Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “FITTING”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Satellite orbit determination

A historic account of the activities of the Satellite OD Group during the MM'71 mission is given along with an assessment of the accuracy of the determined orbit of the Mariner 9 spacecraft. Preflight study results are reviewed, and the major error sources described. Tracking and data fitting strategy actually used in the real time operations is itemized, and Deep Space Network data available for orbit fitting during the mission and the auxiliary information used by the navigation team are described. A detailed orbit fitting history of the first four revolutions of the satellite orbit of Mariner 9 is presented, with emphasis on the convergence problems and the delivered solution for the first orbit trim maneuver. Also included are a solution accuracy summary, the history of the spacecraft orbit osculating elements, the results of verifying the radio solutions with TV imaging data, and a summary of the normal points generated for the relativity experiment.

Jordan, J. F.↗
NASA NTRS1974

The shape of the primary cosmic ray electron spectrum above 10 GeV

A balloon borne measurement of the cosmic ray electron spectrum above 10 GeV is reported in which two new techniques have been used to remove proton background contamination. First, the depth of the spectrometer on one of the flights was more than 40 radiation lengths, enabling hadronically and electromagnetically induced cascades to be differentiated for a subset of the data. Second, electromagnetic cascade starting points were determined to within about 0.1 radiation lengths based upon a calibration with electrons from 5.4 to 18 GeV at the Stanford Linear Accelerator. The resulting spectrum, when fitted with a power law, is steep, but the fit is marginal. A significantly better fit is achieved by assuming a model in which the spectrum is steepening in the measured region.

Silverberg, R. F.↗
NASA NTRS1974

Design data for radars based on 13.9 GHz Skylab scattering coefficient measurements

The author has identified the following significant results. Measurements made at 13.9 GHz with the radar scatterometer on Skylab have been combined to produce median curves of the variation of scattering coefficient with angle of incidence out to 45 deg. Because of the large number of observations, and the large area averaged for each measured data point, these curves may be used as a new design base for radars. A reasonably good fit at larger angles is obtained using the theoretical expression based on an exponential height correlation function and also using Lambert's law. For angles under 10 deg, a different fit based on the exponential correlation function, and a fit based on geometric optics expressions are both reasonably valid.

Moore, R. K.↗
NASA NTRS1975

Flight transition data for angles of attack at Mach 22 with correlations of the data

Boundary-layer transition data for angles of attack from 2.5 to 47 deg from a flight experiment with a cone that reentered at angles of attack up to 75 deg were analyzed and their local flow conditions are presented. The transition data were obtained from both acoustic and electrostatic sensors. The data from the acoustic and electrostatic sensors were correlated by use of three different sets of correlating parameters. For each set of correlating parameters, the transitional and turbulent data from the acoustic and electrostatic sensors were plotted separately. Each of the correlations was compared with a linear curve fit of previous cone-flight data at near zero angle of attack. Results indicate that the data from acoustic sensors falls below the linear curve fits to the flight data and indicates the sensitivity of the sensors. It is shown that the transition data from the electrostatic sensors tends to scatter much more than the data from the acoustic sensors. However, the data from the electrostatic sensors tends to scatter about the linear curve fits based on previous flight data.

Johnson, C. B.↗
NASA NTRS1974

Observation of a driver gas-tangential discontinuity

A complete analysis of an interplanetary disturbance of Nov. 19, 1970 using the Apollo 12-SIDE (Suprathermal Ion Detector Experiment) is presented. The SIDE detectors were pointing at 26.3 degrees from the normal solar-wind direction during the observations. The data were least-squares fitted (using a parabolic hypersurface approximation) to a convected Maxwell-Boltzmann distribution function. The results of the fit combined with two other experiments showed a drastic change in the wind speed (from an steady 352 km/sec down to 219 km/sec), direction, and temperature. Except for a delta-function increase at the onset, the density remained constant. There was a considerable enhancement in the abundance of He and probably of heavier elements. The interplanetary magnetic field exhibited a jump of 21 gamma with a change in latitude from -56 to -76 degrees in solar ecliptic coordinates. It is concluded that the disturbance was due to the driver gas-tangential discontinuity of a solar flare-induced shock wave. The characteristic of the tangential discontinuity fit well with theoretical prediction.

Medrano, R. A.↗
NASA NTRS1975

Studies of cluster X-ray sources, energy spectra for the Perseus, Virgo, and Coma clusters

Final Uhuru X-ray differential-energy spectra are presented for the Perseus, Virgo, and Coma clusters. Power-law and isothermal bremsstrahlung model spectra with low-energy cutoffs are given, and the energy-dependent Gaunt factor is calculated for the bremsstrahlung. The spectra, which are best fits to the Uhuru data between 2 and 10 keV, are compared with previous observations of these sources in the energy range from 0.1 to 100 keV. The problem of parameter estimation is discussed, error bars with 68% confidence are given for the independently determined slope and cutoff parameters, and the 68% confidence limits are plotted for the fitted spectral functions. The data for Perseus above 20 keV marginally favor the bremsstrahlung fit, those for Virgo between 0.25 and 1.0 keV clearly favor that curve, and those for Coma indicate a low-energy turnover or cutoff. Implications of such a cutoff are briefly discussed.

