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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

A note on a corrector formula for the numerical solution of ordinary differential equations

A new corrector formula for predictor-corrector methods for numerical solutions of ordinary differential equations is presented. Two considerations for choosing corrector formulas are given: (1) the coefficient in the error term and (2) its stability properties. The graph of the roots of an equation plotted against its stability region, of different values, is presented along with the tables that correspond to various corrector equations, including Hamming's and Milne and Reynolds'.

Chien, Y.-C.↗
NASA NTRS1980

Analysis and testing of numerical formulas for the initial value problem

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.

Brown, R. L.↗
NASA NTRS1981

Simple formulas for designing an offset multibeam parabolic reflector

Theoretical methods (computer programs) which are available for analyzing reflector performance are of the 'forward' type. Performance parameters can be calculated after the configuration of the reflector is given. In many practical applications, however, the problem is often of the 'inverse' type. The reflector has to be designed on the basis of a given set of performance parameters. Attention is given to a systematic procedure based on simple formulas for solving such an inverse problem. Because of the simplicity of the formulas, the final results obtained from the procedure do not have great accuracy. Thus, they represent only a preliminary design, which can be refined by repeatedly using the forward-type programs.

Lee, S.-W.↗
NASA NTRS1981

Geometrically derived difference formulae for the numerical integration of trajectory problems

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

Mcleod, R. J. Y.↗
NASA NTRS1986

An approximation formula for a class of fault-tolerant computers

An approximation formula is derived for the probability of failure for fault-tolerant process-control computers. These computers use redundancy and reconfiguration to achieve high reliability. Finite-state Markov models capture the dynamic behavior of component failure and system recovery, and the approximation formula permits an estimation of system reliability by an easy examination of the model.

White, A. L.↗
NASA NTRS1988

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Badavi, Forooz F.↗
NASA NTRS1990

An estimating formula for ion-atom association rates in gases

A simple estimating formula is derived for rate coefficients of three-body ion atom association in gases and compare its predictions to experimental data on ion association and three-body radiative charge transfer reactions of singly- and doubly-charged rare-gas ions. The formula appears to reproduce most experimental data quite well. It may be useful for estimating the rates of reactions that have not been studied in the laboratory.

Chatterjee, B. K.↗
NASA NTRS1991

On the position of the near-earth neutral sheet - A comparison of magnetic model predictions with empirical formulas

A detailed comparison of the near-earth neutral sheet position according to several approximations has been made. In particular, two empirical formulas for the neutral sheet location, recently derived from AMPTE/CCE data, have been compared with the corresponding positions derived from Tsyganenko's magnetic field models. Cylindrical coordinates referenced to the geodipole have been used, and the position of the neutral sheet has been identified by the reversal of the radial component of the magnetic field. The analysis reveals that, in the region X(GSM) = -9 to -5 earth radii, abs. value of Y(GSM) not greater than 5 earth radii, close agreement exists between the empirical formulas and the Tsyganenko models. Furthermore, the Tsyganenko models provide a representation for the neutral sheet position in the transition region between near-earth and distant tail models.

Peredo, Mauricio↗
NASA NTRS1935

A deflection formula for single-span beams of constant section subjected to combined axial and transverse loads

In this paper there is presented a deflection formula for single-span beams of constant section subjected to combined axial and transverse loads of the types commonly encountered in airplane design. The form of the equation is obtainable by dimensional analysis. Tables and curves of the non dimensional coefficients are appended to facilitate the use of the formula. The equation is applied to the determination of the spring constant of a beam. Tables and curves are presented to show the variation of the spring constant with changes in the axial load and position along the beam.

Burke, Walter F↗
NASA NTRS1933

Formulas for the Stress Analysis of Circular Rings in a Monocoque Fuselage

The formulas given in this report provide a simplified method for the stress-analysis of fuselage bulkheads that are approximately circular rings of uniform cross section. Complicated load systems acting on a ring can usually be resolved into simplified load systems; and formulas for moment, axial force, and shear for such simplified load systems are given in this report. Illustrative examples showing the use of this method in practical stress-analysis work are also included.

Miller, Roy A↗
NASA NTRS1954

Formulas for the elastic constants of plates with integral waffle-like stiffening

Formulas are derived for the fifteen elastic constants associated with bending, stretching, twisting, and shearing of plates with closely spaced integral ribbing in a variety of configurations and proportions. In the derivation the plates are considered, conceptually, as more uniform orthotropic plates somewhat on the order of plywood. The constants, which include the effectiveness of the ribs for resisting deformations other than bending and stretching in their longitudinal directions, are defined in terms of four coefficients, and theoretical and experimental methods for the evaluation of these coefficients are discussed. Four of the more important elastic constants are predicted by these formulas and are compared with test results. Good correlation is obtained. (author)

Dow, Norris R↗
NASA NTRS1933

General formulas and charts for the calculation of airplane performance

This report presents general formulas for the determination of all major airplane performance characteristics. A rigorous analysis is used, making no assumption regarding the attitude of the airplane at which maximum rate of climb occurs, but finding the attitude at which the excess thrust horsepower is maximum. Equations and charts are developed which show the variation of performance due to a change in any of the customary design parameters. Performance determination by use of the formulas and charts is rapid and explicit. The results obtained by this performance method have been found to give agreement with flight tests that is, in general, equal or superior to results obtained by present commonly used methods.

Oswald, W Bailey↗
NASA NTRS1951

Formulas for the Supersonic Loading, Lift, and Drag of Flat Swept-Back Wings with Leading Edges Behind the Mach Line

The method of superposition of linearized conical flows has been applied to the calculation of the aerodynamic properties, in supersonic flight, of thin flat, swept-back wings at an angle of attack. The wings are assumed to have rectilinear plan forms, with tips parallel to the stream, and to taper in the conventional sense. The investigation covers the moderately supersonic speed range where the Mach lines from the leading-edge apex lie ahead of the wing. The trailing edge may lie ahead of or behind the Mach lines from its apex. The case in which the Mach cone from one tip intersects the other tip is not treated. Formulas are obtained for the load distribution, the total lift, and the drag due to lift. For the cases in which the trailing edge is outside the Mach cone from its apex the formulas are complete. For wings with both leading and trailing edges behind their respective Mach lines, a degree of approximation is necessary. Charts of some of the functions derived are included to facilitate computing, and several examples are worked out in outline.

Cohen, Doris↗
NASA NTRS1953

Charts and approximate formulas for the estimation of aeroelastic effects of the lateral control of swept and unswept wings

Charts and approximate formulas are presented for the estimation of static aeroelastic effects on the spanwise lift distribution, rolling-moment coefficient, and rate of roll due to the deflection of ailerons on swept and unswept wings at subsonic and supersonic speeds. Some design considerations brought out by the results of this report are discussed. This report treats the lateral-control case in a manner similar to that employed in NACA Report 1140 for the symmetric-flight case, and is intended to be used in conjunction with NACA Report 1140 and the charts and formulas presented therein.

Foss, Kenneth A↗
NASA NTRS1961

Simple Formulas for Stagnation-Point Convective Heat Loads in Lunar Return

Simple formulas are given for the stagnation-point convective heat 1 loads in lunar return for two operational modes. The two modes of operation analyzed are typical of moderate heating and of nearly minimum heat loads, respectively. The values of the parameters in a simple two- parameter formula for the total-heat load are given in the lift-drag-ratio range of 0.2 to 1.0 and in the peak loading range of 2g to 10g. For vehicles having a lift-drag ratio near 0.5, which is typical of many proposed lunar return vehicles, the nominal mode had about 20 percent more absorption than the nearly minimum mode.

Grant, Frederick C.↗