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NASA NTRS1972

Application of a one-strip integral method to the unsteady supersonic aerodynamics of an inclined flat surface

The method of integral relations is applied in a one-strip approximation to the perturbation equations governing small motions of an inclined, sharp-edged, flat surface about the mean supersonic steady flow. Algebraic expressions for low reduced-frequency aerodynamics are obtained and a set of ordinary differential equations are obtained for general oscillatory motion. Results are presented for low reduced-frequency aerodynamics and for the variation of the unsteady forces with frequency. The method gives accurate results for the aerodynamic forces at low reduced frequency which are in good agreement with available experimental data. However, for cases in which the aerodynamic forces vary rapidly with frequency, the results are qualitatively correct, but of limited accuracy. Calculations indicate that for a range of inclination angles near shock detachment such that the flow in the shock layer is low supersonic, the aerodynamic forces vary rapidly both with inclination angle and with reduced frequency.

Bennett, R. M.↗

NASA NTRS1973

Laminar film boiling on inclined isothermal flat plates.

Laminar film boiling from an inclined flat plate has been investigated analytically. Using the singular perturbation scheme, the complete set of Navier-Stokes equations is solved. The zeroth-order perturbation coinciding with the boundary-layer equations for vertical flat plates governs the problem. The higher-order perturbations become important near the leading edge and for large values of the inclination angle from the vertical. The assumption of zero interfacial velocity shows that, except for fluids having large (rho x mu) ratios, the results can be predicted using the vertical flat plate results by defining a modified Grashof parameter containing a cos phi term. When the interfacial shear is considered, the solutions indicate that for fluids having large (rho x mu) ratios, the heat transfer rates will be larger (approximately 15% maximum) than those predicted by the simplified model using zero interfacial velocity. In general, the inclination decreases the rate of heat transfer as well as the rate of evaporation.

Nagendra, H. R.↗

NASA NTRS1978

Critical inclinations in satellite theory

The main problem of satellite theory is described in polar coordinates by a Hamiltonian function. It is proposed to find a solution of the Hamiltonian function with the following properties: (1) the reference orbit is Keplerian; (2) no restriction is imposed on the eccentricity; in particular, it is exempt of singularities - real or apparent - for small eccentricities; and (3) no restriction is imposed on the inclination; in particular, it is exempt of singularities - real or apparent - for small inclinations; also it is valid even in the neighborhood of inclinations at which the perigee is stationary.

Deprit, A.↗

NASA NTRS1985

Microwave inversion of leaf area and inclination angle distributions from backscattered data

The backscattering coefficient from a slab of thin randomly oriented dielectric disks over a flat lossy ground is used to reconstruct the inclination angle and area distributions of the disks. The disks are employed to model a leafy agricultural crop, such as soybeans, in the L-band microwave region of the spectrum. The distorted Born approximation, along with a thin disk approximation, is used to obtain a relationship between the horizontal-like polarized backscattering coefficient and the joint probability density of disk inclination angle and disk radius. Assuming large skin depth reduces the relationship to a linear Fredholm integral equation of the first kind. Due to the ill-posed nature of this equation, a Phillips-Twomey regularization method with a second difference smoothing condition is used to find the inversion. Results are obtained in the presence of 1 and 10 percent noise for both leaf inclination angle and leaf radius densities.

Lang, R. H.↗

NASA NTRS1988

Evolution of inclined galactic gas disks. I - A cloud-fluid approach

In this paper, numerical models are developed to follow the time-dependent behavior of inclined gas disks in nonspherical galaxies. Differential equations are developed which describe the time rate of change of the orbits of mass elements composing a thin, smoothly warping and twisting gas disk. These equations include multiple moments due to the nonsphericity of the galactic mass distribution, Coriolis effects arising from determination of orbits in a reference frame which tumbles with the surface figure of the galaxy, and viscous forces arising from cloud-cloud collisions. A cloud-fluid approach is used in determining the viscous forces. Physical arguments are used to determine the maximum permissible local value of the coefficient of kinematic viscosity. For small initial inclinations, analytic expressions are obtained for the inclination as a function of time and for the settling time, and the features of the solution are discussed.

