Search NASA⌕ Search

SEARCH · Search NASA

Results for “least-squares”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry

Curve-fit formulas are presented for the stagnation-point radiative heating rate, cooling factor, and shock standoff distance for inviscid flow over blunt bodies at conditions corresponding to high-speed earth entry. The data which were curve fitted were calculated by using a technique which utilizes a one-strip integral method and a detailed nongray radiation model to generate a radiatively coupled flow-field solution for air in chemical and local thermodynamic equilibrium. The range of free-stream parameters considered were altitudes from about 55 to 70 km and velocities from about 11 to 16 km.sec. Spherical bodies with nose radii from 30 to 450 cm and elliptical bodies with major-to-minor axis ratios of 2, 4, and 6 were treated. Powerlaw formulas are proposed and a least-squares logarithmic fit is used to evaluate the constants. It is shown that the data can be described in this manner with an average deviation of about 3 percent (or less) and a maximum deviation of about 10 percent (or less). The curve-fit formulas provide an effective and economic means for making preliminary design studies for situations involving high-speed earth entry.

Suttles, J. T.↗
NASA NTRS1974

Surface fitting three-dimensional bodies

The geometry of general three-dimensional bodies is generated from coordinates of points in several cross sections. Since these points may not be smooth, they are divided into segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction by fitting parametric cubic-spline curves through coordinate points which define the conic sections in the cross-sectional planes. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines and slopes at selected points. Slopes may be continuous or discontinuous and finite or infinite. After a satisfactory surface fit has been obtained, cards may be punched with the data necessary to form a geometry subroutine package for use in other computer programs. At any position on the body, coordinates, slopes and second partial derivatives are calculated. The method is applied to a blunted 70 deg delta wing, and it was found to generate the geometry very well.

Dejarnette, F. R.↗
NASA NTRS1974

Thermophysical properties of Apollo 14 fines

The vacuum thermal conductivity of lunar fines sample 14163 was measured for the approximate temperature range of 100 to 400 K. Sample densities of 1500 kg/cu m and 1800 kg/cu m were used. The temperature dependence of the conductivity was found to be well represented by the relation k = A + BT-cubed, which is predicted by elementary theory. The coefficients A and B were obtained by least-squares analysis of the data. The thermal diffusivity was calculated for the various densities using specific heat data from the literature along with the measured conductivities. The results are compared with those obtained for Apollo 11, Apollo 12, and terrestrial basalt samples.

Cremers, C. J.↗
NASA NTRS1974

Sequential square root filtering and smoothing of discrete linear systems

A square root information filter/smoother is derived using recursive least-squares arguments. The combined filter/smoother algorithm has the following attributes: (1) it has a square root structure, which enhances numerical accuracy; (2) filter and smoother mechanizations are identical in form, facilitating implementation of the smoother; and (3) storage and computation requirements are modest compared with other smoothing algorithms. Partitioning the results to separate bias parameters provides further computational economies and reduction of storage requirements.

Bierman, G. J.↗
NASA NTRS1974

The 6300 A O/1-D/ airglow and dissociative recombination

Measurements of night-time 6300 A airglow intensities at the Arecibo Observatory have been compared with dissociative recombination calculations based on electron densities derived from simultaneous incoherent backscatter measurements. The agreement indicates that the nightglow can be fully accounted for by dissociative recombination. The comparisons are examined to determine the importance of quenching, heavy ions, ionization above the F-layer peak, and the temperature parameter of the model atmosphere. Comparable fits between the observed and calculated intensities are found for several available model atmospheres. The least-squares fitting process, used to make the comparisons, produces comparable fits over a wide range of combinations of neutral densities and of reaction constants. Yet, the fitting places constraints upon the possible combinations; these constraints indicate that the latest laboratory chemical constants and densities extrapolated to a base altitude are mutually consistent.

Wickwar, V. B.↗
NASA NTRS1974

The two-dimensional tunnel structures of K3Sb5O14 and K2Sb4O11

The structures of K3Sb5O14 and K2Sb4O11 have been solved by the single-crystal X-ray direct method and the heavy-atom method, respectively. The structure of K3Sb5O14 is orthorhombic, with space group Pbam and cell parameters a = 24.247 (4), b = 7.157 (2), c = 7.334 (2) A, Z = 4. The structure of K2Sb4O11 is monoclinic, with space group C2/m and cell parameters a = 19.473 (4), b = 7.542 (1), c = 7.198 (1) A, beta = 94.82 (2) deg, Z = 4. A full-matrix least-squares refinement gave R = 0.072 and R = 0.067, respectively. In both structures, oxygen atoms form an octahedron around each Sb atom and an irregular polyhedron around each K atom. By sharing corners and edges, the octahedra form a skeleton network having intersecting b-axis and c-axis tunnels. The K(+) ions, which have more than ten oxygen near neighbors, are located in these tunnels. Evidence for K(+)-ion transport within and between tunnels comes from ion exchange of the alkali ions in molten salts and anisotropic temperature factors that are anomalously large in the direction of the tunnels.

