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An adaptive psychometric procedure that places each trial at the current most probable Bayesian estimate of threshold is described. The procedure takes advantage of the common finding that the human psychometric function is invariant in form when expressed as a function of log intensity. The procedure is simple, fast, and efficient, and may be easily implemented on any computer.
Some of the progress in computational aerodynamics over the last decade is reviewed. The Numerical Aerodynamic Simulation Program objectives, computational goals, and implementation plans are described.
The capability of two numerical methods, one for transonic and one for supersonic flows, to predict the flow fields about representative fighter aircraft forebodies in the vicinity of the engine inlets was examined. The Mach number range covered was 0.9 to 2.5 and the angle-of-attack range was 0 deg to 25 deg. The computer progams that implement each of the numerical methods are described as to their features and usage, and results are compared with comprehensive wind tunnel data. Although both prediction methods were inviscid, results show that the aerodynamic effects of the forebody, with and without a wing, can be simulated fairly well. Futher work is needed to include the effects of viscosity, including vortex shedding.
A method for assessing the wall interference in transonic two-dimensional wind tunnel tests including the effects of the tunnel sidewall boundary layer was developed and implemented in a computer program named TWINTN4. The method involves three successive solutions of the transonic small disturbance potential equation to define the wind tunnel flow, the equivalent free air flow around the model, and the perturbation attributable to the model. Required input includes pressure distributions on the model and along the top and bottom tunnel walls which are used as boundary conditions for the wind tunnel flow. The wall-induced perturbation field is determined as the difference between the perturbation in the tunnel flow solution and the perturbation attributable to the model. The methodology used in the program is described and detailed descriptions of the computer program input and output are presented. Input and output for a sample case are given.
The Theoretical Mechanics Branch has as one of its long-range goals to work toward solving real-time trajectory optimization problems on board an aircraft. This is a generic problem that has application to all aspects of aviation from general aviation through commercial to military. Overall interest is in the generic problem, but specific problems to achieve concrete results are examined. The problem is to develop control laws that generate approximately optimal trajectories with respect to some criteria such as minimum time, minimum fuel, or some combination of the two. These laws must be simple enough to be implemented on a computer that is flown on board an aircraft, which implies a major simplification from the two point boundary value problem generated by a standard trajectory optimization problem. In addition, the control laws allow for changes in end conditions during the flight, and changes in weather along a planned flight path. Therefore, a feedback control law that generates commands based on the current state rather than a precomputed open-loop control law is desired. This requirement, along with the need for order reduction, argues for the application of singular perturbation techniques.
Numerical techniques that improve the accuracy and stability of algorithms for the small disturbance and full potential equations used to calculate transonic flows are described. For the small disturbance equation, the algorithm improvements are: (1) the use of monotone switches in the type dependent finite differencing, and (2) the use of stable and simple second order accurate spatial differencing; these improvements are for steady and unsteady transonic flows. For the steady full potential equation, the improvement is in the use of a monotone switch in the type dependent finite differencing of an approximate factorization (AF2) algorithm. All these improvements are implemented in present computer codes by making minor coding modifications.
Comparisons of calculated and experimental transonic unsteady pressures and airloads for four of the AGARD Two Dimensional Aeroelastic Configurations and for a rectangular supercritical wing are presented. The two dimensional computer code, XTRAN2L, implementing the transonic small perturbation equation was used to obtain results for: (1) pitching oscillations of the NACA 64A010A; NLR 7301 and NACA 0012 airfoils; (2) flap oscillations for the NACA 64A006 and NRL 7301 airfoils; and (3) transient ramping motions for the NACA 0012 airfoils. Results from the three dimensional code XTRAN3S are compared with data from a rectangular supercritical wing oscillating in pitch. These cases illustrate the conditions under which the transonic inviscid small perturbation equation provides reasonable predictions.
A new formulation is proposed for the problem of parameter estimation in dynamic systems with both process and measurement noise. The formulation applies to continuous-time state space system models with discrete-time measurements. Previous formulations of this problem encountered several theoretical and practical difficulties which are overcome by the new formulation. The most important element of the new formulation is a reparameterization of the unknown noise covariances. A computer program that implements the new formulation is available.
