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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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For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.
A decomposition algorithm is presented which optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.
A weak-interaction solution algorithm is established for aerodynamic flow field prediction about an isolated airfoil. It requires numerical solution of differential equations governing potential flow, viscous and turbulent boundary layer flow, and the turbulent wake flow downstream of a trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. These in turn alter the viscous flow through imposed pressure gradients. Closure for turbulence is accomplished using a second order model. Numerical evaluations assess factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems as solved using a finite element algorithm.
An algorithm for estimating infrared horizon scanner biases for earth-oriented spacecraft is presented. A mathematical description of the proposed algorithm is given, and the algorithm is evaluated for use by two earth-oriented spacecraft: the Applications Explorer Missions-A/Heat Capacity Mapping Mission (AEM-A/HCMM) and Seasat-A. The results of this study indicate that scanner alignment and calibration errors appear as nearly constant biases in the scanner pitch and roll data and that these constant biases can be estimated to within 0.05 degree for AEM-A and 0.03 degree for Seasat-A.
Fast accurate algorithms are presented for computing an optimal attitude which minimizes a quadratic loss function. These algorithms compute an optimal rotation which carries a set of reference vectors into a set of corresponding observation vectors. Simplifications of these algorithms are obtained for the case of small rotation angles. Applications to the Magsat mission are discussed.
A new implicit algorithm for time step integration of finite element structural dynamic equations is presented. Convergence, stability and numerical damping properties are discussed. Due to the way nonlinear structural behavior is taken into account, the algorithm is expected to compare favorably with existing ones. Some simple numerical results are presented. A related explicit algorithm is also derived and shortly discussed.
A new stable and efficient implementation of the Lanczos algorithm is presented. The algorithm is a powerful method for finding a few eigenvalues and eigenvectors at one or both ends of the spectrum of a symmetric matrix A. The algorithm is particularly effective if A is large and sparse in that the only way in which A enters the calculation is through a subroutine which computes Av for any vector v. Thus the user is free to take advantage of any sparsity structure in A and A need not even be represented as a matrix et al.
The paper presents a finite element method for minimum weight design of structures with lower-bound constraints on the natural frequencies, and upper and lower bounds on the design variables. The design algorithm is essentially an iterative solution of the Kuhn-Tucker optimality criterion. The three most important features of the algorithm are: (1) a small number of design iterations are needed to reach optimal or near-optimal design, (2) structural elements with a wide variety of size-stiffness may be used, the only significant restriction being the exclusion of curved beam and shell elements, and (3) the algorithm will work for multiple as well as single frequency constraints. The design procedure is illustrated with three simple problems.
Recently two dissection algorithms (one-way and incomplete nested dissection) have been developed for solving the sparse positive definite linear systems arising from n by n grid problems. Concurrently, vector computers (such as the CDC STAR-100 and TI ASC) have been developed for large scientific applications. An analysis of the use of dissection algorithms on vector computers dictates that vectors of maximum length be utilized thereby implying little or no dissection; on the other hand, minimizing operation counts suggest that considerable dissection be performed. In this paper we discuss the resolution of this conflict by minimizing the total time required by vectorized versions of the two algorithms.
Six algorithms for extracting significant wave height from Geos 3 altimeter data have been compared using simulated Geos 3 data for a single long pass including a variety of sea states and for short segments in the vicinity of NOAA data buoys. The study included algorithms reported by Walsh (1979), Rufenach and Alpers (1978), Gower (1979), Godbey (1965), Fedor (1978) and a real-time model (Miller and Hayne, 1972). Individual differences in results obtained by the algorithms were small, and calculations were found to be in good agreement with surface truth data.
In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.
An algorithm is proposed for a scheme of simultaneous coordinate relaxation. A variant of root-shifting coordinate relaxation, this procedure consists of iterating several vectors at the same time, instead of one at a time. Results of application of the algorithm to test matrices are discussed. For many matrix eigenvalue problems for which coordinate relaxation is a viable approach, the present algorithm is more effective than previous implementations of coordinate relaxation. Total central processor operations should be decreased due to significantly improved convergence.
A flight management algorithm designed to improve the accuracy of delivering the airplane fuel efficiently to a metering fix at a time designated by air traffic control is discussed. The algorithm provides a 3-D path with time control (4-D) for a test B 737 airplane to make an idle thrust, clean configured descent to arrive at the metering fix at a predetermined time, altitude, and airspeed. The descent path is calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard pressure and temperature effects. The flight management descent algorithms and the results of the flight tests are discussed.
An algorithm is presented for calculating both the quantity of compressor bleed flow required to cool the turbine and the decrease in turbine efficiency caused by the injection of cooling air into the gas stream. The algorithm, which is intended for an axial flow, air routine in a properly written thermodynamic cycle code. Ten different cooling configurations are available for each row of cooled airfoils in the turbine. Results from the algorithm are substantiated by comparison with flows predicted by major engine manufacturers for given bulk metal temperatures and given cooling configurations. A list of definitions for the terms in the subroutine is presented.
An algorithm which transfers an aircraft from an initial position and heading to a final position and heading was developed for onboard synthesis of horizontal flight paths. The algorithm finds all solutions possible, and selects the one with minimum path length. Degenerate conditions in which one or more of the basic segments is missing are handled without difficulty. The solution to this problem is derived, and a FORTRAN listing of the algorithm is provided.
A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.
An algorithm for synthesizing optimal aircraft trajectories for specified range was developed and implemented in a computer program written in FORTRAN IV. The algorithm, its computer implementation, and a set of example optimum trajectories for the Boeing 727-100 aircraft are described. The algorithm optimizes trajectories with respect to a cost function that is the weighted sum of fuel cost and time cost. The optimum trajectory consists at most of a three segments: climb, cruise, and descent. The climb and descent profiles are generated by integrating a simplified set of kinematic and dynamic equations wherein the total energy of the aircraft is the independent or time like variable. At each energy level the optimum airspeeds and thrust settings are obtained as the values that minimize the variational Hamiltonian. Although the emphasis is on an off-line, open-loop computation, eventually the most important application will be in an on-board flight management system.
A simple flight management descent algorithm designed to improve the accuracy of delivering an airplane in a fuel-conservative manner to a metering fix at a time designated by air traffic control was developed and flight tested. This algorithm provides a three dimensional path with terminal area time constraints (four dimensional) for an airplane to make an idle thrust, clean configured (landing gear up, flaps zero, and speed brakes retracted) descent to arrive at the metering fix at a predetermined time, altitude, and airspeed. The descent path was calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard pressure and temperature effects. The flight management descent algorithm is described. The results of the flight tests flown with the Terminal Configured Vehicle airplane are presented.