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NASA NTRS1973

Ultraviolet reflectivity and geometrical albedo of Titan

Titan's geometrical albedo of 0.094 plus or minus 0.012 was measured at 4255 A with a 50-A bandpass. From this and the spectral measurements, the geometrical albedo was derived as a function of wavelength. It is found that the wavelength dependences of Titan's UV spectrum and of the spectrum of Saturn's Rings are remarkably similar. No trace of any absorption bands is apparent. These results imply that UV gaseous absorption and Rayleigh scattering play a strongly subdued role in Titan's atmosphere. Any homogeneous atmospheric model implies that the absorber responsible for Titan's UV spectral albedo varies strongly with wavelength. On the other hand, it is found that the UV observations can be satisfied by an absorber having a relatively weak dependence upon wavelength if an inhomogeneous atmospheric model is employed. In particular, a fine dust, which absorbs as the reciprocal of the wavelength, can explain the UV observations, provided that it is preferentially distributed high up in Titan's atmosphere where the optical depth from Rayleigh scattering is low.

Barker, E. S.↗

NASA NTRS1973

Finite element analysis of geometrically nonlinear problems

Recent developments in geometrically nonlinear finite element analysis are reviewed. Following a discussion of the theoretical bases for the construction of finite element equations for geometrically nonlinear analysis, the algorithmic tools for solving the resulting nonlinear equations of the complete system are described. Separate consideration is given to preinstability nonlinear analysis, the calculation of limit points, bifurcation points, and to postbifurcation analysis.

Gallagher, R. H.↗

NASA NTRS1974

Geometric distortions of opticommercial panoramic television systems

One of the problems solvable by the spaceborne television system, topographical surveying, makes high demands on image quality, particularly on the geometric distortions introduced by the television camera. It is the geometric distortions which determine measurement accuracy and, consequently, the possibility of creating reliable planetary surface maps. Comparative analysis of the different television systems capable of solving the problem showed that the requirements on quality of the transmitted images are best satisfied by television cameras with opticomechanical scanning. The design of panoramic television systems and the process of image construction by the opticomechanical camera are discussed. Results indicate that panoramic television cameras have the necessary instrumental accuracy and permit determination of the direction to objects with an error practically equal to the resolution.

Govorov, V. M.↗

NASA NTRS1975

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Estabrook, F. B.↗

NASA NTRS1976

On the surface brightness and geometric albedo of some Martian areas

High-quality photographs of Mars (red, yellow, green, and blue) are used to analyze the surface, limb, and south-polar-cap brightness of Mars. The surface brightness can be fitted with the Lommel-Seeliger reflection law. For the limb and polar-cap brightness, the method suggested by Lumme (1974) has been used to correct for smearing effects. It is found that the brightness increases noticeably when approaching the limb, that the upper limit to optical thickness of the atmosphere in the blue is 0.16, and that the corresponding single-scattering albedo is 0.55, both with uncertainties of about 15%. Values for the geometric albedo and the phase function (at 37-deg phase angle) are also obtained for both the atmosphere and the ground for a central meridian of 0 deg. The south polar cap in September 1973 was nearly circular, with a radius of about 8 deg (heliocentric longitude of 0 deg) and geometric albedos of 0.68 (red), 0.68 (yellow), 0.60 (green), and 0.53 (blue).

Lumme, K.↗

NASA NTRS1976

Computer modeling of electromagnetic problems using the geometrical theory of diffraction

Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.

Burnside, W. D.↗

NASA NTRS1977

Geometrical meaning of the curl operation when A dot curl A does not equal 0

We examine the geometrical interpretation of the vector operation curl for vector fields A such that A dot curl A does not equal 0. It is not possible to construct even locally a surface normal to field lines of A at all points; an explicit geometrical demonstration of this fact is given. Such fields do not admit the construction of orthogonal curvilinear coordinates in which one set of coordinate curves lies along field lines of A.

Barnes, A.↗

NASA NTRS1978

Numerical procedure to determine geometric view factors for surfaces occluded by cylinders

A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.

Sawyer, P. L.↗

NASA NTRS1978

Analysis of simulated measurements of earth emitted radiation using geometric shape factors, and some results from analysis of ESSA 7 and Nimbus 6 data

In the reported study, simulated measurements of earth radiation with wide field-of-view (WFOV) radiometers are reduced to earth fluxes through geometric shape factors. Estimates of emitted flux for global and zonal scales and for regions smaller than the detector field-of-view are compared to fluxes derived directly from a model. Geometric shape factors are used to estimate global, zonal, and regional averages of earth-emitted flux from measurements with WFOV detectors on the ESSA 7 satellite and the Nimbus 6 satellite. Zonal and global averages of emitted flux for each of the 3-month periods of ESSA 7 data are shown in a graph. Another graph shows zonal and global averages of emitted flux for August 1975 obtained with the aid of Nimbus 6. The data are compared to values reported by Green and Smith (1977) who used a spherical harmonic solution.

Weaver, W. L.↗

NASA NTRS1979

Influence of optimized leading-edge deflection and geometric anhedral on the low-speed aerodynamic characteristics of a low-aspect-ratio highly swept arrow-wing configuration

An investigation conducted in the Langley 7 by 10 foot tunnel to determine the influence of an optimized leading-edge deflection on the low speed aerodynamic performance of a configuration with a low aspect ratio, highly swept wing. The sensitivity of the lateral stability derivative to geometric anhedral was also studied. The optimized leading edge deflection was developed by aligning the leading edge with the incoming flow along the entire span. Owing to spanwise variation of unwash, the resulting optimized leading edge was a smooth, continuously warped surface for which the deflection varied from 16 deg at the side of body to 50 deg at the wing tip. For the particular configuration studied, levels of leading-edge suction on the order of 90 percent were achieved. The results of tests conducted to determine the sensitivity of the lateral stability derivative to geometric anhedral indicate values which are in reasonable agreement with estimates provided by simple vortex-lattice theories.

