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At least 631 records · Page 35

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NASA NTRS1974

Use of Green's functions in the numerical solution of two-point boundary value problems

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

Gallaher, L. J.↗

NASA NTRS1974

Optimal rocket thrust profile shaping using third degree spline function interpolation

Optimal solid-rocket thrust profiles for the parallel-burn, solid-rocket-assisted space shuttle are investigated. Solid-rocket thrust profiles are simulated by using third-degree spline functions, with the values of the thrust ordinates defined as parameters. The profiles are optimized parametrically, using the Davidon-Fletcher-Powell penalty function method, by minimizing propellant weight subject to state and control inequality constraints and to terminal boundary conditions. This study shows that optimizing a control variable parametrically by using third-degree spline function interpolation allows the control to be shaped so that inequality constraints are strictly adhered to and all corners are eliminated. The absence of corners, which is realistic in nature, makes this method attractive from the viewpoint of solid rocket grain design.

Johnson, I. L.↗

NASA NTRS1974

Effect of prolonged space flight on cardiac function and dimensions

Echocardiographic studies were performed preflight 5 days before launch and on recovery day and 1, 2, 4, 11, 31 and 68 days postflight. From these echocardiograms measurements were made. From these primary measurements, left ventricular end-diastolic volume, end-systolic volume, stroke volume, and mass were derived using the accepted assumptions. Findings in the Scientist Pilot and Pilot resemble those seen in trained distance runners. Wall thickness measurements were normal in all three crewmembers preflight. Postflight basal studies were unchanged in the Commander on recovery day through 68 days postflight in both the Scientist Pilot and Pilot, however, the left ventricular end-diastolic volume, stroke volume, and mass were decreased slightly. Left ventricular function curves were constructed for the Commander and Pilot by plotting stroke volume versus end-diastolic volume. In both astronauts, preflight and postflight data fell on the same straight line demonstrating that no deterioration in cardiac function had occurred. These data indicate that the cardiovascular system adapts well to prolonged weightlessness and suggest that alterations in cardiac dimensions and function are unlikely to limit man's future in space.

Henry, W. L.↗

NASA NTRS1974

Pulmonary function evaluation during and following Skylab space flights

Previous experience during the Apollo postflight exercise testing indicated no major changes in pulmonary function. Although pulmonary function has been studied in detail following exposure to hypoxic and hyperoxic environments, few studies have dealt with normoxic environments at reduced total pressure as encountered during the Skylab missions. Forced vital capacity was measured during the preflight and postflight periods of the Skylab 2 mission. Initial in-flight measurements of vital capacity were obtained during the last two weeks of the second manned mission (Skylab 3). Comprehensive pulmonary function screening was accomplished during the Skylab 4 mission. The primary measurements made during Skylab 4 testing included residual volume determination, closing volume, vital capacity, and forced vital capacity and its derivatives. In addition, comprehensive in-flight vital capacity measurements were made during the Skylab 4 mission. Vital capacity was decreased slightly during flight in all Skylab 4 crewmen. No major preflight to postflight changes were observed in the other parameters.

Sawin, C. F.↗

NASA NTRS1975

A photometric function for diffuse reflection by particulate materials

A photometric function is proposed to describe the diffuse reflection of radiation by particulate materials. Both multiple scattering and the dominant effects of particle shadowing are included and the function is verified by comparisons with the photometries of laboratory surfaces. Brightness measurements of planetary and other diffusely scattering surfaces can be used to calculate the brightness for geometries other than those used in the measurements and for which the Minnaert function does not apply. The measurements also can be directly related to such surface characteristics as particle size, single-particle albedo, and compactness.

Meador, W. E.↗

NASA NTRS1974

Stability properties of functional difference equations

Hale and Cruz (1970) have defined the concept of a stable difference operator, and have found that this class of operators is sometimes 'super sensitive' to perturbations. In the present paper, a subclass of general functional difference equations is derived which retain their stability under appropriate perturbations. Also, the results of Hale and Cruz are extended to include difference equations on the Banach space of p-th power integrable functions, and essentially bounded functions.