Steiman-Cameron, Thomas Y.↗

NASA NTRS1990

Ground-based experiments on thermal and thermosolutal convection in inclined low-aspect-ratio enclosures

Thermal and thermosolutal convection driven by buoyancy forces are investigated experimentally in inclined low-aspect-ratio enclosures. Thermal and thermosolutal convection are important in crystal growth processes. The transport process in the fluid phase during the growth of a crystal has a profound influence on the structure and quality of the solid phase. The present work is concerned with natural convection in a shallow rectangular enclosure with imposed inclined temperature and/or concentration gradients. Various complex flow patterns are observed with different experimental conditions. A flow instability under certain conditions is reported. The flow instability is found to depend not only on the thermal and solutal Grashof numbers, the aspect ratios, but also the inclined angles.

Wang, L. W.↗

NASA NTRS1990

Is the earth's dipole actually inclined with respect to the rotation axis?

Planetary exploration by deep space probes in recent years has shown that the dipole moment of some magnetized planets has a surprisingly large inclination angle with respect to the rotation axis. Applying the method developed for the source surface magnetic field of the sun (a spherical surface of 2.5 solar radii), it is suggested that the main dipole of the earth and the magnetized planets may actually be axial (the magnetic moment being parallel or antiparallel to the rotation axis), and that two or three smaller dipoles near the core surface could be responsible for the apparent inclination of the main dipole. In formulating a dynamo theory of the planetary magnetic field, such a possibility should be considered, as well as the inclined dipole case.

Akasofu, S.-I.↗

NASA NTRS1994

A test of source-surface model predictions of heliospheric current sheet inclination

The orientation of the heliospheric current sheet predicted from a source surface model is compared with the orientation determined from minimum-variance analysis of International Sun-Earth Explorer (ISEE) 3 magnetic field data at 1 AU near solar maximum. Of the 37 cases analyzed, 28 have minimum variance normals that lie orthogonal to the predicted Parker spiral direction. For these cases, the correlation coefficient between the predicted and measured inclinations is 0.6. However, for the subset of 14 cases for which transient signatures (either interplanetary shocks or bidirectional electrons) are absent, the agreement in inclinations improves dramatically, with a correlation coefficient of 0.96. These results validate not only the use of the source surface model as a predictor but also the previously questioned usefulness of minimum variance analysis across complex sector boundaries. In addition, the results imply that interplanetary dynamics have little effect on current sheet inclination at 1 AU. The dependence of the correlation on transient occurrence suggests that the leading edge of a coronal mass ejection (CME), where transient signatures are detected, disrupts the heliospheric current sheet but that the sheet re-forms between the trailing legs of the CME. In this way the global structure of the heliosphere, reflected both in the source surface maps and in the interplanetary sector structure, can be maintained even when the CME occurrence rate is high.

Burton, M. E.↗

NASA NTRS1994

East-west inclination of large-scale photospheric magnetic fields

Sixteen years of Wilcox Solar Observatory (WSO) magnetogram data have been studied to determine the solar cycle variation and latitude dependence of the east-west inclination of photospheric magnetic field lines. East-west inclination is here defined as the angle between a field line and its local radial vector, as projected onto the plane of the latitude and line of sight. Inclination is determined by a least-squares fit of observed magnetic fields to a simple projection model, and is found to depend on polarity and to change with the solar cycle. Leading and following polarities are tipped towards each by about 9 deg and have an overall net tilt in the direction of rotation (to the west) of 0.6 deg. New cycles are seen to begin at high latitudes and to grow through the lower latitudes over approximately 5 years, providing evidence for an extended cycle length of 16-18 years.

Shrauner, J. A↗

NASA NTRS1959

The Effect of Leading-Edge Sweep and Surface Inclination on the Hypersonic Flow Field Over a Blunt Flat Plate

An investigation of the effects of variation of leading-edge sweep and surface inclination on the flow over blunt flat plates was conducted at Mach numbers of 4 and 5.7 at free-stream Reynolds numbers per inch of 6,600 and 20,000, respectively. Surface pressures were measured on a flat plate blunted by a semicylindrical leading edge over a range of sweep angles from 0 deg to 60 deg and a range of surface inclinations from -10 deg to +10 deg. The surface pressures were predicted within an average error of +/- 8 percent by a combination of blast-wave and boundary-layer theory extended herein to include effects of sweep and surface inclination. This combination applied equally well to similar data of other investigations. The local Reynolds number per inch was found to be lower than the free-stream Reynolds number per inch. The reduction in local Reynolds number was mitigated by increasing the sweep of the leading edge. Boundary-layer thickness and shock-wave shape were changed little by the sweep of the leading edge.

