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At least 415 records · Page 23

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NASA NTRS1985

An experimental and analytical investigation of isolated rotor flap-lag stability in forward flight

For flap-lag stability of isolated rotors, experimental and analytical investigations are conducted in hover and forward flight on the adequacy of a linear quasi-steady aerodynamics theory with dynamic inflow. Forward flight effects on lag regressing mode are emphasized. Accordingly, a soft inplane hingeless rotor with three blades is tested at advance ratios as high as 0.55 and at shaft angles as high as 20 deg. The 1.62-m model rotor is untrimmed with an essentially unrestricted tilt of the tip path plane. By computerized symbolic manipulation, an analytical model is developed in substall to predict stability margins with mode indentification. It also predicts substall and stall regions to help explain the correlation between theory and data. The correlation shows both the strengths and weaknesses of the data and theory, and promotes further insights into areas in which further study is needed in substall and stall.

Gaonkar, Gopal H.↗

NASA NTRS1987

Analytical caustic surfaces

This document discusses the determination of caustic surfaces in terms of rays, reflectors, and wavefronts. Analytical caustics are obtained as a family of lines, a set of points, and several types of equations for geometries encountered in optics and microwave applications. Standard methods of differential geometry are applied under different approaches: directly to reflector surfaces, and alternatively, to wavefronts, to obtain analytical caustics of two sheets or branches. Gauss/Seidel aberrations are introduced into the wavefront approach, forcing the retention of all three coefficients of both the first- and the second-fundamental forms of differential geometry. An existing method for obtaining caustic surfaces through exploitation of the singularities in flux density is examined, and several constant-intensity contour maps are developed using only the intrinsic Gaussian, mean, and normal curvatures of the reflector. Numerous references are provided for extending the material of the present document to the morphologies of caustics and their associated diffraction patterns.

Schmidt, R. F.↗

NASA NTRS1988

An analytical method for ditching analysis of an airborne vehicle

A simple analytical method has been introduced for aerohydrodynamic load analysis of an airborne configuration during water ditching. The method employs an aerodynamic panel code, based on linear potential flow theory, to simulate the flow of air and water around an aircraft configuration. The free surface separating the air and water region is represented by doublet sheet singularities. Although all the theoretical load distributions are computed for air, provisions are made to correct the pressure coefficients obtained on the configuration wetted surfaces to account for the water density. As an analytical tool, the Vortex Separation Aerodynamic (VSAERO) code is chosen to carry out the present investigation. After assessing the validity of the method, its first application is to analyze the water ditching of the Space Shuttle configuration at a 12 degree attitude.

Linear potential flow↗

NASA NTRS1987

Investigation of the feasibility of an analytical method of accounting for the effects of atmospheric drag on satellite motion

An analytic technique for accounting for the joint effects of Earth oblateness and atmospheric drag on close-Earth satellites is investigated. The technique is analytic in the sense that explicit solutions to the Lagrange planetary equations are given; consequently, no numerical integrations are required in the solution process. The atmospheric density in the technique described is represented by a rotating spherical exponential model with superposed effects of the oblate atmosphere and the diurnal variations. A computer program implementing the process is discussed and sample output is compared with output from program NSEP (Numerical Satellite Ephemeris Program). NSEP uses a numerical integration technique to account for atmospheric drag effects.

Bozeman, Robert E.↗

NASA NTRS1988

Analytical determination of critical crack size in solar cells

Although solar cells usually have chips and cracks, no material specifications concerning the allowable crack size on solar cells are available for quality assurance and engineering design usage. Any material specifications that the cell manufacturers use were developed for cosmetic reasons that have no technical basis. Therefore, the Applied Solar Energy Corporation (ASEC) has sponsored a continuing program for the fracture mechanics evaluation of GaAs. Fracture mechanics concepts were utilized to develop an analytical model that can predict the critical crack size of solar cells. This model indicates that the edge cracks of a solar cell are more critical than its surface cracks. In addition, the model suggests that the material specifications on the allowable crack size used for Si solar cells should not be applied to GaAs solar cells. The analytical model was applied to Si and GaAs solar cells, but it would also be applicable to the semiconductor wafers of other materials, such as a GaAs thin film on a Ge substrate, using appropriate input data.

