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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.

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NASA NTRS1971

An analysis and comparison of several trajectory optimization methods

The sensitivities of the convergence characteristics of the methods to initially assumed parameters and trial solution, convergence times, computer logic, and storage requirements are discussed. Numerical comparison of the convergence characteristics is made by considering a minimum time, low thrust, Earth-Mars transfer trajectory. A modified quasi-linearization method reduces convergence time by approximately 70% when compared with the generalized Newton-Raphson method and allows the terminal boundary to be specified by a general function of the problem variables. A uniquely specified and easily determined, time dependent weighting matrix for the gradient techniques accelerates the shaping of the optimal control program and improves the convergence characteristics during the terminal iterations. Convergence envelopes, indicating how sensitive the convergence characteristics are to initially assumed parameters, are plotted for the perturbation and quasi-linearization methods. Several iteration schemes are proposed which increase the size of the convergence envelopes and decrease the sensitivity of the method to initially assumed parameters.

Lewallen, J. M.↗
NASA NTRS1972

Analysis of an arched outer-race ball bearing considering centrifugal forces

A Newton-Raphson method of iteration was used in evaluating the radial and axial projection of the distance between the ball center and the outer raceway groove curvature center (V and W). Fatigue life evaluations were made. The similar analysis of a conventional bearing can be directly obtained from the arched bearing analysis by simply letting the amount of arching be zero (g = 0) and not considering equations related to the unloaded half of the outer race. The analysis was applied to a 150-mm angular contact ball bearing. Results for life, contact loads, and angles are shown for a conventional bearing (g = 0) and two arched bearings (g = 0.127 mm (0.005 in.), and 0.254 mm (0.010 in.)). The results indicate that an arched bearing is highly desirable for high speed applications. In particular, for a DN value of 3 million (20,000 rpm) and an applied axial load of 4448 N (1000 lb), an arched bearing shows an improvement in life of 306 percent over that of a conventional bearing. At 4.2 million DN (28,000 rpm), the corresponding improvement is 340 percent. It was also found for low speeds, the arched bearing does not offer the advantages that it does for high speed applications.

Hamrock, B. J.↗
NASA NTRS1972

Flight-determined derivatives and dynamic characteristics of the CV-990 airplane

Flight-determined longitudinal and lateral-directional stability and control derivatives are presented for the CV-990 airplane for various combinations of Mach number, altitude, and flap setting throughout the flight envelope up to a Mach number of 0.87. Also presented are the dynamic characteristics of the aircraft calculated from the flight-obtained derivatives and the measured phugoid characteristics. The derivative characteristics were obtained from flight records of longitudinal and lateral-directional transient oscillation maneuvers by using a modified Newton-Raphson digital derivative determination technique. Generally the derivatives exhibited consistent variation with lift coefficient in the low-speed data and with Mach number and altitude in the high-speed data. Many also varied with flap deflection, notably spoiler effectiveness and directional stability.

Gilyard, G. B.↗
NASA NTRS1972

Optimized solution of Kepler's equation

A detailed description is presented of KEPLER, an IBM 360 computer program used for the solution of Kepler's equation for eccentric anomaly. The program KEPLER employs a second-order Newton-Raphson differential correction process, and it is faster than previously developed programs by an order of magnitude.

Kohout, J. M.↗
NASA NTRS1972

SCIP2 flight instrumentation specification for parameter identification: User's guide

SCIP2 which is a digital computer program that can be used to investigate the effects of instrumentation errors on the accuracy of aircraft stability and control derivatives identified from flight test data is presented. The program is based on the assumptions that the aircraft differential equations of motion are linear and consist of small perturbations about a quasisteady flight condition. It is also assumed that a Newton-Raphson optimization technique is used for identifying the estimates of the parameters. A summary of the equations which are coded in the program are included.

Taniguchi, N.↗
NASA NTRS1972

Analysis of an arched outer-race ball bearing considering centrifugal forces.