Coe, P. L., Jr.↗

NASA NTRS1980

Geometric modeling and analysis of large latticed surfaces

The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design.

Nayfeh, A. H.↗

NASA NTRS1980

Simulation study of geometric shape factor approach to estimating earth emitted flux densities from wide field-of-view radiation measurements

A study was performed on the use of geometric shape factors to estimate earth-emitted flux densities from radiation measurements with wide field-of-view flat-plate radiometers on satellites. Sets of simulated irradiance measurements were computed for unrestricted and restricted field-of-view detectors. In these simulations, the earth radiation field was modeled using data from Nimbus 2 and 3. Geometric shape factors were derived and applied to these data to estimate flux densities on global and zonal scales. For measurements at a satellite altitude of 600 km, estimates of zonal flux density were in error 1.0 to 1.2%, and global flux density errors were less than 0.2%. Estimates with unrestricted field-of-view detectors were about the same for Lambertian and non-Lambertian radiation models, but were affected by satellite altitude. The opposite was found for the restricted field-of-view detectors.

Weaver, W. L.↗

NASA NTRS1980

Geometric methods in computational fluid dynamics

General methods for the construction of geometric computational fluid dynamic algorithms are presented which simulate a variety of flow fields in various nontrivial regions. Included are: basic developments with tensors; various forms for the equations of motion; generalized numerical methods and boundary conditions; and methods for mesh generation to meet the strong geometric constraints of turbomachines. Coordinate generation is shown generally to yield mesh descriptions from one or more transformations that are smoothly joined together to form a composite mesh.

Eiseman, P. R.↗

NASA NTRS1980

Some important geometrical features of conic-section-generated offset reflector antennas

Geometrical characteristics of conic-section-generated offset reflectors are studied in a unified fashion. Some unique geometrical features of the reflector rim constructed from the intersection of the reflector surface and a cone or cylinder are explored in detail. It is found that the intersection curve (rim) of the rotationally generated conic-section reflector surface and a circular cone with its tip at the focal point is always a planar curve and has a circular projection on the focal plane only for the offset parabolic reflector. Furthermore, in this case, the line going through the center of the circle, parallel to the focal axis, and the central axis of the cone do not intersect the reflector surface at the same point. Numerical results are presented to demonstrate some unique features of offset parabolic reflectors.

Jamnejad-Dailami, V.↗

NASA NTRS1980

Geometrical rectification of spin-scan images from Pioneer 11

Images of Saturn received from Pioneer 11 suffer from geometrical distortions due to the curvilinear scan lines and the unequal sampling intervals in orthogonal directions, which are inherent in spin-scan imaging. In this paper geometrical image rectification by polynomial transformation based on control points is discussed. Factors that affect the accuracy of reconstruction are shown to include the spatial distribution and spatial density of control points, and the order of the polynomial distortion model. A computer implementation of the technique is described.

Strickland, R. N.↗

NASA NTRS1981

Comparisons between geometrical optics and Lorenz-Mie theory

Both the Lorenz-Mie and geometrical optics theories are used in calculating the scattered light patterns produced by transparent spherical particles over a wide range of diameters, between 1.0 and 100 microns, and for the range of forward scattering angles from zero to 20 deg. A detailed comparison of the results shows the greater accuracy of the geometrical optics theory in the forward direction. Emphasis is given to the simultaneous sizing and velocimetry of particles by means of pedestal calibration methods.

Ungut, A.↗

NASA NTRS1982

Geometric verification

Present LANDSAT data formats are reviewed to clarify how the geodetic location and registration capabilities were defined for P-tape products and RBV data. Since there is only one geometric model used in the master data processor, geometric location accuracy of P-tape products depends on the absolute accuracy of the model and registration accuracy is determined by the stability of the model. Due primarily to inaccuracies in data provided by the LANDSAT attitude management system, desired accuracies are obtained only by using ground control points and a correlation process. The verification of system performance with regards to geodetic location requires the capability to determine pixel positions of map points in a P-tape array. Verification of registration performance requires the capability to determine pixel positions of common points (not necessarily map points) in 2 or more P-tape arrays for a given world reference system scene. Techniques for registration verification can be more varied and automated since map data are not required. The verification of LACIE extractions is used as an example.

Grebowsky, G. J.↗

NASA NTRS1982

The far-ultraviolet spectra and geometric albedos of Jupiter and Saturn

Spectra and geometric albedoes in the range 1200 to 1940 A are compiled for Jupiter and Saturn on the basis of IUE observations. The spectra of both planets are dominated by H Lyman-alpha emission line at 1216 A, although absorption bands of C2H2 are apparent at longer wavelengths, particularly in the spectrum of Saturn, and the C I line at 1657 A is also observed. Geometric albedoes show emission features corresponding to the weak H2 Lyman and Werner bands around 1230-1280 A, auroral Lyman band emission, C I emission, and C2H2 absorption from 1600 to 1900 A. A model of atmospheric absorption in homogeneously mixed atmospheres of H2 and trace molecular absorbers is then presented and fit to the Jupiter albedo, resulting in a predicted atmosphere containing C2H2 and an unidentified molecular or particulate absorber. Finally, north-south maps of Jupiter continuum emission show limb darkening, and a comparison of equatorial and polar spectra indicates a polar increase in C2H2 absorption and weaker polar H2 emissions than previously reported.

Clarke, J. T.↗