Kellogg, E.↗
NASA NTRS1976

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

Vijayashankar, V. S.↗
NASA NTRS1977

The galactic halo question: New size constraints from galactic gamma-ray data

The SAS-2 gamma-ray data is analyzed making use of recent CO line emission and other data for determining the large-scale distribution of galactic gas. A nonuniform distribution of cosmic rays in the galaxy is implied. This fact rules out large trapping halo models and extragalactic origin models. Detailed models of diffusion halos of various sizes perpendicular to the galactic plane are considered. In such models, the scale perpendicular to the plane has a strong effect in determining the radial distribution of cosmic rays. Such radial distributions are calculated for cylindrical coordinate models. The implied gamma-ray longitude distributions are then calculated and compared with the SAS-2 data for goodness-of-fit. Assuming the sources to be supernova remnants or pulsars, cosmic ray nucleon halo models with scale heights greater than 3 kpc are found to provide a poor fit to the gamma-ray longitude data (probability of 6% or less). Thin halo, or source dominated diffusion models are found to provide a good fit to the gamma-ray data, with an upper limit scale height of approximately 3 kpc.

Stecker, F. W.↗
NASA NTRS1977

Computation of the inviscid supersonic flow about cones at large angles of attack by a floating discontinuity approach

The technique of floating shock fitting is adapted to the computation of the inviscid flowfield about circular cones in a supersonic free stream at angles of attack that exceed the cone half-angle. The resulting equations are applicable over the complete range of free-stream Mach numbers, angles of attack and cone half-angles for which the bow shock is attached. A finite difference algorithm is used to obtain the solution by an unsteady relaxation approach. The bow shock, embedded cross-flow shock, and vortical singularity in the leeward symmetry plane are treated as floating discontinuities in a fixed computational mesh. Where possible, the flowfield is partitioned into windward, shoulder, and leeward regions with each region computed separately to achieve maximum computational efficiency. An alternative shock fitting technique which treats the bow shock as a computational boundary is developed and compared with the floating-fitting approach. Several surface boundary condition schemes are also analyzed.

Daywitt, J.↗
NASA NTRS1977

Axel dust on Saturn and Titan

The observed sharp drop in the geometric albedo of Titan shortward of 6000 A (also observed for Jupiter and Saturn) has been tentatively attributed to the presence of small absorbing particles referred to as Axel dust. The properties of Axel dust particles are studied, with the effect of scattering included through Mie theory, in an attempt to obtain a physically plausible set of parameters that properly characterizes the dust. Quantitative characteristics of the dust are described, scattering and absorption properties of various particle size distributions are calculated, and fits are made to observations of Titan and Saturn. It is found that: (1) a flat distribution of particle radii up to 0.1 micron and an imaginary part of the refractive index that varies as the -2.5 power of wavelength produce a good fit for Titan provided the extinction optical depth of the satellite's atmosphere is about 10 at 5000 A; (2) a clear layer of about 7 km-am hydrogen is required above the dust for a good fit to Saturn with the same dust properties; and (3) the inclusion of dust significantly increases the computed abundance of methane over the value given by reflecting-layer models.

Podolak, M.↗
NASA NTRS1977

Flight inspection data and crack initiation times

Lockheed C-130 service-flight inspection data is reduced by means of fracture mechanics and statistical analysis into a form from which the probability of time to crack initiation and the distribution of initial flaw sizes for various locations on the aircraft can be determined. Crack sizes are normalized by extrapolating a growing crack backwards from its first recorded size to .03 inches (crack initiation size) yielding the time to crack initiation. In a similar fashion, the crack is grown backwards to a time equal to zero to yield an initial flaw size. In order to perform the discussed computations, crack growth constants were computed for each individual location and were analyzed statistically. Statistical distributions were fitted to times to crack initiation and to initial flaw sizes in order to describe their expected behavior. Weibull and Johnson distributions have been found to fit the data reasonably well but for a better fit convolution integrals of Poisson load distributions and Weibull strength distributions are needed.

Johnson, W. S.↗
NASA NTRS1978

Some mesh generation requirements and methods

Discretized solution algorithms, which find solutions of field equations in a two or three dimensional field, generally use meshes which are fitted to the field boundary to allow convenient formulation of boundary conditions there. A mesh is defined to be the image of a rectangular grid in computational space under a mesh mapping which maps computational space into physical space. It is not necessary that all of computational space be mapped onto the region of interest in physical space. Parts of it can be excised to give a better fit to the boundary. Many different excisions can be made to fit a single boundary; the choice depends on the mesh arrangement desired in the field.