Hong, H. Y.-P.↗
NASA NTRS1974

Analysis of longitudinal thickness-shear stiffness of a monolayer filamentary composite

The longitudinal thickness-shear behavior of a rectangular cross-section prism containing circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Saint-Venant flexure problem modeled by a tip-loaded cantilever composite beam and solution is obtained by the boundary-point least-squares method. It is shown that the longitudinal thickness-shear modulus is much greater than the in-plane shear modulus for a monofilament composite and therefore an independent analysis is necessary to predict the longitudinal thickness-shear behavior of the composite. Numerical results are presented in graphical form for various values of fiber volume fraction and material parameters typical of modern advanced composites.

Chang, S.↗
NASA NTRS1974

Rate of recombination of oxygen atoms and CO at temperatures below ambient

The measurements reported were conducted with 30.0 torr CO, 40.0 torr argon, and varying amounts of carbon dioxide from about 20 to 230 torr. Measurements were made at 277, 272, 263, and 257 K. The pseudo-first-order decay rate as a function of carbon dioxide pressure is shown in a graph. An Arrhenius plot for the rate constants obtained from the measurements is also presented. A value for the activation energy was determined on the basis of a linear least-squares fit to the data.

Inn, E. C. Y.↗
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 NTRS1974

Digital adaptive flight control design using single stage model following indices

Simple mechanical linkages are often unable to cope with many control problems associated with high-performance aircraft. This has led to the development of digital fly-by-wire control systems and in particular digital adaptive controllers that can be efficiently adjusted during system operation. To this effect, a control law has been derived based upon the minimization of a single-stage weighted combination of control energy and the squared error between the states of a linear plant and model. This control logic is interfaced with an on-line weighted least-squares estimator and a Kalman state filter. The utility of the resultant control system is illustrated by its application to the linearized dynamics of a typical fighter aircraft.

Alag, G.↗
NASA NTRS1974

The contamination of lunar highland rocks by KREEP - Interpretation by mixing models

A mixing model method was used to determine the component abundance in the Apollo 16 and 17 soils. This method uses the chemical composition of the soils for up to 30 elements and a weighted least-squares mixing model technique. Elements included in the calculations are: Si, Ti, Al, Ca, Fe, Mg, P, Cr, Mn, Na, K, Rb, Ba, U, Th, La, Ce, Sm, Eu, Sr, Yb, Y, Sc, V, Zr, Nb, Co, Ni, Li, Au, and Ir. The method was used to examine the possibility that some of the highland rocks such as VHA and low-K Fra Mauro basalt are mixtures. The results of the mixing model calculations show that it is possible that these rocks are mixtures of KREEP, troctolite, 'anorthosites', and a meteoritic component. The Rb-Sr systematics are consistent with such a model for the genesis of the highland rocks. KREEP has high relative concentrations of Rb, U, and radiogenic Sr and Pb and its model age of about 4.4 AE dominates the model age of all the 'contaminated' highland rocks.

Schonfeld, E.↗
NASA NTRS1974

Constraints on lunar structure

A brief review is given of the constraints placed on lunar structure and composition by seismic data and density models. Bounds on the crustal velocity structure in Mare Cognitum are derived using travel-time data from artificial impacts, and a velocity model is determined on the basis of synthetic seismograms. It is shown that the velocities of P- and S-waves in the mantle can be fixed by a least-squares analysis of arrival times from meteor impacts and moonquakes, and that lunar density can be determined from the seismic structure, mean density, and moment of inertia. Olivine-pyroxene mixtures and certain olivine-rich compositions are found to be consistent with the seismic-velocity and density limits. Maximum radii are calculated for pure Fe and pure FeS cores, and it is concluded that the possibility of an ancient lunar magnetic dynamo may have to be reevaluated in the light of these figures.

Dainty, A. M.↗
NASA NTRS1990

Satellite material contaminant optical properties

The Air Force Wright Research and Development Center and the Arnold Engineering Development Center are continuing a program for measuring optical effects of satellite material outgassing products on cryo-optic surfaces. Presented here are infrared (4000 to 700 cm(-1)) transmittance data for contaminant films condensed on a 77 K geranium window. From the transmittance data, the contaminant film refractive and absorptive indices (n, k) were derived using an analytical thin-film interference model with a nonlinear least-squares algorithm. To date 19 materials have been studied with the optical contents determined for 13 of those. The materials include adhesives, paints, composites, films, and lubricants. This program is continuing and properties for other materials will be available in the future.