Chen, C. P.↗

NASA NTRS1988

Analytical approximation of a distorted reflector surface defined by a discrete set of points

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Acosta, Roberto J.↗

NASA NTRS1987

An analytical solution to obtain the optimum source location using multiple direction finders on a spherical surface

An analytical solution is presented for determining the optimum location of a radiating source on the surface of a sphere, given multiple bearings. The bearings are assumed to have small errors of the order of 0-10 deg. The optimum location is found by minimizing the sum of the squares of the perpendicular great-circle distances from the source to the bearing lines. This is achieved analytically through an eigenvalue approach, rather than the usual iterative, numerical approach. Bearings of different weight are taken into account by approximating the distance from each direction finder to the source. The result is general and may have wide application. Since it is simple and nearly as fast as the triangulation technique for source location, it is now used in the SUNY-Albany East Coast Lightning Detection Network to compute the optimum location for lightning in real time.

Orville, Richard E., Jr.↗

NASA NTRS1986

Analytical and experimental studies of the surface flaw

This paper uses the Newman-Raju model, the Paris crack growth rate law, and a fixed R ratio to demonstrate the analytical considerations associated with predicting stress intensity distributions and fatigue crack growth of surface flaws under conditions of small-scale yielding. Problems which lie outside the realm of the model used in the analytical description are presented. It is concluded that, while the model employed provides remarkable predictive capability in a variety of surface flaw problems, many exceptional cases remain to be modeled.

Smith, C. W.↗

NASA NTRS1988

Analytical and experimental validation of the Oblique Detonation Wave Engine concept

The Oblique Detonation Wave Engine (ODWE) for hypersonic flight has been analytically studied by NASA using the CFD codes which fully couple finite rate chemistry with fluid dynamics. Fuel injector designs investigated included wall and strut injectors, and the in-stream strut injectors were chosen to provide good mixing with minimal stagnation pressure losses. Plans for experimentally validating the ODWE concept in an arc-jet hypersonic wind tunnel are discussed. Measurements of the flow field properties behind the oblique wave will be compared to analytical predictions.

Adelman, Henry G.↗

NASA NTRS1988

An analytical method for the ditching analysis of an airborne vehicle

Pressure coefficient↗

NASA NTRS1988

An analytic-geometric model of the effect of spherically distributed injection errors for Galileo and Ulysses spacecraft - The multi-stage problem

In previous work the problem of injecting the Galileo and Ulysses spacecraft from low earth orbit into their respective interplanetary trajectories has been discussed for the single stage (Centaur) vehicle. The central issue, in the event of spherically distributed injection errors, is what happens to the vehicle? The difficulties addressed in this paper involve the multi-stage problem since both Galileo and Ulysses will be utilizing the two-stage IUS system. Ulysses will also include a third stage: the PAM-S. The solution is expressed in terms of probabilities for total percentage of escape, orbit decay and reentry trajectories. Analytic solutions are found for Hill's Equations of Relative Motion (more recently called Clohessy-Wiltshire Equations) for multi-stage injections. These solutions are interpreted geometrically on the injection sphere. The analytic-geometric models compare well with numerical solutions, provide insight into the behavior of trajectories mapped on the injection sphere and simplify the numerical two-dimensional search for trajectory families.

Longuski, James M.↗

NASA NTRS1988

Sampling Mars: Analytical requirements and work to do in advance

Sending a mission to Mars to collect samples and return them to the Earth for analysis is without doubt one of the most exciting and important tasks for planetary science in the near future. Many scientifically important questions are associated with the knowledge of the composition and structure of Martian samples. Amongst the most exciting questions is the clarification of the SNC problem- to prove or disprove a possible Martian origin of these meteorites. Since SNC meteorites have been used to infer the chemistry of the planet Mars, and its evolution (including the accretion history), it would be important to know if the whole story is true. But before addressing possible scientific results, we have to deal with the analytical requirements, and with possible pre-return work. It is unlikely to expect that a possible Mars sample return mission will bring back anything close to the amount returned by the Apollo missions. It will be more like the amount returned by the Luna missions, or at least in that order of magnitude. This requires very careful sample selection, and very precise analytical techniques. These techniques should be able to use minimal sample sizes and on the other hand optimize the scientific output. The possibility to work with extremely small samples should not obstruct another problem: possible sampling errors. As we know from terrestrial geochemical studies, sampling procedures are quite complicated and elaborate to ensure avoiding sampling errors. The significance of analyzing a milligram or submilligram sized sample and putting that in relationship with the genesis of whole planetary crusts has to be viewed with care. This leaves a dilemma on one hand, to minimize the sample size as far as possible in order to have the possibility of returning as many different samples as possible, and on the other hand to take a sample large enough to be representative. Whole rock samples are very useful, but should not exceed the 20 to 50 g range, except in cases of extreme inhomogeneity, because for larger samples the information tends to become redundant. Soil samples should be in the 2 to 10 g range, permitting the splitting of the returned samples for studies in different laboratories with variety of techniques.

