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At least 793 records · Page 44

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NASA NTRS1974

Determining iconometric parameters of imaging devices using a wide-angle collimator

The problem of determining the iconometric parameters of the imaging device can be solved if the camera being calibrated is used to obtain the image of a group of reference points, the directions to which are known. In order to specify the imaging device coordinate system, it is sufficient in principle to obtain on the picture the images of three reference points which do not lie on a single straight line. Many more such points are required in order to determine the distortion corrections, and they must be distributed uniformly over the entire field of view of the camera being calibrated. Experimental studies were made using this technique to calibrate photographic and phototelevision systems. Evaluation of the results of these experiments permits recommending collimators for calibrating television and phototelevision imaging systems, and also short-focus small-format photographic cameras.

Ziman, Y. L.↗

NASA NTRS1974

Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades

The equations of motion are developed by two complementary methods, Hamilton's principle and the Newtonian method. The resulting equations are valid to second order for long, straight, slender, homogeneous, isotropic beams undergoing moderate displacements. The ordering scheme is based on the restriction that squares of the bending slopes, the torsion deformation, and the chord/radius and thickness/radius ratios are negligible with respect to unity. All remaining nonlinear terms are retained. The equations are valid for beams with mass centroid axis and area centroid (tension) axis offsets from the elastic axis, nonuniform mass and stiffness section properties, variable pretwist, and a small precone angle. The strain-displacement relations are developed from an exact transformation between the deformed and undeformed coordinate systems. These nonlinear relations form an important contribution to the final equations. Several nonlinear structural and inertial terms in the final equations are identified that can substantially influence the aeroelastic stability and response of hingeless helicopter rotor blades.

Hodges, D. H.↗

NASA NTRS1975

Calculations of the cosmic ray modulation in interplanetary space taking into account the possible dependence of the transport travel for the scattering of the particles and of the velocity of the solar winds on the angles they make with the helioequator plane: The case of isotropic diffusion

The modulation of galactic cosmic rays is studied by the magnetic heterogeneities stream on the assumption that the diffusion coefficient is reduced whereas the solar wind velocity is increased with the growth of the angle between the sun's rotation axis and the direction of solar plasma motion. The stationary plane problem of isotropic diffusion is solved as it applies to two cases: (1) with due account of particle retardation by the antiphermium mechanism; and (2) without an account of the above mechanism. This problem is solved by the grid method in the polar coordinate system. The results of the calculations are followed by a discussion of the method of solution and of the errors.

Dorman, L. I.↗

NASA NTRS1975

Supercritical wing sections 2, volume 108

A mathematical theory for the design and analysis of supercritical wing sections was previously presented. Examples and computer programs showing how this method works were included. The work on transonics is presented in a more definitive form. For design, a better model of the trailing edge is introduced which should eliminate a loss of fifteen or twenty percent in lift experienced with previous heavily aft loaded models, which is attributed to boundary layer separation. How drag creep can be reduced at off-design conditions is indicated. A rotated finite difference scheme is presented that enables the application of Murman's method of analysis in more or less arbitrary curvilinear coordinate systems. This allows the use of supersonic as well as subsonic free stream Mach numbers and to capture shock waves as far back on an airfoil as desired. Moreover, it leads to an effective three dimensional program for the computation of transonic flow past an oblique wing. In the case of two dimensional flow, the method is extended to take into account the displacement thickness computed by a semi-empirical turbulent boundary layer correction.

Bauer, F.↗

NASA NTRS1974

Measurement of the lidar cross sections of cube corner arrays for laser ranging of satellites

The satellite coordinate system necessary to describe the location and orientation of each cube corner in the array is discussed. The method of optical testing is described along with the gain function, and computational methods for deriving the gain function and experimental values for it. The velocity aberration is derived as a function of satellite orbit, a complete method for cross section evaluation is described, and finally the radar equation is described.

Minott, P. O.↗

NASA NTRS1974

Relativistic effects of the rotation of the earth on remote clock synchronization

A treatment is given of relativistic clock synchronization effects due to the rotation of the earth. Unlike other approaches, the point of view of an earth fixed coordinate system is used which offers insight to many problems. An attempt is made to give the reader an intuitive grasp of the subject as well as to provide formulae for his use. Specific applications to global timekeeping, navigation, VLBI, relativistic clock experiments, and satellite clock synchronization are discussed. The question of whether atomic clocks are ideal clocks is also treated.

Reinhardt, V.↗

NASA NTRS1975

Data analysis for Skylab proton spectrometer

The measured values are compared to values derived from a proton environment model. Spectral data are compared, the omni-directional fluxes are found, a range of assumed pitch angle distributions are established, and the values which would be seen by an idealized proton spectrometer immersed in the model environment are computed. The measured values and calculated values are summed over time, then ratiod to provide spectral correction factors. The data are tabulated according to location, pitch angle, energy, assumed pitch angle distribution, and orientation in the earth-fixed coordinate system. With the aid of this data, detailed corrections to the proton model environment are derived. Best-fit, energy-dependent pitch angle distributions are also obtained. Some information is derived concerning the east-west asymmetry.

Hill, C. W.↗

NASA NTRS1975

NASTRAN modifications for recovering strains and curvatures

Modifications to the NASTRAN structural analysis computer program are described. The modifications allow the recovery of strain and curvature data for the general two-dimensional elements, in addition to the usual stress data. Option features allow the transformation of the strain/curvature (or stress) data to a common coordinate system and representation at the grid points of the structural model rather than at the conventional element center locations. Usage information is provided which will allow present users of NASTRAN to easily utilize the new capability.