Melvin, W. R.↗

NASA NTRS1975

Velocity autocorrelation functions in model liquid metals

Starting from interatomic potentials and static radial distribution functions, a self-consistent iteration scheme has been used to calculate velocity autocorrelation functions in liquid metals. The interatomic forces are treated directly. The calculation bypasses the details of the many-body dynamics and it is not necessary to introduce any additional parameters. Several simplifications may be used without introducing appreciable deviations. The results are in good agreement with computer experiments on liquid sodium at 383 K, suggesting that the velocity autocorrelation function may be a simpler quantity than previously supposed.

Tsang, T.↗

NASA NTRS1974

Distinguishing between CAT and non-CAT areas by use of discriminant function analysis

The investigation considered is concerned with a method in which a statistical approach is employed to determine algebraic functions involving selected synoptic-scale parameters which would indicate areas and altitudes of CAT in the stratosphere over the western U.S. The statistical approach selected is based on discriminant function analysis. The functions are determined from combinations of synoptic-scale parameters and stratospheric turbulence data. It was found in the investigation that there is a relationship between selected combinations of synoptic-scale parameters of the upper troposphere and lower stratosphere and stratospheric clear-air turbulence.

Clark, T. L.↗

NASA NTRS1975

A transformation method for constrained-function minimization

A direct method for constrained-function minimization is discussed. The method involves the construction of an appropriate function mapping all of one finite dimensional space onto the region defined by the constraints. Functions which produce such a transformation are constructed for a variety of constraint regions including, for example, those arising from linear and quadratic inequalities and equalities. In addition, the computational performance of this method is studied in the situation where the Davidon-Fletcher-Powell algorithm is used to solve the resulting unconstrained problem. Good performance is demonstrated for 19 test problems by achieving rapid convergence to a solution from several widely separated starting points.

Park, S. K.↗

NASA NTRS1976

An evaluation of the method for determining the Whitham F-function using distributions of downwash and sidewash angles

The method of computing the Whitham F function using distributions of downwash and sidewash angles was evaluated with two different models. F functions which were calculated for a half angle cone cylinder at M infinites = 2.01, using theoretically and experimentally derived flow angles, show that the method is sensitive to small inaccuracies in the measured flow angles. An oblique wing transport model was tested at 0 deg angle of attack at M infinitely = 2.01. In this test, two different probes were used at two different distances from the model. The pressure signature derived from the F function was extrapolated and compared to the pressure signature measured at the distance of 0.87 body lengths with the static pressure probe. The agreement between the two pressure signatures was poor due to the many inaccuracies involved in using a probe designed to measure flow angularity.

Mendoza, J. P.↗

NASA NTRS1976

Coefficients of associated Legendre functions

The exact coefficients for the explicit forms of the associated Legendre functions Pm for integer values of m,n=0,1,2,...25 are presented in tabular form together with two cross-referenced listings of the zeroes for these functions rounded to five decimal places. The unfactored coefficients and the interger coefficients are presented in adjacent columns for each function. The greatest common factor and divisor have been removed and listed separately for the integer coefficients.

Peasley, Q. D.↗

NASA NTRS1976

Partition function corrections

The vibration-rotation interaction coupling in diatomic molecules is analyzed and first-order expressions for the energy levels are deduced. Corrections to the partition function to account for this coupling are derived. The effects of long-range intermolecular forces due to induced dipole-induced dipole interactions, dipole-induced dipole interactions, charge-dipole interactions, and charge-charge interactions are considered. London's quantized oscillator model of the induced dipole-induced dipole interaction is developed. The partition function including effects of such dispersion forces is derived and is shown to lead to the virial equation of state. For a model combining the hard sphere and long-range attractive type potentials, this is found to lead to the van der Waals equation of state. The equation of state near the critical point is presented in reduced form (thermodynamic variables expressed in units of critical point values). Finally, approximate corrections to the electronic partition functions are derived to account for perturbations of excited electronic states induced by neighboring neutral particles, heavy ions, and fast electron collisions.

