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Three-dimensional system uses two additional mirrors and path compensators. It is essentially three mutually-orthogonal one-dimensional systems with common focus. Laser beam is split into four parts, three of which are object beams; and fourth is reference beam. Size of each ellipse depends on magnitude of velocity vectors.
A boundary layer approach for the solution of the flow field induced over a two-dimensional surface obstruction, such as a building or other man-made structure, is proposed. Adopting a specific geometry in the form of a semi-elliptical cylinder, the characteristics of atmospheric shear flow over a rough terrain are coupled with the well-known boundary layer equations. Two approaches are presented to incorporate the pressure field and boundary conditions which exist within the large viscous region over the obstruction. The first considers a region in the immediate vicinity of the body in which the pressure distribution and outer boundary condition on the velocity are computed from potential theory for flow over the elliptical cylinder. The second approach considers a much larger region of influence, extending from the surface to the undisturbed flow at large heights above the obstruction. Methods which appear to provide an improved theoretical model of the flow over the ellipse, such as a technique for simulating the effect of the seperation regions upstream and downstream of the body, are also presented.
The author has identified the following significant results. Lakes in the Arctic Coastal Plain of Alaska are dominantly elongate, with their long axes parallel and trending about N 9 W. On ERTS-1 imagery, an additional strong east-trending regional lineation, not previously recognized on aerial photographs or in field study, was noted. In addition, the alignment of many small lakes forms a large and a small ellipse superimposed on the regional lineation. Fischer and Lathram find that the trend of this lineation is parallel to the trend of deflections in contours of the magnetic and gravity fields in the area, and parallel to westerly deflections in the northwest ends of northwest-trending folds mapped to the south. These data suggest that heretofore unsuspected structures may be concealed beneath Quaternary mantling sediments in the area of the image. The strata in these folds would be younger than those tapped by the oil wells of the Umiat field to the south, and favorable sandstone facies may occur in the area. The significance of these observations to oil exploration in northern Alaska needs to be evaluated further.
The feasibility and practicality of employing an aerobraking trajectory for return of the reusable Space Tug from geosynchronous and other high energy missions was investigated. The aerobraking return trajectory modes from high orbits employ transfer ellipses which have low perigee altitudes wherein the earth's sensible atmosphere provides drag to reduce the Tug descent delta velocity requirements and thus decrease the required return trip propulsive energy. An aerobraked Space Tug, sized to the Space Shuttle payload capability and dimensional constraints, can accomplish 95 percent of the geosynchronous missions with a single Shuttle/Tug launch per mission. Aerodynamics, aerothermodynamics, trajectory, quidance and control, configuration concepts, materials, weights and performance parameters were identified. Sensitivities to trajectory uncertainties, atmospheric anomalies and re-entry environments were determined. New technology requirements and future studies required to further enhance the aerobraking potential were identified.
Using a singular solution for a part circular crack, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50 and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the ''equivalent'' semi-elliptical flaw results was not valid for a/2c less than 0.20. Best overall agreement for the moderate (a/t approximately 0.5) to deep flaws (a/t approximatelly 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory, when compared on the basis of equivalent flaw depth and area.
A simple stress intensity factor expression is given for a deep edge crack in a plate in tension. The shapes of cracks opened by tension or bending are approximated by conic sections, and the conic section coefficients are related to plate geometry by very simple empirical equations. The magnitude of the crack displacement is a function of applied load, plate geometry, and the elastic constants of the plate material. The shape of a loaded crack in a semiinfinite plate is, approximately, a portion of an ellipse whose semimajor axis is about three times the crack length. As the crack length (relative to the plate width) increases, the crack shape becomes parabolic, then hyperbolic, the acuity of the hyperbola increasing with the relative crack length.
Quantitative size and shape analyses have been carried out on six lunar fines from Apollo 14 and 15 by computer evaluation of scanning electron microscope images (CESEMI). For the size range of 0.50 to 30 microns diameter, the distributions are log-normal on a number count basis. This finding is in contrast with results for coarser materials in the fines reported by King et al. suggesting the operation of a different process. Aspect ratios range from 0.1 to 1.0 with an average value of about 0.6. Only slight differences are observed among samples. A shape complexity factor (ratio of particle perimeter to ellipse perimeter) also varies only slightly among the six samples.
An optimal Space Shuttle ascent-flyback trajectory shaping capability is presented which is based on the accelerated gradient parameter optimization technique. A typical atmospheric flight branched optimization problem is analyzed which required the determination of 31 parameters. This parameter set includes the description of the vehicle attitude control angles for three branches of Shuttle flight: first stage ascent, second stage ascent, and first stage flyback. The important in-flight inequality constraints required to maintain the integrity of the vehicle are considered. Results indicate that for a launch into a 55 deg inclined ellipse, a 13% increase in payload can be realized by using optimal control in the first-stage ascent rather than the conventional gravity-turn steering.