Koeberl, Christian↗

NASA NTRS1989

Analytical model of a five degree of freedom magnetic suspension and positioning system

An analytical model of a five degree of freedom magnetic suspension and positioning system is presented. The suspended element is a cylinder which is composed of permanent magnet material and the magnetic actuators are air core electromagnets mounted in a planar array. The analytical model consists of an open loop representation of the suspension and positioning system with electromagnet currents as inputs and displacements and rates in inertial coordinates as outputs. The uncontrolled degree of freedom is rotation about the long axis of the suspended cylinder.

Groom, Nelson J.↗

NASA NTRS1988

A second-order analytic analysis for frozen orbits

An analytical method for studying characteristics of frozen orbits using mean orbital elements is presented. By removing some of the approximations of Brouwer and Kosai (1959) and using the method of integration by parts, an analytic solution is obtained accurate to the second order in the sense of expansion of the perturbing potential of an aspherical approximation. The solution applies to orbits at and near the critical inclination as well as to frozen orbits and, of course, to unfrozen orbits. The analysis reveals that a frozen orbit can be interpreted as an orbit in which movements of the long-periodic part of the rate of change of periapsis cancels the secular part exactly at any time.

Tang, Charles C. H.↗

NASA NTRS1989

An analytic development of orbit determination for a distant, planetary orbiter

With the advent of the Mariner '71 Mission, NASA has been sending spacecraft to orbit various distant bodies within the solar system. At present, there is still no adequate theory describing the inherent state estimation accuracy, based on two-way, coherent range-rate data. It is the purpose of this article to lay the groundwork for a general elliptic theory, and in addition to provide an analytic solution for the special case of circular orbits. It is shown that circular orbits about distant planets may suffer singularities in over-all position error estimation. These singularities are due to orbit inclination, placement of the line-of-nodes, and insignificant cross-velocity at the start and end of retrograde motion when orbiting a superior planet. Even though these conclusions appear to yield poor state estimation, one should not be unduly alarmed inasmuch as the stated conditions for singularity are not maintained for extended periods during typical mission scenarios. However, mission analysts should be aware of these potential pitfalls and realize that spuriously large results for circular orbiters can be obtained and are not the result of incorrect assumptions or faulty software. The general elliptic problem appears so involved that analytic inversion at this time is just not feasible, and in any case the resulting expression for the position error would likely be so lengthy that any understanding would be lost in the maze.

Russell, R. K.↗

NASA NTRS1989

Comparison of analytical methods for calculation of wind loads

The following analysis is a comparison of analytical methods for calculation of wind load pressures. The analytical methods specified in ASCE Paper No. 3269, ANSI A58.1-1982, the Standard Building Code, and the Uniform Building Code were analyzed using various hurricane speeds to determine the differences in the calculated results. The winds used for the analysis ranged from 100 mph to 125 mph and applied inland from the shoreline of a large open body of water (i.e., an enormous lake or the ocean) a distance of 1500 feet or ten times the height of the building or structure considered. For a building or structure less than or equal to 250 feet in height acted upon by a wind greater than or equal to 115 mph, it was determined that the method specified in ANSI A58.1-1982 calculates a larger wind load pressure than the other methods. For a building or structure between 250 feet and 500 feet tall acted upon by a wind rangind from 100 mph to 110 mph, there is no clear choice of which method to use; for these cases, factors that must be considered are the steady-state or peak wind velocity, the geographic location, the distance from a large open body of water, and the expected design life and its risk factor.

Minderman, Donald J.↗

NASA NTRS1990

A review of the analytical simulation of aircraft crash dynamics

A large number of full scale tests of general aviation aircraft, helicopters, and one unique air-to-ground controlled impact of a transport aircraft were performed. Additionally, research was also conducted on seat dynamic performance, load-limiting seats, load limiting subfloor designs, and emergency-locator-transmitters (ELTs). Computer programs were developed to provide designers with methods for predicting accelerations, velocities, and displacements of collapsing structure and for estimating the human response to crash loads. The results of full scale aircraft and component tests were used to verify and guide the development of analytical simulation tools and to demonstrate impact load attenuating concepts. Analytical simulation of metal and composite aircraft crash dynamics are addressed. Finite element models are examined to determine their degree of corroboration by experimental data and to reveal deficiencies requiring further development.

Fasanella, Edwin L.↗

NASA NTRS1989

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Podhorodeski, R. P.↗