Wood, B. E.↗
NASA NTRS1954

Application of several methods for determining transfer functions and frequency response of aircraft from flight data

In the process of analyzing the longitudinal frequency-response characteristics of aircraft, information on some of the methods of analysis has been obtained by the Langley Aeronautical Laboratory of the National Advisory Committee for Aeronautics. In the investigation of these methods, the practical applications and limitations were stressed. In general, the methods considered may be classed as: (1) analysis of sinusoidal response, (2) analysis of transient response as to harmonic content through determination of the Fourier integral by manual or machine methods, and (3) analysis of the transient through the use of least-squares solutions of the coefficients of an assumed equation for either the transient time response or frequency response (sometimes referred to as curve-fitting methods). (author)

Eggleston, John M↗
NASA NTRS1955

Measurement and Analysis of Wing and Tail Buffeting Loads on a Fighter Airplane

The buffeting loads measured on the wing and tail of a fighter airplane during 194 maneuvers are given in tabular form, along with the associated flight conditions. Measurements were made at altitudes of 30,000 to 10,000 feet and at speeds up to a Mach number of 0.8. Least-squares methods have been used for a preliminary analysis of the data. The agreement between the results of this analysis and the loads measured in stalls is sufficiently good to suggest the examination of the buffeting of other airplanes on the same basis.

Huston, Wilber B↗
NASA NTRS1960

Determination of Satellite Orbits from Radar Data

An optimum method for determining satellite orbits from radar data is presented in this report. Offering a good combination of speed and accuracy, the method makes use of orbit inclination and orbit elements in the plane, and proceeds with a differential correction of the orbit elements. Rapid, accurate methods of computing orbit elements are required to predict satellite positions for acquisition by other radars at points later along the orbit. In some cases the data are limited to a single pass over the observing station. The dynamical method is described in detail, and its accuracy is compared with those of two other methods: the purely geometrical, and the least-squares geometrical. By this optimum method the computing time, including the differential correction time, is 1 minute. Without differential correction, the rough determination takes from 10 to 20 seconds with approximately 5 miles positional uncertainty.

Cahill, W. F.↗
NASA NTRS1961

A Method of Estimating Residuals in Orbital Theory

The degree of approximation used in determining the orbits of earth satellites is reflected in the residuals (differences between calculated and observed positions). The least-squares procedure generally used to fit theory to observation tends to obscure the significance of theoretical parameters, so that the physical sources of residuals cease to be apparent. A method is outlined herein for estimating the magnitude of the residuals to be expected from an approximate theory presumed to have one missing or incorrect term.

Lecar, Myron↗
NASA NTRS1960

Supersonic Aerodynamic Characteristics of a Low-Drag Aircraft Configuration having an Arrow Wing of Aspect Ratio 1.86 and a Body of Fineness Ratio 20

A free-flight rocket-propelled-model investigation was conducted at Mach numbers of 1.2 to 1.9 to determine the longitudinal and lateral aero-dynamic characteristics of a low-drag aircraft configuration. The model consisted of an aspect-ratio -1.86 arrow wing with 67.5 deg. leading-edge sweep and NACA 65A004 airfoil section and a triangular vertical tail with 60 deg. sweep and NACA 65A003 section in combination with a body of fineness ratio 20. Aerodynamic data in pitch, yaw, and roll were obtained from transient motions induced by small pulse rockets firing at intervals in the pitch and yaw directions. From the results of this brief aerodynamic investigation, it is observed that very slender body shapes can provide increased volumetric capacity with little or no increase in zero-lift drag and that body fineness ratios of the order of 20 should be considered in the design of long-range supersonic aircraft. The zero-lift drag and the drag-due-to-lift parameter of the test configuration varied linearly with Mach number. The maximum lift-drag ratio was 7.0 at a Mach number of 1.25 and decreased slightly to a value of 6.6 at a Mach number of 1.81. The optimum lift coefficient, normal-force-curve slope, lateral-force-curve slope, static stability in pitch and yaw, time to damp to one-half amplitude in pitch and yaw, the sum of the rotary damping derivatives in pitch and also in yaw, and the static rolling derivatives all decreased with an increase in Mach number. Values of certain rolling derivatives were obtained by application of the least-squares method to the differential equation of rolling motion. A comparison of the experimental and calculated total rolling-moment-coefficient variation during transient oscillations of the model indicated good agreement when the damping-in-roll contribution was included with the static rolling-moment terms.

Gillespie, Warren, Jr.↗