This study examines the yield criteria for anisotropic laminated media. It will be shown that for laminated media with isotropic layers, the criterion of Tsai and Wu is a direct extension of Von Mises'. Also presented here is a set of equations governing the relative positions of the yield ellipses. Furthermore, a general expression for the yield condition of a laminated medium composed of generally anisotropic layers is obtained.
The pattern of geodesic synchrotron radiation emitted by a charge in an orbit close to the circular photon orbit at 3M around a nonrotating black hole of mass M is studied. The analysis is carried out using Stokes parameters, which completely characterize the state of the wave. The linear polarization, as observed at infinity, is total in the orbital plane and not smaller than 90% at the half-width of the beam. At the poles, pure circular polarization would be observed. In the region between the orbit plane and the poles the polarization shows features not present in ordinary synchrotron radiation. In our model, parameters more sensitive to deviations from the orbital plane are the Stokes parameter s (sub 2) and the tilt angle of the polarization ellipse.
The relative motion of two particles on adjacent orbits about the same primary has been investigated under the condition that both motions have the same period. The geometrical properties of the relative displacement and velocity traces, on representative planes, are studied. A complete state of the motion is given; and, the range and range-rate variations, over one or more orbits, are described. It has been found that cusps appear on some of the traces provided that a proper relationship exists between the eccentricity and inclination. (Here, one particle moves on a circular path while the second moves on an ellipse). The conditions for which cusps appear are given, and typical traces are shown.
Analysis of the plasma processes and the hydromagnetic aspects involved in the evolution of the solar system. In order to reduce the speculative element as far as possible, the present analysis tries to connect the cosmogonic processes as directly as possible to laboratory plasma physics and to space phenomena actually observed today. Models of the Laplacian type have been made obsolete by magnetohydrodynamics. Furthermore they are in conflict with observations. A new model is suggested. A plasma surrounding a rotating central body may attain a state of partial corotation which is determined by the balance between gravitation and the centrifugal force acting on a plasma in a dipole field. Condensation from a partially corotating plasma results in grains orbiting in ellipses with e = 1/3 and finally accreting to bodies at 2/3 of the central distance of the point of condensation. An application of the theory of the Saturnian rings and to the asteroidal belt shows that the fall-down ratio 2/3 (derived from the geometry of a dipole field) is essential for the understanding of their structure. The structure of the groups of planets and satellites is also discussed, but only in a preliminary way.
An application of the compressibility correction developed by Lieblein and Stockman (1972) to the calculation of flow in axisymmetric inlets is described. The results with experimental data from wind tunnel model tests are compared. The configuration is a conventional subsonic inlet with a NACA series one external cowl shape and a two-to-one ellipse internal lip. It is shown that the compressibility correction gives a relatively good approximation to the internal compressible flow behavior, and thus should be useful in the design and analysis of engine nacelle inlets.
A holographic motion picture camera system producing resolution of front surface detail is described. The system utilizes a beam of coherent light and means for dividing the beam into a reference beam for direct transmission to a conventional movie camera and two reflection signal beams for transmission to the movie camera by reflection from the front side of a moving scene. The system is arranged so that critical parts of the system are positioned on the foci of a pair of interrelated, mathematically derived ellipses. The camera has the theoretical capability of producing motion picture holograms of projectiles moving at speeds as high as 900,000 cm/sec (about 21,450 mph).
Methods for solving three dimensional crack problems are discussed. The stress intensity factor for the case of uniform pressure on the surface crack is analysis. An analysis of concentrated forces acting on the crack faces parallel to the crack front of a half-plane crack was made. Two dimensional calculations were made using the exact solution for the stress field around an elliptical hole in a uniformly stretched plate. The strain energy density was computed in the neighborhood of the ends of narrow, but sharp, ellipses.
The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.
A computer code which rapidly calculates time optimal combined high- and low-thrust transfers between two geocentric orbits in the presence of a strong gravitational field has been developed as a mission analysis tool. The low-thrust portion of the transfer can be between any two arbitrary ellipses. There is an option for including the effect of two initial high-thrust impulses which would raise the spacecraft from a low, initially circular orbit to the initial orbit for the low-thrust portion of the transfer. In addition, the effect of a single final impulse after the low-thrust portion of the transfer may be included. The total Delta V for the initial two impulses must be specified as well as the Delta V for the final impulse. Either solar electric or nuclear electric propulsion can be assumed for the low-thrust phase of the transfer.
Methods are described for calculating left ventricular (LV) dimensions and chamber volumes from radiographic films. The use of biplane films for the calculation of LV volume and volume change is based on the assumption of an ellipsoidal geometry. Calculation of LV volumes from biplane films usually overestimated known volumes in postmortem hearts regardless of the methods used for volume calculation. The reasons for this are probably best explained by the fact that a smooth-surface ellipse is used to represent the irregular cavity of the LV chamber. LV volume calculated from data in a single plane compared favorably and closely with volumes calculated from biplane films. A table of normal values of ventricular volume established by angiographic studies is presented.