Thrust-load analysis of a 150-mm angular contact ball bearing, taking into account centrifugal forces but omitting gyroscopics, elastohydrodynamics, and thermal effects. A Newton-Raphson method of iteration is used to evaluate the radial and axial projection of the distance between the ball center and the outer raceway groove curvature center. Fatigue life of the bearing is evaluated. Results for life, contact loads, and angles are given for a conventional bearing and two arched bearings.

Hamrock, B. J.↗
NASA NTRS1973

An historical survey of computational methods in optimal control.

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Polak, E.↗
NASA NTRS1973

Optimization of self-acting herringbone journal bearing for maximum stability

Groove parameters were determined to maximize the stability of herringbone grooved journal bearings. Parameters optimized were groove depth, width, length, and angle. Optimization was performed using a small eccentricity, infinite groove analysis in conjunction with: (1) a previously developed Newton-Raphson procedure for bearings with the smooth member rotating or with the grooved member rotating at low compressibility numbers, and (2) a newly-developed vector technique for bearings with the grooved member rotating at high compressibility numbers. The design curves enable one to choose the optimum bearing for a wide range of operating conditions. These include: (1) compressibility numbers from 0 (incompressible) to 80, (2) length to diameter ratios from 1/4 to 2, and (3) smooth or grooved member rotating. Compared to bearings optimized to maximize load capacity, bearings optimized for stability: (1) allow a thousandfold increase in bearing-supported mass in some cases before onset of instability (the most dramatic increase are for bearings with small L/D operating at high compressibility numbers), and (2) lose no more than 77-percent of their load capacity in any case studied. Stability is much greater when the grooved member rotates.

Fleming, D. P.↗
NASA NTRS1972

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Scott, R. K.↗
NASA NTRS1974

A comparison of two methods of extracting stability derivatives from flight test data

Two methods for extracting stability derivatives from flight data are compared. A modified Newton-Raphson quasilinearization minimization technique and a digital-analog (hybrid) matching technique were used to analyze the same data maneuvers obtained from two aircraft. About 70 maneuvers from an F-111E aircraft were analyzed over a Mach number range of 0.3 to 2.0 and an angle of attack range of 3 to 19 degrees. About 20 maneuvers were analyzed for the X-24A lifting body at Mach numbers of 0.5, 0.8, and 0.9, and an angle of attack range of 4 to 13 degrees. Stability derivatives were extracted from these maneuvers and the results from the two techniques, along with wind tunnel results, were compared.

Kirsten, P. W.↗
NASA NTRS1974

Identification of M2/F3 stability and control derivatives from flight data containing gust effects

The application of the maximum likelihood identification technique to M2/F3 lifting body flight data containing wind gust effects is discussed. With the objective of this effort being the identification of the stability and control derivatives, it is shown first that the output error technique (or modified Newton-Raphson) fails to fit the recorded data accurately. The means of applying the maximum likelihood technique to this problem are then discussed and the results given which indicate an accurate fit to the data. The question of derivative signs opposite to the wind tunnel values is then addressed and the results of three techniques for dealing with this problem are presented. These techniques are a priori weighting, fixing parameter values, and rank deficient inverses.

Stepner, D. E.↗
NASA NTRS1974

Determination of propulsion-system-induced forces and moments of a Mach 3 cruise aircraft

During the joint NASA/USAF flight research program with the YF-12 airplane, the Dutch roll damping was found to be much less during automatic inlet operation than during fixed inlet operation at Mach numbers greater than 2.5 and with the yaw stability augmentation system off. It was concluded that the significant reduction in Dutch roll damping was due to the forces and moments induced by the variable-geometry features of the inlet. Two stability-derivative extraction techniques were applied to the flight data; the recently developed Newton-Raphson technique and the time vector method. These techniques made it possible to determine the forces and moments generated by spike and bypass door movement.

Gilyard, G. B.↗