Creager, Marcus O.↗

NASA NTRS2002

Inclination Angles of Black Hole X-Ray Binaries Manifest Strong Gravity around Black Holes

System inclination angles have been determined for about 15 X-ray binaries, in which stellar mass black holes are considered to exist. These inclination angles range between 25 degrees and 80 degrees, but peaked between 60-70 degrees. This peak is not explained in the frame work of Newtonian gravity. However, this peak is reproduced naturally if we model the observed X-ray radiations as being produced in the accretion disks very close to the black hole horizons, where the extremely strong general and special relativistic effects, caused by the extremely strong gravity near the black hole horizons, modify the local radiation significantly as the X-rays propagate to the remote observer. Therefore the peak of the inclination angle distribution provides evidence or strong gravity around stellar mass black holes.

Zhang, S. N.↗

NASA NTRS2012

Evidence for Quasi-Periodic X-ray Dips from an ULX: Implications for the Binary Motion and the Orbital Inclination

We report results from long-term X-ray (0.3-8.0 keY) monitoring of the ultraluminous X-ray source NGC 5408 X-1 with the Swift/X-Ray Telescope. Our primary results are: (1) the discovery of quasi-periodic dips in the X-ray intensity that recur on average every 243 days, (2) the detection of an energy-dependent (variability amplitude decreases with increasing energy), quasi-sinusoidal X-ray modulation with a period of 112.6 +/- 4 days the amplitude of which decreases during the second half of the light curve and (3) energy spectral evidence for an increase in photoelectric absorption during the last continuous segment of the data, possibly due to a change in the ionization state of the circumbinary material. We interpret the X-ray modulations in the context of binary motion in analogy to that seen in high-inclination low-mass X-ray binaries. If correct, this implies that NGC 5408 X-1 is in a binary with an orbital period of 243 +/- 23 days in contrast to the 115.5 day quasi-sinusoidal period previously reported. In addition, if the X-ray modulation is caused by vertically structured obscuring material in the accretion disk (similar to the phenomenon of dipping LMXBs), this would imply a high value for the inclination of the orbit. A comparison with estimates from accreting X-ray binaries suggests an inclination approx > 60 deg. We note that, in principle, a precessing accretion disk could also produce the observed X-ray modulations.

Pasham, Dheeraj R.↗

NASA NTRS2019

Localization of Binary Black Hole Mergers with Known Inclination

The localization of stellar-mass binary black hole mergers using gravitational waves is critical in understanding the properties of the binaries' host galaxies, observing possible electromagnetic emission from the mergers, or using them as a cosmological distance ladder. The precision of this localization can be substantially increased with prior astrophysical information about the binary system. In particular, constraining the inclination of the binary can reduce the distance uncertainty of the source. Here we present the first realistic set of localizations for binary black hole mergers, including different prior constraints on the binaries' inclinations. We find that prior information on the inclination can reduce the localization volume by a factor of 3. We discuss two astrophysical scenarios of interest: (i) follow-up searches for beamed electromagnetic/neutrino counterparts and (ii) mergers in the accretion disks of active galactic nuclei.

Corley, K. Rainer↗

NASA NTRSDate not supplied

The High Inclination Solar Mission (HISM)

The High Inclination Solar Mission (HISM) is an out-of-the-ecliptic solar sail mission concept for observing the Sun and the heliosphere. The mission profile is based on the Solar Polar Imager concept: initially spiraling in to a 0.48 AU ecliptic orbit, then increasing the orbital inclination at a rate of up to 10° degrees per year, ultimately reaching a heliographic inclination of >75°.The orbital profile is achieved using solar sails based on the sail design for the Solar Cruiser mission, currently in Phase-A study at NASA Marshall Space Flight Center. An initial instrument complement was assumed for the study, consisting of a combination of remote, in-situ, and plasma wave instruments with a total mass of 66 kg. These provide a comprehensive suite of instruments to study the solar polar regions and connections to the heliosphere. The 7,000 m sail used in the mission assessment is a direct extension of the 4-quadrant 1,666 m Solar Cruiser design and employs the same type of high strength composite boom, deployment mechanism, and membrane technology. The sail system modeled is spun (~1 rpm) to assure required boom characteristics with margin. The spacecraft bus features a fine-pointing 3-axisstabilized instrument platform that allows full science observations as soon as the spacecraft reaches a solar distance of 0.48 AU. The spacecraft provides 95W power to science instruments and 8 Gbit/day downlink capability.

