Computation and analysis
Direct summation of series involving higher transcendental functions, integrals of confluent hypergeometric functions, and computer methods for approximating continuous functions
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Results for “Approximation methods”
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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A polynomial method for determining local emission intensity by Abel inversion
Polynomial method for approximating radiation intensity from plasma light source represented by Abel transforms
Moore, D.↗
The variational method 2 - Perturbation theory
Variational method to approximate solutions of perturbation equations, perturbation analyses, and use of perturbation theory to infer variational principle
Epstein, S. T.↗
Analysis of irrational transfer functions for distributed-parameter systems
Algorithmic and digital computer method for approximating irrational transfer functions by rational functions in control systems
Chen, C.-F.↗
Multiple zeros of polynomials
Analysis of four iterative methods for approximating zeros of polynomial expressions using digital computer
Wood, C. A.↗
Communication system modeling
This report presents the results of work on communications systems modeling and covers three different areas of modeling. The first of these deals with the modeling of signals in communication systems in the frequency domain and the calculation of spectra for various modulations. These techniques are applied in determining the frequency spectra produced by a unified carrier system, the down-link portion of the Command and Communications System (CCS). The second modeling area covers the modeling of portions of a communication system on a block basis. A detailed analysis and modeling effort based on control theory is presented along with its application to modeling of the automatic frequency control system of an FM transmitter. A third topic discussed is a method for approximate modeling of stiff systems using state variable techniques.
Holland, L. D.↗
Prediction of flow profiles in arteries from local measurements.
This paper develops an approximate numerical method for calculating flow profiles in arteries. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the large deformations of the arterial wall. The method, assuming axially symmetric flow, determines velocity distribution and wall shear at a given location from the locally measured values of the pressure, pressure gradient, and pressure-radius relation. The computed results agree well with the corresponding experimental data.
Ling, S. C.↗
Effects of interplanetary magnetic field on the propagation of flare-generated interplanetary shock waves.
The effects of an interplanetary magnetic field on the propagation of flare-generated interplanetary shock waves are investigated with an approximate analytical method. It is found that the interplanetary magnetic field is relatively unimportant for strong shocks as far as the shock speed and transit time are concerned. It has more significant effects for weak shocks. However, in all the situations examined, the error committed if the magnetic field is neglected is no more than 10%. It is suggested that a model without a magnetic field gives sufficiently accurate numerical results for the propagation of flare-generated shocks.
Tam, C. K. W.↗
Welded printed circuit (pc) stick
Printed-circuit stick module has reduced comb technique to six steps, cutting process time by approximately 50%. Method incorporates all type of components into one assembly. It reduces design and fabrication time for 14-lead flat pack to less than four hours and for the 22-lead flat pack to four hours. Average weight of each flat pack is also reduced to 2 g.
Kreis, F.↗
Analysis of unsteady thermal boundary layers
The velocity and temperature distribution in an unsteady thermal boundary layer is analyzed by an approximate integral method. The case of a flat plate in a free stream having small harmonic velocity oscillations about a steady mean value is treated in detail. The resulting velocity profiles agree with the available experimental data. These profiles are used to predict the thermal convection when the plate and the stream are at constant but different temperature levels. The flow oscillations cause harmonic temperature oscillations plus a small steady feedback effect which reduces the mean heat transfer to the plate. The amount of decrease is represented by a single coefficient, which is presented graphically.
Miller, R. W.↗
Control optimization, stabilization and computer algorithms for aircraft applications
Computationally useful algorithms are considered that can aid the control engineer in designing systems control in linear time invariant dynamics for aircraft applications. Structural aspects of system identification, matrix parameterization, and the effect of feedback on identifiability of systems. Adaptive and stochastic control model constructions are projected, and a method for approximate identification of aircraft characteristics and subsequent generation of control signals is outlined.
Mitter, S. K.↗
A nonlinear analysis of pulsatile flow in arteries.
An approximate numerical method for calculating flow profiles in arteries is developed. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the nonlinear behaviour and large deformations of the arterial wall. Through the locally measured values of the pressure, pressure gradient, and pressure-radius function, the velocity distribution and wall shear at a given location along the artery can be determined. The computed results agree well with the corresponding experimental data.
