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At least 217 records · Page 12

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NASA NTRS1976

Expansion of the gravitational potential with computerized Poisson series

The paper describes a recursive formulation for the expansion of the gravitational potential valid for both the tesseral and zonal harmonics. The expansion is primarily in rectangular coordinates, but the classical orbit elements or equinoctial orbit elements can be easily substituted. The equations of motion for the zonal harmonics in both classical and equinoctial orbital elements are described in a form which will result in closed-form expressions for the first-order perturbations. In order to achieve this result, the true longitude or true anomaly have to be used as independent variables.

Broucke, R.↗

NASA NTRS1976

Preliminary scaling laws for plasma current, ion kinetic temperature, and plasma number density in the NASA Lewis Bumpy Torus plasma

Parametric variation of independent variables which may affect the characteristics of the NASA Lewis Bumpy Torus plasma have identified those which have a significant effect on the plasma current, ion kinetic temperature, and plasma number density, and those which do not. Empirical power-law correlations of the plasma current, and the ion kinetic temperature and number density were obtained as functions of the potential applied to the midplane electrode rings, the background neutral gas pressure, and the magnetic field strength. Additional parameters studied include the type of gas, the polarity of the midplane electrode rings (and hence the direction of the radial electric field), the mode of plasma operation, and the method of measuring the plasma number density. No significant departures from the scaling laws appear to occur at the highest ion kinetic temperatures or number densities obtained to date.

Roth, J. R.↗

NASA NTRS1976

Stability of neutral equations with constant time delays

A method was developed for determining the stability of a scalar neutral equation with constant coefficients and constant time delays. A neutral equation is basically a differential equation in which the highest derivative appears both with and without a time delay. Time delays may appear also in the lower derivatives or the independent variable itself. The method is easily implemented, and an illustrative example is presented.

Barker, L. K.↗

NASA NTRS1976

The Relation of Finite Element and Finite Difference Methods

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Vinokur, M.↗

NASA NTRS1976

A wind tunnel investigation of circular and straked cylinders in transonic cross flow

Pressure distributions around circular and circular/strake cylinders were measured in a wind tunnel at Mach numbers from 0.6 to 1.2 with Reynolds number independently variable from 10,000 to 100,000. The local pressures are integrated over the cylinder surface to determine the variation of drag coefficient with both Mach number and Reynolds number. Effects of tunnel blockage are evaluated by comparing results from circular cylinders of various diameters at common Mach and Reynolds number conditions. Compressibility effects are concluded to be responsible for a flight reduction of the drag coefficient near Mach 0.7. Drag increases with strake height, presumably approaching a maximum drag corresponding to a flat plate configuration.

Macha, J.↗

NASA NTRS1976

Control of thermal balance by a liquid circulating garment based on a mathematical representation of the human thermoregulatory system

Test data and a mathematical model of the human thermoregulatory system were used to investigate control of thermal balance by means of a liquid circulating garment (LCG). The test data were derived from five series of experiments in which environmental and metabolic conditions were varied parametrically as a function of several independent variables, including LCG flowrate, LCG inlet temperature, net environmental heat exchange, surrounding gas ventilation rate, ambient pressure, metabolic rate, and subjective/obligatory cooling control. The resultant data were used to relate skin temperature to LCG water temperature and flowrate, to assess a thermal comfort band, to demonstrate the relationship between metabolic rate and LCG heat dissipation, and so forth. The usefulness of the mathematical model as a tool for data interpretation and for generation of trends and relationships among the various physiological parameters was also investigated and verified.

Kuznetz, L. H.↗

NASA NTRS1977

A method to estimate weight and dimensions of aircraft gas turbine engines. Volume 1: Method of analysis

Weight and envelope dimensions of aircraft gas turbine engines are estimated within plus or minus 5% to 10% using a computer method based on correlations of component weight and design features of 29 data base engines. Rotating components are estimated by a preliminary design procedure where blade geometry, operating conditions, material properties, shaft speed, hub-tip ratio, etc., are the primary independent variables used. The development and justification of the method selected, the various methods of analysis, the use of the program, and a description of the input/output data are discussed.

Pera, R. J.↗

NASA NTRS1976

The computation of relative motion with increased precision

Encke's method as modified by Potter to increase the accuracy of orbit computations of gravitationally interacting bodies is applied to the problem of relative motion of non-interacting space vehicles. This technique is then combined with a simple transformation of the independent variable to arrive at a system of equations from which the relative motion may be determined with increased precision.

Nacozy, P.↗

NASA NTRS1976

K/S two-point-boundary-value problems

A method for developing the missing general K/S (Kustaanheimo/Stiefel) boundary conditions is presented, with use of the formalism of optimal control theory. As an illustrative example, the method is applied to the K/S Lambert problem to derive the missing terminal condition. The necessary equations are developed for a solution to this problem with the generalized eccentric anomaly, E, as the independent variable. This formulation, requiring the solution of only one nonlinear, well-behaved equation in one unknown, E, results in considerable simplification of the problem.

