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NASA NTRS1972

The mass-zero spin-two field and gravitational theory.

Demonstration that the conventional theory of the mass-zero spin-two field with sources introduces extraneous nonspin-two field components in source regions and fails to be covariant under the full or restricted conformal group. A modified theory is given, expressed in terms of the physical components of mass-zero spin-two field rather than in terms of 'potentials,' which has no extraneous components inside or outside sources, and which is covariant under the full conformal group. For a proper choice of source term, this modified theory has the correct Newtonian limit and automatically implies that a symmetric second-rank source tensor has zero divergence. It is shown that possibly a generally covariant form of the spin-two theory derived here can be constructed to agree with general relativity in all currently accessible experimental situations.

Coulter, C. A.↗

NASA NTRS1972

Theoretical frameworks for testing relativistic gravity. IV - A compendium of metric theories of gravity and their post-Newtonian limits.

Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.

Ni, W.-T.↗

NASA NTRS1973

Spacetimes with Killing tensors

The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.

Hughston, L. P.↗

NASA NTRS1974

On evaluating compliance with air pollution levels 'not to be exceeded more than once a year'

Under a sampling program operated in conformity with EPA guidelines, calculational procedures are described for estimating the corresponding ambient pollution level. The statistical independence of the data, the commutativity of expectation and exponential operations, and the statistical variability of the calculated results are quantitatively evaluated. It is shown that the recommended sampling frequencies of every third to every sixth day are inadequate in determining conformity when the standards are expressed as levels not to be exceeded more than once a year.

Neustadter, H. E.↗

NASA NTRS1975

Raman spectra of gases. XVI - Torsional transitions in ethanol and ethanethiol

The Raman spectra of gaseous ethanol and ethanethiol have been investigated. Thiol torsional fundamentals for the gauche conformer of EtSH and EtSD have been observed and the asymmetric potential function for this vibration has been calculated. Methyl torsional transitions and overtones have also been observed for both of these molecules. Barriers to internal rotation for the methyl top are calculated to be 3.77 and 3.84 kcal/mol for the EtSH and EtSD compounds, respectively. Hydroxyl torsional fundamentals were observed at 207 and 170 per cm in the EtOH and EtOD spectra, respectively. Overtones of the methyl torsion in both molecules yield a barrier to internal rotation of 3.62 kcal/mol for the gauche conformer.

Durig, J. R.↗

NASA NTRS1976

Extending the Lorentz transformation by characteristic coordinates

The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in a restricted region near the axis of the motion. In such coordinates the velocity of light remains invariant even for observers moving with variable velocity. By a particular choice of the scale relation the restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of constant velocity and locally in the case of variable velocity.

Jones, R. T.↗

NASA NTRS1976

Analysis of accelerated motion in the theory of relativity

Conventional treatments of accelerated motion in the theory of relativity have led to certain difficulties of interpretation. Certain reversals in the apparent gravitational field of an accelerated body may be avoided by simpler analysis based on the use of restricted conformal transformations. In the conformal theory the velocity of light remains constant even for experimenters in accelerated motion. The problem considered is that of rectilinear motion with a variable velocity. The motion takes place along the x or x' axis of two coordinate systems.

Jones, R. T.↗

NASA NTRS1975

Vibrational spectra and structure of biphosphine and biphosphine-d4

Infrared and Raman spectra have been obtained for biphosphine and biphosphine-d4 in both solid and vapor phases. From the spectral data, it is concluded that only one conformer exists in both solid and fluid phases and that this is the gauche conformer. A normal-coordinate analysis has also been performed, in which the 24 vibrational frequencies of the two isotopes have been fitted by 10 force constants to an overall average error of 1.0%. The PED indicates that there is practically no mixing of the normal modes in the P2H4 molecule but the P-P stretch and the PD2 wagging modes are extensively mixed for the P2D4 molecule.

Odom, J. D.↗

NASA NTRS1977

Transformations from an oblate spheroid to a plane and vice versa: The equations used in the cartographic projection program MAP2

The relationships between the coordinates of a point on the surface on an oblate spheroid and the coordinates of the projection of that point in several common map projections are discussed. Because several of the projections are conformal, the theory of conformally mapping an oblate spheroid to the plane is summarized. For each projection considered, the equations which map the spheroid to the plane and their inverses are given.

Elliott, D. A.↗

NASA NTRS1974

Raman spectra of gaseous and solid N2F4

The Raman spectrum of gaseous N2F4 at a pressure of 760 Torr was recorded with a spectral slit width of 3 kaysers. Ten of the expected eleven fundamentals of the symmetric motions of both the gauche and trans isomers give rise to strongly polarized Raman lines. These new data require a reassignment of some of the fundamentals for both the C2 and C2h conformers. The Raman of the solid at 18 K was also recorded. Both conformers were found in the solid even after annealing the sample for 9 hr at a temperature of 101.6 K and 3 hr at a temperature of 106.8 K. Bands attributable to the gauche isomer became more intense relative to those for the trans isomer after several hours of annealing.