Ling, S. C.↗
Optical Properties of atmospheric dust from twilight observations
Three methods of approximation are described and used to separate the primary twilight brightness from the observed brightness. Photoelectric observations obtained are combined with observations from a balloon and from the observatory to derive the atmospheric scattering phase functions of 0.37 micron and 0.58 micron as a function of height. Comparison of these data with data for a Rayleigh atmosphere provide information on the optical properties of dust in the upper atmosphere.
Divari, N. B.↗
Computer extension and analytic continuation of Stokes' expansion for gravity waves
Stokes' infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic. Stokes' expansion has been found to be incapable of yielding the highest wave for any value of the water depth since convergence is limited by a square-root branch-point some distance short of the maximum. By reformulating the problem using a different independent parameter, the highest waves are obtained correctly. Series summation and analytic continuation are facilitated by the use of Pade approximants. The method is valid in principle for any finite value of the wavelength and solutions of high accuracy can be obtained for most values of the wave height and water depth.
Schwartz, L. W.↗
Cold air study of the effect on turbine stator blade aerodynamic performance of coolant ejection from various trailing edge slot geometries. 2: Comparison of experimental and analytical results
Experimentally determined efficiencies of turbine stator blades having trailing-edge coolant ejection are compared with efficiencies predicted from two previously published approximate analytical methods. The experimental results were obtained from two-dimensional data with the temperature of the primary and coolant flows both being nearly ambient. Data from five stator blade configurations having different slotted trailing-edge geometries were included in the comparison. The two analytical methods gave results which agreed reasonably well with experimental results. An average of the absolute values of differences between experimental and predicted efficiencies for all five blade configurations showed that one method gave average efficiency differences which were about 1.3 percent different than experimental efficiencies, while the other method gave average efficiency differences that were about 0.7 percent different than experimental. However, in some instances, maximum differences of as much as 4 percent occurred. A comparison between experimental and analytical results indicated that the ratio of trailing-edge slot width to trailing-edge thickness influences the measured efficiencies to a greater extent than is accounted for by either analytical model.
Prust, H. W., Jr.↗
A new structural analysis/synthesis capability - ACCESS
The creation of an efficient automated capability for minimum weight design of structures is reported. The ACCESS 1 computer program combines finite element analysis techniques and mathematical programming algorithms using an innovative collection of approximation concepts. Design variable linking, constraint deletion techniques and approximate analysis methods are used to generate a sequence of small explicit mathematical programming problems which retain the essential features of the design problem. Organization of the finite element analysis is carefully matched to the design optimization task. The efficiency of the ACCESS 1 program is demonstrated by giving results for several example problems.
Schmit, L. A.↗
An analysis of the strong zonal circulation within the stratosphere of Venus
A dynamic model is presented for the strong zonal circulation within the stratosphere of Venus which was observed by Mariner 10 and Venera. Rotational effects are neglected, a compressible and radiating atmosphere is considered, and diurnal radiative heating is shown to be negligible in the lower stratosphere (below 85 km). Analysis of the model indicates that propagating internal gravity waves generated by solar heating of the upper stratosphere may induce mean zonal velocities within the upper and lower stratosphere which would have a retrograde direction. The nonlinear equations of motion and energy are solved by an approximate analytical method to determine the magnitude of the zonal velocity, which is found to increase from zero at the tropopause to about 200 m/sec at the 85-km level. The calculated velocity near the UV cloud level compares favorably with the observed value of 100 m/sec.
Ramanathan, V.↗
A Method for Calculating the Induced Pressure Distribution Associated with a Jet in a Crossflow
A model is presented which can be used to study the loss of lift during hovering and horizontal flight of the VTOL aircraft. The model numerically predicts the pressure distribution induced by a round, turbulent, unheated, subsonic jet exhausting normally through a flat plate into a subsonic crossflow. The complete model assumes that the predominant features of the flow are jet entrainment and a pair of contrarotating vortices which form downstream of the jet. Experimentally determined vortex properties and a reasonable assumption concerning jet entrainment were used. Potential flow considerations were used except in the wake region, where a simple method for approximating the pressure distribution was suggested. The calculated pressure distribution, lift, and pitching moments on the flat plate are presented for a jet to crossflow velocity ratio of 8 and were compared with experimental results. A computer program is given which was used to calculate the pressure distribution across the flat plate.
Dietz, W. E., Jr.↗