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Desired roots are first isolated by Sturm sequence procedure. Then special variant of inverse iteration technique is applied for individual determination of each root along with its vector. Program was written in FORTRAN V for UNIVAC 1100-series computers.
Some of the existing methods to globally approximate the roots of transcendental equations namely, Graeffe's method, are studied. Summation of the reciprocated roots, Whittaker-Bernoulli method, and the extension of Bernoulli's method via Koenig's theorem are presented. The Aitken's delta squared process is used to accelerate the convergence. Finally, the suitability of these methods is discussed in various cases.
The stress corrosion cracking (SCC) resistance of 18Ni maraging steel (grades 200, 250, 300, and 350) was determined in 3.5 percent salt (NaCl) solution, synthetic sea water, high humidity, and outside MSFC atmosphere. All grades of the maraging steel were found to be susceptible to SCC in varying degrees according to their strengths, with the lowest strength steel (grade 200) being the least susceptible and the highest strength steel (grade 350), the most susceptible to SCC. The SCC resistance of 250 grade maraging steel was also evaluated in salt and salt-chromate solutions using fracture mechanics techniques. The threshold value, K sub SCC, was found to be approximately 44 MN/sq m square root m, (40 ksi square root in.) or 40 percent of the K sub Q value.
A numerical analysis of the pressure distribution of a lubricant in contact with a rough surface was conducted. The magnitude of the pressures was determined by their root mean square value for the contact of two dimensional cylinders. The pressure was found to vary in the following manner: (1) the location in the contact, (2) the spectrum or frequency content of the surface roughness, (3) the mean plateau film thickness, and (4) the root mean square value of the surface roughness. Mathematical models are developed to show the relationships of the parameters.
By adjusting composition, metastable gamma (austenite) and epsilon (hexagonal) martensite may be retained in Fe-Mn and Fe-Mn-Cr alloys and used to impact toughness through the TRIP mechanism. The resulting alloys have excellent toughness at cryogenic temperatures. The best alloys obtained to date are: Fe-20Mn, with sigma (sub y) = 79ksi and K sub IC = 275ksi square root of (in) at 77 K, and Fc-16Mn-8Cr, with sigma sub y = 85ksi and K sub IC = 72ksi square root of (in) at 77 K.
The structure of the drift instability was examined in several density regimes. Let sub e be the total electron mean free path, k sub z the wave-vector component along the magnetic field, and the ratio of perpendicular ion diffusion to parallel electron streaming rates. At low densities (k sub z lambda 1) the drift mode is isothermal and should be treated kineticly. In the finite heat conduction regime square root of m/M k sub z Lambda sub 1) the drift instability threshold is reduced at low densities and increased at high densities as compared to the isothermal threshold. Finally, in the energy transfer limit (k sub z kambda sub e square root of m/M) the drift instability behaves adiabatically in a fully ionized plasma and isothermally in a partially ionized plasma for an ion-neutral to Coulomb collision frequency ratio.
Rotary plant growth accelerating apparatus for increasing plant yields by effectively removing the growing plants from the constraints of gravity and increasing the plant yield per unit of space is described. The apparatus is comprised of cylindrical plant beds supported radially removed from a primary axis of rotation, with each plant bed being driven about its own secondary axis of rotation and simultaneously moved in a planetary path about the primary axis of rotation. Each plant bed is formed by an apertured outer cylinder, a perforated inner cylinder positioned coaxially, and rooting media disposed in the space between. A rotatable manifold distributes liquid nutrients and water to the rooting media through the perforations in the inner cylinders as the plant beds are continuously rotated by suitable drive means.
The implementation of the algorithms used in the flight program to approximate elementary functions and mathematical procedures was checked. This was done by verifying that at least one, and in most cases, more than one function computed through the use of the algorithms was calculated properly. The following algorithms were checked: sine-cosine, arctangent, natural logarithm, square root, inverse square root, as well as the vector dot and cross products.
A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.
A gust alleviation system for aircraft flying in turbulent air was analyzed. A vane sensor (with noise) was used to measure vertical gusts, and elevators and flaps were used to reduce the root-mean-square value of the normal accelerations associated with the aircraft response to gusts. Since turbulence has stochastic properties, stochastic control theory was used in the analysis. A quadratic performance-index function involving normal acceleration and control deflections was minimized. Application of the analysis was illustrated by a short take-off and landing (STOL) airplane in flight through turbulent air. Effects of varying the noise characteristics of the vane sensor and of a weighting matrix in the performance-index function were determined. Calculations were performed as required by stochastic control theory to obtain the root-mean-square response of the airplane to turbulence. Results show that good alleviation was calculated when the intensity of the measurement noise was about 3.6 percent of the vane deflection angles.
A FORTRAN digital computer program which performs the general analysis of linearized control systems is described. State variable techniques are used to analyze continuous, discrete, and sampled data systems. Analysis options include the calculation of system eigenvalues, transfer functions, root loci, root contours, frequency responses, power spectra, and transient responses for open- and closed-loop systems. A flexible data input format allows the user to define systems in a variety of representations. Data may be entered by inputing explicit data matrices or matrices constructed in user written subroutines, by specifying transfer function block diagrams, or by using a combination of these methods.
