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Closed loop system with reference to different gyro stabilization loops present in modern space vehicle inertial measuring unit, using Prony exponential series curve fitting method as analytical tool
Solar cycle prediction based upon random number technique, Fourier curve fits and power spectra analysis
Least squares method theory and application to curve fitting, data smoothing, and solution of overdetermined sets of equations
Curve fitting for optimum redundance reduction on sampled data, describing polygonal and approximate polygonal techniques
Curve fitting for modified paired comparisons using linearized nonlinear regression
Techniques overcome equipment limitations that restrict other computer techniques in solving trivial cases. The use of curve fitting by quadratic interpolation greatly reduces required digital storage space.
Aerodynamic derivatives were obtained for the M2-F2 lifting body flight vehicle in the subsonic flight region between Mach numbers of 0.41 and 0.64 and altitudes of 7000 feet to 45,000 feet. The derivatives were determined by a flight time history curve-fitting process utilizing a hybrid computer. The flight-determined derivatives are compared with wind-tunnel and predicted values. Modal-response characteristics, calculated from the flight derivatives, are presented.
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
The refractive indices of 2H SiC were measured over the wavelength range 435.8 to 650.9 nm by the method of minimum deviation. At the wavelength lambda = 546.1 nm, the ordinary index n sub 0 was 2.6480 and the extraordinary index n sub e was 2.7237. The estimated error (standard deviation) in the measured values is 0.0006 for n sub 0 and 0.0009 for n sub e. The experimental data were curve fitted to the Cauchy equation for the index of refraction as a function of wavelength. The birefringence of 2H SiC was found to vary from 0.0719 at lambda = 650.9 nm to 0.0846 at lambda = 435.8 nm.
For the small, high performance reactors required for space electric applications, adequate neutronic analysis is of crucial importance, but in terms of computational time consumed, nuclear calculations probably yield the least amount of detail for mission analysis study. It has been found possible, after generation of only a few designs of a reactor family in elaborate thermomechanical and nuclear detail to use simple curve fitting techniques to assure desired neutronic performance while still performing the thermomechanical analysis in explicit detail. The resulting speed-up in computation time permits a broad detailed examination of constraints by the mission analyst.
The landing contact conditions for the HL-10, M2-F2/F3, and the X-24A lifting body vehicles are analyzed statistically for 81 landings. The landing contact parameters analyzed are true airspeed, peak normal acceleration at the center of gravity, roll angle, and roll velocity. Ground measurement parameters analyzed are lateral and longitudinal distance from intended touchdown, lateral distance from touchdown to full stop, and rollout distance. The results are presented in the form of histograms for frequency distributions and cumulative frequency distribution probability curves with a Pearson Type 3 curve fit for extrapolation purposes.
Equilibrium surface segregation of aluminum in a copper-10-atomic-percent-aluminum single crystal alloy oriented in the /111/ direction was demonstrated by using Auger electron spectroscopy. This crystal was in the solid solution range of composition. Equilibrium surface segregation was verified by observing that the aluminum surface concentration varied reversibly with temperature in the range 550 to 850 K. These results were curve fitted to an expression for equilibrium grain boundary segregation and gave a retrieval energy of 5780 J/mole (1380 cal/mole) and a maximum frozen-in surface coverage three times the bulk layer concentration. Analyses concerning the relative merits of sputtering calibration and the effects of evaporation are also included.
A computer program to analyze Mossbauer data is presented in detail. The least-squares curve fitting techniques described apply to single line spectra, single hyperfine spectra, or when the constituent spectra are separated well enough to let the individual absorption peaks stand alone. The present program is not adapted for complex spectra resulting from the existence of several local environments in the absorber iron alloy. Sample problems are presented to aid the user in setting up and running the program. The program is written in FORTRAN 4 language for the Control Data 6000 series digital computer with the SCOPE 3.0 operating system and requires approximately 115,000 octal locations of core storage. A typical case with one absorption peak runs in 20 seconds, and a typical problem with six absorption peaks requires 50 seconds.
A computer program was developed that selects, from a list of candidate functions, the approximating functions and associated coefficients which result in the best curve fit of a given set of numerical data. The advantages of the approach used here are: (1) Multivariable approximations can be performed. (2) Flexibility with respect to the type of approximations used is available. (3) The program is designed to choose the best terms to be used in the approximation from an arbitrary list of possible terms so that little knowledge of the proper approximating form is required. (4) Recursion relations are used in determining the coefficients of the approximating functions, which reduces the computer execution time of the program.
Computer programs for flow fields around planetary entry vehicles require real-gas equilibrium thermodynamic properties in a simple form which can be evaluated quickly. To fill this need, polynomial approximations were found for thermodynamic properties of air and model planetary atmospheres. A coefficient-averaging technique was used for curve fitting in lieu of the usual least-squares method. The polynomials consist of terms up to the ninth degree in each of two variables (essentially pressure and density) including all cross terms. Four of these polynomials can be joined to cover, for example, a range of about 1000 to 11000 K and 0.00001 to 1 atmosphere (1 atm = 1.0133 x 100,000 N/m sq) for a given thermodynamic property. Relative errors of less than 1 percent are found over most of the applicable range.
Measurement of the refractive indices of 2H SiC over the wavelength range from 435.8 to 650.9 nm by the method of minimum deviation. A curve fit of the experimental data to the Cauchy dispersion equation yielded, for the ordinary index, n sub zero = 2.5513 + 25,850/lambda squared + 8.928 x 10 to the 8th power/lambda to the 4th power and, for the extraordinary index, n sub e = 2.6161 + 28,230/lambda squared + 11.490 x 10 to the 8th power/lambda to the 4th power when lambda is expressed in nm. The estimated error (standard deviation) in these values is plus or minus 0.0006 for n sub zero and plus or minus 0.0009 for n sub e. The birefringence calculated from these expressions is about 20% less than previously published values.
Pressure data from a 20-degree cone-cylinder in a variable porosity wind tunnel for the Mach range 0.2 to 5.0 are compared to an interference free standard in order to determine wall interference effects. Four 20-degree cone-cylinder models representing an approximate range of percent blockage from one to six were compared to curve-fits of the interference free standard at each Mach number and errors determined at each pressure tap location. The average of the absolute values of the percent error over the length of the model was determined and used as the criterion for evaluating model blockage interference effects. The results are presented in the form of the percent error as a function of model blockage and Mach number.
The primary aim of this investigation was verification of basic methods which are to be used in cataloging elastomer dynamic properties (stiffness and damping) in terms of viscoelastic model constants. These constants may then be used to predict dynamic properties for general elastomer shapes and operating conditions, thereby permitting optimum application of elastomers as energy absorption and/or energy storage devices in the control of vibrations in a broad variety of applications. The efforts reported involved: (1) literature search; (2) the design, fabrication and use of a test rig for obtaining elastomer dynamic test data over a wide range of frequencies, amplitudes, and preloads; and (3) the reduction of the test data, by means of a selected three-element elastomer model and specialized curve fitting techniques, to material properties. Material constants thus obtained have been used to calculate stiffness and damping for comparison with measured test data. These comparisons are excellent for a number of test conditions and only fair to poor for others. The results confirm the validity of the basic approach of the overall program and the mechanics of the cataloging procedure, and at the same time suggest areas in which refinements should be made.