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NASA NTRS1975

The treatment of bias in the square-root information filter/smoother

The Dyer-McReynolds square-root information filter (SRIF) is rederived, using recursive least-square arguments. The result is applied to a system composed partly of biases. The filter sensitivity matrix, computed covariance, and consider covariance for this augmented system are reviewed. A new computationally attractive representation for the smoothed estimates, in terms of a smoothed sensitivity matrix and a smoothed computed covariance is presented.

Bierman, G. J.↗

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 NTRS1975

Airborne infrared polarimeter

An infrared polarimeter was built to measure the degree of linear polarization and the direction of vibration of radiation scattered upwards by clouds, between 1.1 and 3.5 microns, with a 1.5-deg field of view, using a rotating wire-grid polarization analyzer. A PbS detector is cooled to 192 K by condensing freon-13. This AEROPOL instrument operates under minicomputer control, giving a polarization least-squares solution every 2.5 s. The polarimeter was flown on the NASA CV-990 aircraft, in a remote-sensing study of terrestrial cloud particle sizes and shapes.

Coffeen, D. L.↗

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 NTRS1975

Numerical procedure for analyzing Langmuir probe data

A numerical procedure is proposed for analyzing Langmuir probe data in the presence of a two-group plasma containing both primary and Maxwellian electrons. The procedure is known as a least-squares differential-correction technique for determining the unknown coefficients of the governing equation. It is shown that for a given set of input data the results of the analysis are unique and independent of the initial estimate of electron temperature, that convergence is fastest when electron temperature is overestimated, that the results are sensitive to the region of the curve used as input and also to the voltage increment, and that plasma properties determined by the proposed numerical procedure are either consistent with those determined graphically or closer to expected values. With a suitable data acquisition system, the Fortran IV program worked out for this procedure could be used to provide real-time plasma diagnostic information for an operating ion thruster.

Beattie, J. R.↗

NASA NTRS1975

Diffusion in liquid metal systems

Physical properties of twenty liquid metals are reported; some of the data on such liquid metal properties as density, electrical resistivity, thermal conductivity, and heat capacity are summarized in graphical form. Data on laboratory handling and safety procedure are summarized for each metal; heat-transfer-correlations for liquid metals under various conditions of laminar and turbulent flow are included. Where sufficient data were available, temperature equations of properties were obtained by the method of least-squares fit. All values of properties given are valid in the given liquid phase ranges only. Additional tabular data on some 40 metals are reported in the appendix. Included is a brief description of experiments that were performed to investigate diffusion in liquid indium-gallium systems.

Ukanwa, A. O.↗

NASA NTRS1975

Surface fitting three-dimensional bodies

The geometry of general three-dimensional bodies was generated from coordinates of points in several cross sections. Since these points may not be on smooth curves, they are divided into groups forming 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 through longitudinal curves. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines or specifying slopes at selected points. This method was used to surface fit a 70 deg slab delta wing and the HL-10 Lifting Body. The results for the delta wing were very close to the exact geometry. Although there is no exact solution for the lifting body, the surface fit generated a smooth surface with cross-sectional planes very close to prescribed coordinate points.

Dejarnette, F. R.↗

NASA NTRS1975

Experimental evaluation of multiplane-multispeed rotor balancing through multiple critical speeds

The experimentally proven range of application of the influence-coefficient balancing method, especially the least-squares procedure, is extended to include the case of multiple bending critical speeds within the operating range of a test rotor. Tests were conducted on a laboratory quality machine capable of speeds up to 18,000 rpm in order to investigate several distinct practical aspects of flexible-rotor balancing. These include: (1) balancing for operation through four bending critical speeds, (2) balancing of rotors mounted in both rigid and flexible bearing supports, (3) balancing of rotors with various amounts of measured vibration-response data and different numbers of correction planes, and (4) balancing of rotors with different arbitrary initial-unbalance configurations. The results show that a lightly damped, flexible rotor can be balanced systematically and efficiently through four bending critical speeds. It is concluded that the influence-coefficient method should be equally applicable to rotors or shafts having more than four bending critical speeds in their operating-speed ranges.

Tessarzik, J. M.↗

NASA NTRS1975

Lunar occultation of Saturn. I - The diameters of Tethys, Dione, Rhea, Titan, and Iapetus

The diameters of Tethys, Dione, Rhea, Titan and Iapetus were determined from observations of their March 30, 1974, lunar occultations, made with the Mauna Kea 224 and 61 cm telescopes. Light curves were obtained simultaneously in four colors, and the difference between the time of occultation at the two telescopes provided a direct measurement of the slope of the lunar limb, found to be small in all cases. The satellite diameters were determined by least-squares fits of model occultation light curves to the data. Titan's diameter must be at least 5800 km, much larger than the currently accepted value of 5000 km, making it the largest satellite in the solar system. This larger diameter implies a low mean density. For the other four satellites arguments are presented in favor of accepting the occultation diameters corresponding to limb darkened disks. Except for Titan, the lunar occultation diameters generally agree with previous diskmeter and radiometric determinations.

Elliot, J. L.↗

NASA NTRS1975

Evaluation of the dual differential radiometer for remote sensing of sediment and chlorophyll in turbid waters

The dual differential radiometer (DDR) was tested to determine its capability for measuring suspended sediment and chlorophyll in turbid waters. Measurements were obtained from a boat dock and from a helicopter with combinations of sample and reference filters with peak transmissions at various wavelengths. Water samples were taken concurrently and were analyzed for light scattering, particle count, and total chlorophyll. Least-squares estimates of the linear relationship between DDR output and the water parameters yielded correlation coefficients of less than 0.7. Under the turbid water conditions of the present tests, the DDR did not accurately measure either suspended sediment or chlorophyll. A precise knowledge of the spectral signatures of various pollutants might enable appropriate filters to be selected for tuning the DDR to monitor a particular pollutant.

Witte, W. G.↗

NASA NTRS1975

Development of a digital adaptive optimal linear regulator flight controller

Digital adaptive controllers have been proposed as a means for retaining uniform handling qualities over the flight envelope of a high-performance aircraft. Towards such an implementation, an explicit adaptive controller, which makes direct use of online parameter identification, has been developed and applied to the linearized lateral equations of motion for a typical fighter aircraft. The system is composed of an online weighted least-squares parameter identifier, a Kalman state filter, and a model following control law designed using optimal linear regulator theory. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for onboard implementation.

Berry, P.↗

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.↗