Dickson, L. J.↗
NASA NTRS1978

Precision orbit computations for Starlette

The Starlette satellite, launched in February 1975 was designed to minimize the effects of nongravitational forces and to obtain the highest possible accuracy for laser range measurements. Analyses of the first four months of laser tracking data from nine stations have confirmed the stability of the orbit and the precision to which the satellite's position can be established. Initial orbit computations using the GSFC GEM - 7 gravity model produced rms fits of about 8 to 10 meters for arc lengths of 5 days. After tailoring a gravity model specifically to Starlette, the rms fits for the 5 day arcs were reduced significantly to the 1 to 2 meter level. An rms fit of 4.3 meters was obtained for a 90 day arc. Five day arcs overlapped by 2.5 days showed rms satellite position differences generally less than 2 meters. Prediction errors at the end of two months were less than 30 milliseconds.

Marsh, J. G.↗
NASA NTRS1978

Structure and evolution of solar radio bursts at 26.4 MHz

Results are reported for multiple-baseline interferometric measurements of type II, III, IV, and V solar radio bursts at 26.4 MHz. Thirty-two burst events in a two-month period are analyzed by fitting a double-Gaussian two-dimensional source-brightness distribution model to the observed interferometer visibility function. The multibaseline time-sharing interferometer system employed is described in detail, the model-fitting technique is outlined, and values of the model-fit parameters are given for all 32 cases, which include two type II bursts, three type IV bursts, 17 type III bursts, seven type V bursts, and three bursts of type III, V pairs. The temporal evolution of source structure, size, and motion is examined for the different burst types. The core-halo source structure for the type III bursts is interpreted in comparison to two models, one of which assumes scattering and refraction of a point source while the other postulates primarily refraction from an ensemble of sources distributed over a wide sector in solar longitude.

Chen, H. S.-L.↗
NASA NTRS1978

Observations of the hard X-ray spectrum of the impulsive phase of solar flares

The impulsive solar hard X-ray spectrum provides a direct diagnostic on the impulsive energy release of the flare. The data from the hard X-ray (14-342 keV) spectrometer on OSO 7 have been examined for events covering a wide energy range to determine the photon spectrum more precisely. This resulted in a sample of 38 events. The data have been fitted with either single- or double-power laws, and with an exponential spectrum, as from thermal bremsstrahlung. The chi-squared statistic between two-parameter fits strongly favors the exponential fit, particularly at peak intensity when the widest energy range is sampled. This result supports a single-temperature thermal source of the impulsive solar hard X-rays with temperatures in the range 4.7-31 keV and emission measures in the range from 8.4 x 10 to the 43rd to 6.0 x 10 to the 46th per cu cm. The temperature reaches a single maximum and then rapidly decays, but the emission measure usually increases throughout, even after temperature maximum, for data with 10-s resolution.

Elcan, M. J.↗
NASA NTRS1979

Further analysis of SAS 3 observations of the rapid burster /MXB 1730-335/

SAS 3 observations of the rapid burster MXB 1730-335 are analyzed with specific reference to the rapidly repetitive type II bursts and also the type I bursts. It is found that: (1) there are two stable patterns in the recurrence of the rapidly repetitive type II bursts, designated modes I and II; (2) the range of type II burst energies is a factor of about 100 for mode I and a factor of about 10 for mode II; (3) type II burst spectra are best fitted by a blackbody of constant temperature (of the order of 18 million K), constant column density, and decreasing intensity; and (4) type I bursts are best fitted by a blackbody spectrum with decreasing temperature (approximately 24 million K during the first few seconds and 16 million K about 10 sec later). The spectral fits for both types of burst are shown to yield sizes for the emission region comparable to the radius of a neutron star. A model for the rapid burster is suggested.

Marshall, H. L.↗
NASA NTRS1980

Cosmic ray studies with a gas Cherenkov counter in association with an ionization spectrometer

The results from a balloon-borne gas Cherenkov counter (threshold 16.5 GeV/nucleon) and an ionization spectrometer are presented. The gas Cherenkov counter provides an absolute energy distribution for the response of the calorimeter for 5 or = Z 26 nuclei of cosmic rays. The contribution of scintillation to the gas Cherenkov pulse height was obtained by independently selecting particles below the gas Cherenkov threshold using the ionization spectrometer. Energy spectra were derived by minimizing the chi squared between Monte Carlo simulted data and flight data. Best fit power laws, dN/dE = AE-gamma, were determined for C, N, O, Ne, Mg, and Si. The power laws, all consistent with E (-2.7) are not good fits to the data. A better fit is obtained using the spectrum derived from the spectrometer. The data from the ionization calorimeter and the gas Cherenkov are thus completely self-consistent.

Balasubrahmanyan, V. K.↗
NASA NTRS1980

Discrete Tchebycheff orthonormal polynomials and applications

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Lear, W. M.↗