The pressure distribution over thin oblique airfoils at subsonic speeds is studied. It is found that the flows again can be obtained by the superposition of elementary conical flow fields. In the case of the sweptback wing the pressure distributions remain qualitatively similar at subsonic and supersonic speeds. Thus a distribution similar to the Ackeret type of distribution appears on the root sections of the sweptback wing at M = 0. The resulting positive pressure drag on the root section is balanced by negative drags on outboard sections.
Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.
Experiments were performed on the photooxidation of NH3 at room temperature and the photolysis of NH3-NO mixtures in order to determine the reaction paths of NH2 with O2. NH3 was photolyzed (NH3 + E yields NH2 + H) in the presence of O2 above 0.6 torr at 213.9 nm and 25 C, producing N2 and N2O. Only N2 and N2O were produced with any significant quantum yield, and their quantum yield was invariant with reaction conditions, which imposes a great number of constraints reducing the number of possible reactions greatly. It is argued that the N2 must be produced from the NH2O2 radical which was produced by the reaction between NH2 and O2. Subsequent reactions leading to N2 and N2O are speculative. In the photolysis of NH3 in the presence of NO and NO-O2 mixtures, the products identified were N2, H2, and N2O. Without the presence of O2, the reaction scheme after photolysis is (2) NH2 + NO yields N2 + H2O, (3) H + NO + M yields HNO + M, (4) H + HNO yields H2 + NO, and (5) 2HNO yields N2O + H2O. The average value for the ratio k3 times the square root of k5 divided by k4 was computed to be (1.6 plus or minus 0.6) times 10 to the minus 28th cm to the exponent 9/2 per square root sec. In addition, the presence of 113 mtorr of O2 had no effect on the quantum yields of N2 or H2, so it appears that it does not deactivate electronically excited NH3.
An automated digital computer procedure is presented in this paper which enables efficient solution of the eigenvalue problem associated with the supersonic panel flutter phenomena. The step-by-step incremental solution procedure is based on an inverse iteration technique which effectively utilizes solution results from the previous step in determining such results during the current solution step. Also, the computations are limited to the determination of a few specific roots only, which are expected to contain the flutter mode, and this is achieved at each step without having to compute any other root. The structural discretization achieved by the finite-element method yields highly banded stiffness, mass, and aerodynamic matrices; the aerodynamic matrix evaluated by the linearized piston theory is real but unsymmetric in nature. The solution algorithm presented in this paper fully exploits the banded form of the associated matrices, and the resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most efficient and economical when compared to existing procedures of such analysis. Numerical results are presented for a two-dimensional panel flutter problem.
A class of infrared detectors is proposed, and experimental results are presented for a prototype device. The material used is LaF3, an ionic conductor with a capacitance that varies exponentially with temperature. The detectivity of a prototype detector is estimated from measured signal voltages and incident power, and a Johnson noise voltage is calculated from the measured resistance. At a modulation frequency of 20 Hz, the estimated detectivity is about 2 million cm/sq root Hz/W. For the parameters characterizing this device, the estimated detectivity is consistent with a theoretical prediction. The theory further predicts an optimum detectivity of about 1 billion cm/sq root Hz/W for much thinner devices than the prototypes.
The successful application of high creep strength, directionally solidified gamma/gamma prime-delta (Ni-19.7Cb-6Cr-2.5Al) eutectic superalloy turbine blades requires the development of suitable coatings for airfoil, root and internal blade surfaces. In order to improve coatings for the gamma/gamma prime-delta alloy, the current investigation had the goals of (1) refining promising coating compositions for directionally solidified eutectics, (2) evaluating the effects of coating/ substrate interactions on the mechanical properties of the alloy, and (3) evaluating diffusion aluminide coatings for internal surfaces. Burner rig cyclic oxidation, furnace cyclic hot corrosion, ductility, and thermal fatigue tests indicated that NiCrAlY+Pt(63 to 127 micron Ni-18Cr-12Al-0.3Y + 6 micron Pt) and NiCrAlY(63 to 127 micron Ni-18Cr-12Al-0.3Y) coatings are capable of protecting high temperature gas path surfaces of eutectic alloy airfoils. Burner rig (Mach 0.37) testing indicated that the useful coating life of the 127 micron thick coatings exceeded 1000 hours at 1366 K (2000 deg F). Isothermal fatigue and furnance hot corrosion tests indicated that 63 micron NiCrAlY, NiCrAlY + Pt and platinum modified diffusion aluminide (Pt + Al) coating systems are capable of protecting the relatively cooler surfaces of the blade root. Finally, a gas phase coating process was evaluated for diffusion aluminizing internal surfaces and cooling holes of air-cooled gamma/gamma prime-delta turbine blades.
Linear filters, including the conventional Kalman filter and versions of square root filters devised by Potter and Carlson, are studied for potential application on streaming computers. The square root filters are known to maintain a positive definite covariance matrix in cases in which the Kalman filter diverges due to ill-conditioning of the matrix. Vectorization of the filters is discussed, and comparisons are made of the number of operations and storage locations required by each filter. The Carlson filter is shown to be the most efficient of the filters on the Control Data STAR-100 computer.