Durig, J. R.↗

NASA NTRS1977

Calculation of transonic potential flowfields about complex, three-dimensional configurations

Methods for extending iterative, finite-difference calculations of transonic potential flowfields to complex three-dimensional configurations are discussed. One particularly attractive approach is to use relatively simple conformal mappings in combination with shearing transformations to generate computational domains that are nearly-conformally mapped from the physical space in one family of coordinate surfaces, and which map the complex boundaries to grid surfaces. The application of such a method to a general wing-body combination or to a multi-bladed fan is discussed. A transformation to map the wing-fuselage or fan-hub combination to a convenient computational domain is proposed. The transformation is useful in its own right for treating the two-dimensional problems of flow past a profile in a wind tunnel or through a cascade. Some results of preliminary calculations are presented.

Caughey, D. A.↗

NASA NTRS1979

An improved supersonic, three-dimensional, external, inviscid flow field code

A numerical procedure was developed to compute the inviscid super/hypersonic flow fields about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects for equilibrium air are included using curve fits of Mollier charts. This report deals only with modifications to these procedures in four specific areas: inlet mass ingestion, subsonic axial Mach number, improved conformal mappings, and vehicles flying at yaw. In each area both the modifications to the computational procedures and computer code are discussed.

Marconi, F.↗

NASA NTRS1979

Logarithmic spiral grids for image processing

A picture digitization grid based on logarithmic spirals rather than Cartesian coordinates is presented. Expressing this curvilinear grid as a conformal exponential mapping reveals useful image processing properties. The mapping induces a computational simplification that suggests parallel architectures in which most geometric transformations are effected by data shifting in memory rather than arithmetic on coordinates. These include fast, parallel noise-free rotation, scaling, and some projective transformations of pixel defined images. Conformality of the mapping preserves local picture-processing operations such as edge detection.

Weiman, C. F. R.↗

NASA NTRS1980

Grid generation using classical techniques

A brief historical review of conformal mapping and its applications to problems in fluid mechanics and electromagnetism is presented. The use of conformal mapping as a grid generator is described. The philosophy of the 'closed form' approach and its application to a Neumann problem is discussed. Karman-Trefftz mappings and grids for ablated, three dimensional bodies are also discussed.

Moretti, G.↗

NASA NTRS1981

An evaluation of head-up displays in civil transport operations

To determine the advantages and disadvantages of head-up displays (HUD) in civil transport approach and landing operations, an operational evaluation was conducted on the flight simulator for advanced aircraft at Ames. A non-conformal HUD concept which contained raw data and Flight Director command information, and a conformal, flight path HUD concept was designed to permit terminal area maneuvering, intercept, final approach, flare, and landing operations. Twelve B-727 line pilots (Captains) flew a series of precision and non-precision approaches under a variety of environmental and operational conditions, including wind shear, turbulence and low ceilings and visibilities. A preliminary comparison of various system and pilot performance measures as a function of display type (Flight Director HUD, Flight Path HUD, or No HUD) indicates improvements in precision and accuracy of aircraft flight path control when using the HUDs. The results also demonstrated some potentially unique advantages of a flight path HUD during non-precision approaches.

Lauber, J. K.↗

NASA NTRS1981

Food packing optimization

The development of a universal closure lid for the space shuttle food package is reported. The revised lid needs a folded configuration which, when unfolded, fully conforms to the interior surfaces of the food cup. Experimental thermoform molds were fabricated and test lids formed. The lid material not in contact with the food conformed to the cup interior without wrinkles, permitting full nesting of the cups. The final lid design was established and thermoform tooling designed and fabricated. Lids formed on these molds were tested for strength. The heating elements were replaced and repositioned to eliminate any hot spots which may cause warpage.

Source record↗

NASA NTRS1982

Map projections for larger-scale mapping

For the U.S. Geological Survey maps at 1:1,000,000-scale and larger, the most common projections are conformal, such as the Transverse Mercator and Lambert Conformal Conic. Projections for these scales should treat the Earth as an ellipsoid. In addition, the USGS has conceived and designed some new projections, including the Space Oblique Mercator, the first map projection designed to permit low-distortion mapping of the Earth from satellite imagery, continuously following the groundtrack. The USGS has programmed nearly all pertinent projection equations for inverse and forward calculations. These are used to plot maps or to transform coordinates from one projection to another. The projections in current use are described.

Snyder, J. P.↗

NASA NTRS1982

Molecular structure of r/GCG/d/TATACGC/ - A DNA-RNA hybrid helix joined to double helical DNA

The molecule r(GCG)d(TATACGC) is self-complementary and forms two DNA-RNA hybrid segments surrounding a central region of double helical DNA; its molecular structure has been solved by X-ray analysis. All three parts of the molecule adopt a conformation which is close to that seen in the 11-fold RNA double helix. The conformation of the ribonucleotides is partly determined by water molecules bridging between the ribose O2' hydroxyl group and cytosine O2. The hybrid-DNA duplex junction contains no structural discontinuities. However, the central DNA TATA sequence has some structural irregularities.

Wang, A. H.-J.↗