Source record↗

NASA NTRS1976

The proper weighting function for retrieving temperatures from satellite measured radiances

One class of methods for converting satellite measured radiances into atmospheric temperature profiles, involves a linearization of the radiative transfer equation: delta r = the sum of (W sub i) (delta T sub i) where (i=1...s) and where delta T sub i is the deviation of the temperature in layer i from that of a reference atmosphere, delta R is the difference in the radiance at satellite altitude from the corresponding radiance for the reference atmosphere, and W sub i is the discrete (or vector) form of the T-weighting (i.e., temperature weighting) function W(P), where P is pressure. The top layer of the atmosphere corresponds to i = 1, the bottom layer to i = s - 1, and i = s refers to the surface. Linearization in temperature (or some function of temperature) is at the heart of all linear or matrix methods. The weighting function that should be used is developed.

Arking, A.↗

NASA NTRS1976

Advanced space system concepts and their orbital support needs (1980 - 2000). Volume 3: Detailed data. Part 1: Catalog of initiatives, functional options, and future environments and goals

The following areas were discussed in relation to a study of the commonality of space vehicle applications to future national needs: (1) index of initiatives (civilian observation, communication, support), brief illustrated description of each initiative, time periods (from 1980 to 2000+) for implementation of these initiatives; (2) data bank of functional system options, presented in the form of data sheets, one for each of the major functions, with the system option for near-term, midterm, and far-term space projects applicable to each subcategory of functions to be fulfilled; (3) table relating initiatives and desired goals (public service and humanistic, materialistic, scientific and intellectual); and (4) data on size, weight and cost estimations.

Bekey, I.↗

NASA NTRS1976

Pulmonary function evaluation during the Skylab and Apollo-Soyuz missions

Previous experience during Apollo postflight exercise testing indicated no major changes in pulmonary function. Pulmonary function has been studied in detail following exposure to hypoxic and hyperoxic normal gravity environments, but no previous study has reported on men exposed to an environment that was both normoxic at 258 torr total pressure and at null gravity as encountered in Skylab. Forced vital capacity (FVC) was measured during the preflight and postflight periods of the Skylab 2 mission. Inflight measurements of vital capacity (VC) were obtained during the last 2 weeks of the second manned mission (Skylab 3). More detailed pulmonary function screening was accomplished during the Skylab 4 mission. The primary measurements made during Skylab 4 testing included residual volume determination (RV), closing volume (CV), VC, FVC and its derivatives. In addition, VC was measured in flight at regular intervals during the Skylab 4 mission. Vital capacity was decreased slightly (-10%) in flight in all Skylab 4 crewmen. No major preflight-to-postflight changes were observed. The Apollo-Soyuz Test Project (ASTP) crewmen were studied using equipment and procedures similar to those employed during Skylab 4. Postflight evaluation of the ASTP crewmen was complicated by their inadvertent exposure to nitrogen tetroxide gas fumes upon reentry.

Sawin, C. F.↗

NASA NTRS1975

The dynamic transfer function for a cavitating inducer

Knowledge of the dynamic performance of pumps is essential for the prediction of transient behavior and instabilities in hydraulic systems; the necessary information is in the form of a transfer function which relates the instantaneous or fluctuating pressure and mass flow rate at inlet to the same quantities in the discharge from the pump. The presence of cavitation within the pump can have a major effect on this transfer function since dynamical changes in the volume of cavitation contribute to the difference in the instantaneous inlet and discharge mass flow rates. The present paper utilizes results from free streamline cascade theory to evaluate the elements in the transfer function for a cavitating inducer and shows that the numerical results are consistent with the characteristics observed in some dynamic tests on rocket engine turbopumps.

Brennen, C.↗

NASA NTRS1976

An experimental method to obtain the elastic strain energy function from torsion-tension tests

It is shown that by employing a torsion-tension test, it is possible to have a complete mapping near the origin of the two principal strain invariants associated with the rate of change of the strain energy function. However, the mathematical representation of the twist moment and normal forces vs strain and the strain energy function are complex. This problem is solved by using a set of solid cylindrical bars with different diameters such that the difference in diameter of two successive bars is small. The stress-strain equations can be grossly oversimplified by considering differences in twist moment and normal force as a function of difference in radius.

Peng, S. T. J.↗

NASA NTRS1975

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

Mukhopadhyay, A. K.↗