights the least and has the greatest range capability, however, producibility and maintainability factors favor nonintegral tank concepts.

Pirrello, C. J.↗

NASA NTRS1976

Experimental aerodynamic characteristics for slender bodies with thin wings and tail at angles of attack from 0 deg to 58 deg and Mach numbers from 0.6 to 2.0

An experimental investigation was conducted by wind tunnel to measure the static aerodynamic characteristics for bodies of circular and elliptic cross section with various thin flat plate wings and a thin tail consisting of horizontal and vertical parts. The wings had aspect ratios of 4 and taper ratios of about 0, 0.25, and 0.5. Two additional wings, which had taper ratios near 0.25 and aspect ratios of about 3 and 5, were also tested in combination with the bodies and tail. All wings had about the same planform area. The exposed area of the horizontal portion of the tail was about 33 to 36 percent of the exposed area of the wings. The exposed area of the vertical tail fin was about 22 to 24 percent of the exposed area of the wings. The elliptic body, with an a/b = 2 cross section, had the same length and axial distribution of cross sectional area as the circular body. The circular body had a cylindrical aftersection of fineness ratio 7, and it was tested with the wings and tail in combination with tangent ogive noses that had fineness ratios of 2.5, 3.0, 3.5, and 5.0. In addition, an ogive nose with a rounded tip and an ogive nose with two different nose strake arrangements were used. Nineteen configuration combinations were tested at Mach numbers of 0.6, 0.9, 1.5, and 2.0 at angles of attack from 0 to 58 deg. The Reynolds numbers, based on body base diameter, were about 4.3 X 100,000.

Jorgensen, L. H.↗

NASA NTRS1976

Single-stage experimental evaluation of low aspect ratio, highly loaded blading for compressors. Part 9: Stage F and stage G, volume 1

Two single-stage, 0.77 hub/tip ratio axial-flow compressors were tested to evaluate the effectiveness of low aspect ratio blading as a means of obtaining higher stage loadings. One compressor, designated Stage F, was comprised of circular arc blading with an aspect ratio of 0.9 for both the rotor and stator. This compressor was tested with uniform inlet flow, hub radial, tip radial, and 180 deg arc circumferential inlet distortion. The second compressor, designated Stage G, was comprised of multiple circular arc blading with an aspect ratio of 1.0 for both the rotor and stator. This compressor was tested with uniform inlet flow only. Design rotor tip speeds for Rotor F and Rotor G were 285 m/sec (934 ft/sec) and 327 m/sec (1,074 ft/sec) respectively. Both stages operated at high loading levels with adequate efficiency and operating range. The peak efficiencies and corresponding average stage diffusion factors for Stages F and G at design rotor speed were 86.4% and 84.1% and 0.59 and 0.55 respectively. The surge margin at peak efficiency for Stage F was 12.6% and the corresponding value for Stage G was 16.5%. Both stages experienced a loss in efficiency with increasing rotor speed; however, the multiple circular arc rotor delayed the characteristic loss in efficiency within increasing Mach number to higher Mach number.

Cheatham, J. G.↗