Hennrich, C. W.↗

NASA NTRS1975

Program to Optimize Simulated Trajectories (POST). Volume 1: Formulation manual

A general purpose FORTRAN program for simulating and optimizing point mass trajectories (POST) of aerospace vehicles is described. The equations and the numerical techniques used in the program are documented. Topics discussed include: coordinate systems, planet model, trajectory simulation, auxiliary calculations, and targeting and optimization.

Brauer, G. L.↗

NASA NTRS1974

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries.

Kouyoumjian, R. G.↗

NASA NTRS1974

Orientational invariance of the rotational transition probability in the sudden approximation

Semiclassical collisions of an atom with a rigid-rotor molecule are examined in the sudden approximation. The rotational transition probability is shown to be invariant with respect to the choice of orientation for the molecular coordinate system; this fact contradicts recently reported results of a computer analysis. The present analysis may lead to an improved interpretation of recent molecular beam measurements.

Stallcop, J. R.↗

NASA NTRS1974

The influence of the direction of the geomagnetic dipole on the position of the neutral sheet

An analysis of neutral sheet crossings detected by the NASA-Goddard Space Flight Center magnetometer on the Explorer 34 satellite has shown that the diurnal wobble of the geomagnetic dipole measurably influences the position of the neutral sheet at 30 earth radii. Viewed in the solar-ecliptic coordinate system, the dipole wobble originates from the 11 deg angle between the earth's spin axis and the dipole axis, has a period of 24 hours, and can be resolved into components of motion perpendicular and parallel to the earth-sun line. The perpendicular component exerts a torque on the magnetotail and causes the neutral sheet to pivot about an axis approximately parallel to the solar wind direction. The parallel component encourages the neutral sheet to move above and below the solar-magnetospheric equatorial plane with an amplitude of 1 earth radius. This latter motion is consistent with the neutral sheet's being hinged at a geocentric distance of 5.25 earth radii.

Bowling, S. B.↗

NASA NTRS1974

Secular-invariant relationships among internal geomagnetic field coefficients

Some features of the secular variation of the geomagnetic field are examined. Contours encircling constant magnetic flux (third adiabatic invariant), corresponding to a shell of field lines in secular motion, reveal a general westward drift that is longitude and latitude dependent (with minima in the north Pacific and south Atlantic areas). Some invariant relationships appear among the field coefficients in the tilted, centered dipole (geomagnetic) coordinate system.

Roederer, J. G.↗

NASA NTRS1974

Free geometric adjustment of the OSU/NGSP global network /solution WN-4/

The paper presents the results of the OSU WN 4 geometric adjustment for the coordinates of 152 satellite tracking stations. The results, when referred to the WN 4 ellipsoid of a = 6,378,127.8 m and 1/f = 298.25 produce geoid undulations consistent with dynamically determined ones. The average standard deviation in a Cartesian coordinate is plus or minus 4.0 m; in height, plus or minus 2.7 m. Comparisons with coordinates obtained from dynamic solutions show significant inconsistencies in the orientation of the coordinate systems.

Mueller, I. I.↗

NASA NTRS1975

Numerical solution of the Navier-Stokes equations with topography

A finite difference scheme for solving the equations of fluid motion in a generalized coordinate system has been constructed. The scheme conserves mass and all the first integral moments of the motion. The scheme also advectively 'almost conserves' second moments, in that the magnitude of implicit numerical smoothing is typically about an order smaller than explicit viscosity and diffusion. Calculations with the model support the theoretical conjecture that the difference scheme is stable whenever the analogous Cartesian scheme is stable. The scheme has been used to calculate dry atmospheric convection due to differential heating between top and bottom of mountainous terrain. The general small-scale characteristics of mountain up-slope winds have been simulated. In addition, the results have demonstrated the crucial role played by the eddy diffusivities and the environmental stability, in determining both the quantitative and the qualitative features of the circulation.

Gal-Chen, T.↗

NASA NTRS1975

Surface coordinates and cartography of Mercury

A control net of Mercury has been established photogrammetrically by using the Mariner 10 pictures; coordinates of 1328 points are given. The Mariner 10 coordinate system uses a system of longitudes in which the twentieth meridian passes through the center of the small crater Hun Kal and the spin axis is assumed normal to the orbital plane. A reference mosaic of Mercury has been published, and a series of 1:5,000,000 maps is now being produced.

Davies, M. E.↗

NASA NTRS1975

A generalized hyperbolic marching technique for three-dimensional supersonic flow with shocks

The current paper introduces a generalized, nonorthogonal coordinate system for application to supersonic flows with such large angles between streamlines of the initial Cauchy data and the marching direction that the velocity component in the marching direction is actually subsonic. Finite-difference operators are developed to solve the three-dimensional, steady, inviscid conservation equations of fluid flow referenced to this general frame. Moreover, a new method of aligning the difference mesh to the bow shock wave is presented which eliminates both the necessity for differencing the free-stream flow properties and the spurious fluctuations that often arise in conservative variables when they are differenced across the discontinuity. Results are given for the case of flow past a conical surface.

Rizzi, A. W.↗

NASA NTRS1975

Acoustic eigenmodes of corrugated ducts

Acoustic propagation in two-dimensional corrugated ducts is analyzed. A transform is made to a coordinate system that matches the duct walls. The resulting wave equation separates in space and time. The spatial differential equation is then solved by expanding in the eigenfunctions of a flat-walled duct. The prescription for this expansion is given by the appropriate application of time-independent perturbation theory. Calculations of first-order corrections for a periodic duct of both finite and infinite length are presented.

Succi, G. P.↗