Jezewski, D. J.↗

NASA NTRS1976

Linearization of dynamical systems using integrals of the motion

A method is presented which transforms certain nonlinear differential equations of dynamics into linear equations by introducing an independent variable and utilizing the integrals of motion. As examples of special interest, the linearizations of unperturbed and perturbed Keplerian motions are discussed.

Szebehely, V.↗

NASA NTRS1977

An Analytical State Transition Matrix for Orbits Perturbed by an Oblate Spheroid

An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.

Mueller, A. C.↗

NASA NTRS1978

Development of a winter wheat adjustable crop calendar model

The author has identified the following significant results. After parameter estimation, tests were conducted with variances from the fits, and on independent data. From these tests, it was generally concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson's triquadratic form, in general use for spring wheat, was found to show promise for winter wheat, but special techniques and care were required for its use. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with daily environmental values as independent variables.

Baker, J. R.↗

NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗

NASA NTRS1978

Supersonic flow over ablated nosetips using an unsteady, implicit numerical procedure

The axisymmetric supersonic flow over passive, that is, nonablating, indented nosetips of reentry vehicles is determined using an unsteady implicit numerical algorithm which solves either the inviscid Euler equations or the 'thin-layer' Navier-Stokes equations. A nonorthogonal independent variable transformation is used to map the distorted physical region, containing multiple zones of embedded subsonic flow into a rectangular computational domain at whose boundaries the required permeable or impermeable boundary conditions are simulated. Use of the implicit algorithm results in faster convergence to the steady state because of a larger allowable time step over conventional explicit schemes. The numerical results obtained compare favorably with existing experimental data for very mildly and severely indented blunt nosetips.

Kutler, P.↗

NASA NTRS1977

Single-axis attitude determination accuracy

This paper extends the analysis of attitude determination accuracy introduced at the 1975 American Astronautical Society/American Institute of Aeronautics and Astronautics (AAS/AIAA) Astrodynamics Conference. It contains more generalized expressions, new geometrical relations, and additional applications. A complete set of attitude accuracy equations for both arc-length (portion of a great circle) and rotation-angle (dihedral angle) measurements are presented. These expressions can then be applied to determine the geometrical conditions under which a specified accuracy can be achieved by using either the attitude or a selected reference-vector direction as the independent variable. Representative applications to attitude determination accuracy studies and launch window analyses are discussed. The clear physical interpretation and straightforward graphical procedures greatly simplify mission analysis, maneuver planning, hardware configuration studies, and interpretation of results.

Chen, L. C.↗

NASA NTRS1977

An element formulation for perturbed motion about the center of mass

The perturbed motion of a rigid body about its center of mass, is formulated in terms of the six elements: l, the magnitude of the angular momentum vector; h, the total energy; delta and epsilon, two linear functions of the independent variable; and psi(1) and theta (1), two Euler angles that orientate the inertial frame with respect to the unperturbed solution. Solutions from the element formulation and the original Euler equations are numerically compared using shuttle-type data. For applied torques smaller than a given magnitude, the element formulation produced the following results: (1) larger step sizes in the numerical integration of the differential equations, resulting in an overall computational time-saving, and (2) more significant figures of accuracy in the computation of the variables describing the state of the rigid body.

Donaldson, J. D.↗

NASA NTRS1978

Methods used for Space Shuttle SRB thrust shape design

Optimization of the Space Shuttle trajectory is discussed with reference to the low acceleration profile required for Shuttle missions. Static tests of the nominal flight curve are described in terms of impulse requirements, vacuum thrust, and burn time. Attention is given to BARF (Burning Anomaly Rate Factor), and it is noted that mandrel fabrication is intended to include the flexibility to counter BARF, should it occur. Test results are presented in which both BARF and specific impulse are considered as independent variables. It was found that no erosive burning occurred, BARF did not occur, specific impulse was on the order of 265 sec, and flow anomalies in the star region produced head-to-aft stagnation pressure drops in excess of theoretical predictions. In other areas, good agreement is noted between theoretical prediction and empirical data.

Baker, J.↗

NASA NTRS1978

On the attitude motion of an orbiting rigid body under the influence of gravity gradient torque

An investigation is made of the rotational motion of a rigid body orbiting the earth, under the influence of the geogravity-gradient torque. The attitude dynamics are formulated as perturbations from a nominal case. The perturbed equations are solved asymptotically, by the multiple scales technique. The independent variable, time, is extended into a space of higher dimension by means of new scales, fast, slow, etc. Integration of the equations is carried out separately in the new variables. The rapid and slow aspects of the attitude dynamics are systematically separated, resulting in a more efficient computer implementation and enhanced physical insight. The theory is applied to predict the attitude dynamics of an asymmetric rigid body satellite. A comparison is made of the maximum errors as the step size increases as predicted by the multiple scales solution and direct numerical integration. An improvement in computational speed of an order of magnitude is demonstrated.

Tao, Y. C.↗