solar sail↗

NASA NTRSDate not supplied

The ACCP Inclined Orbit Project: Enabling New and Synergistic Aerosol Remote Sensing Inversions

Atmospheric aerosols have high spatiotemporal variations due to their diverse sources including windblown dust, wildfires, volcanic eruptions, and anthropogenic emissions. These aerosols also have strong diurnal emission characteristics that influence long-range transport, air quality, Earth’s radiation budget, biogeochemical cycles, and weather forecasting. While current sensors can measure the steady-state of global 3D cloud and aerosol properties, we lack the observational datasets to discover the diurnal variability of aerosols, even at seasonal and regional scales, because these missions utilize sun synchronous orbits. An Aerosols and Clouds, Convection and Precipitation (ACCP) observing system has been established as part of NASA’s new Earth System Observatory (ESO) to fulfill the science needs presented in the 2017 Earth Science Decadal Survey. The selected ACCP architecture encompasses sensors in two orbit planes, one of which utilizes an inclined orbit (nominally ~55 degrees at a 407 km altitude) to advance our understanding of aerosol and cloud properties and target the dynamics of the cloud and aerosol processes on sub-daily time scales. The anticipated instrumentation suite for the ACCP Inclined Orbit Project is a Stereo Camera System, Polarimeter, Microwave Radiometer, Two-Frequency Radar, and Backscatter Lidar. The polarimeter is expected to have multiple wavelength bands and viewing angles to enable accurate retrievals of aerosol microphysical and optical properties. The backscatter lidar will provide vertical profiles of attenuated backscatter and depolarization ratio at two wavelengths, with better daytime signal-to-noise ratio than previous space-based lidar systems to improve aerosol detection/typing and estimates of aerosol optical properties. The stereo camera system, while designed primarily for clouds, will also provide aerosol plume heights and air motions at the plume heights. This invited presentation will provide (1) an overview of the ACCP Inclined Orbit Project, (2) a description of the new sensor capabilities and orbital characteristics, and (3) a preview of the potential for new synergistic aerosol inversion techniques.

John E Yorks↗

NASA NTRS1993

Flow and acoustic field due to an inclined plate with a downstream splitter

In the present work, the high Reynolds number flow past an inclined plate with a splitter plate placed in its wake is considered numerically. A numerical conformal mapping technique is employed to transform the two-plate system into the same number of cylinders: the flow field is assumed to be two-dimensional. The vortex shedding from the inclined plate is modelled using the discrete vortex method. It is shown that the splitter plate has a profound effect on the development of the flow over a range of values of a suitably defined offset parameter and for a range of positions of the leading edge of the splitter plate. The acoustic field is also calculated and the spectrum reflects the flow results.

DISCRETE VORTEX METHOD↗

NASA NTRS1969

Recovery considerations for possible high inclination long duration earth orbital missions

Problem areas are discussed and various solutions proposed. One of the major recovery problems encountered with missions having higher orbital inclinations than previous missions is the greater likelihood of severe weather conditions in the landing zones, especially if landing zones are optimized for orbital coverage considerations. Restricting the reentry window and increasing in-orbit wait times can partially eliminate the weather problem, but the possibility of emergency landings at higher latitudes still exists. It can be expected that the increased confidence level in spacecraft reliability that will exist by the time the high-inclination missions are flown will reduce the probabilities of an emergency landing in an unfavorable recovery location to a very low level.

Obriant, T. E.↗

NASA NTRS1975

Solutions of the motion of synchronous satellites with arbitrary eccentricity and inclination

A first order, semianalytical theory for the long term motion of resonant satellites is presented. The theory is valid for all eccentricities and inclinations and for all commensurability ratios. The method allows the inclusion of all the zonal and tesseral harmonics as well as luni solar perturbations and radiation pressure. The method is applied to a synchronous satellite including only the J sub 2 and J sub 22 harmonics. Global, long term solutions for this problem, eccentricity, argument of perigee, and inclination are obtained.

Nacozy, P. E.↗