Current methods for calculating transonic flows with the small-disturbance potential equation are typically only first-order accurate in the supersonic regions of the flow. However, calculations using the full-potential equation show significant improvements in accuracy when second-order methods are used instead of first-order methods. In this paper, algorithms for the small-disturbance equations are presented, for both steady and unsteady flows, with spatial differencing that is second-order accurate in both the subsonic and supersonic regions of the flow. These algorithms are stable, simple extensions of implicit monotone algorithms; the former are only first-order accurate spatially in the supersonic regions. Several calculations in one and two dimensions have been made, and the first- and second-order calculations are compared. In one dimension, the calculations include the four types of shock-wave motion. In two dimensions, the comparisons include steady flow over a Korn airfoil and unsteady flow over a pitching airfoil. All the comparisons in two dimensions show that the new methods are just as stable numerically as the old methods, but improve the accuracy of the solutions. The algorithm improvements can be implemented in present computer codes by making minor coding modifications.
Some of the progress in computational aerodynamics over the last decade is reviewed. The Numerical Aerodynamic Simulation Program objectives, computational goals, and implementation plans are described. Previously announced in STAR as N84-16139
An analysis to obtain the buckling loads of a rectangular orthotropic plate with a centrally located cutout is described. Cutout shapes can be elliptical, circular, rectangular, or square. The boundary conditions considered in the analysis are simply supported unloaded edges and either clamped or simply supported loaded edges. The plate is loaded in uniaxial compression by either uniform edge displacement or uniform edge stress. A computer program that implements this analysis is described, and the program use is demonstrated by sample problems.
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.
Comparisons of calculated and experimental transonic unsteady pressures and airloads for four of the AGARD Two Dimensional Aeroelastic Configurations and for a rectangular supercritical wing are presented. The two dimensional computer code, XTRAN2L, implementing the transonic small perturbation equation was used to obtain results for: (1) pitching oscillations of the NACA 64A010A; NLR 7301 and NACA 0012 airfoils; (2) flap oscillations for the NACA 64A006 and NRL 7301 airfoils; and (3) transient ramping motions for the NACA 0012 airfoils. Results from the three dimensional code XTRAN3S are compared with data from a rectangular supercritical wing oscillating in pitch. These cases illustrate the conditions under which the transonic inviscid small perturbation equation provides reasonable predictions.
Signal analysis techniques for the detection and classification of incipient mechanical failures in turbomachinery were developed, implemented and evaluated. Signal analysis techniques available to describe dynamic measurement characteristics are reviewed. Time domain and spectral methods are described, and statistical classification in terms of moments is discussed. Several of these waveform analysis techniques were implemented on a computer and applied to dynamic signals. A laboratory evaluation of the methods with respect to signal detection capability is described. Plans for further technique evaluation and data base development to characterize turbopump incipient failure modes from Space Shuttle main engine (SSME) hot firing measurements are outlined.
A system for digital inteferogram evaluation based on an image-processing system connected to a host computer has been implemented. The system supports one- and two-dimensional interferogram evaluations. Interferograms are digitized, enhanced, and segmented. The fringe coordinates are extracted, and the fringes are represented as polygon data structures. Fringe numbering and fringe interpolation modules are implemented. The system supports editing and interactive features as well as graphic visualization. An application of the system to the evaluation of double exposure interferograms from the transonic flow field around a helicopter blade and the reconstruction of the 3-D flow field are given.
An investigation to develop, implement, and evaluate signal analysis techniques for the detection and classification of incipient mechanical failures in turbomachinery is reviewed. A brief description of the Space Shuttle Main Engine (SSME) test/measurement program is presented. Signal analysis techniques available to describe dynamic measurement characteristics are reviewed. Time domain and spectral methods are described, and statistical classification in terms of moments is discussed. Several of these waveform analysis techniques have been implemented on a computer and applied to dynamc signals. A laboratory evaluation of the methods with respect to signal detection capability is described. A unique coherence function (the hyper-coherence) was developed through the course of this investigation, which appears promising as a diagnostic tool. This technique and several other non-linear methods of signal analysis are presented and illustrated by application. Software for application of these techniques has been installed on the signal processing system at the NASA/MSFC Systems Dynamics Laboratory.
A real time computer program was implemented on a F-15 jet fighter to monitor in-flight engine performance of a Digital Electronic Engine Controlled (DEES) F-100 engine. The application of two gas generator methods to calculate in-flight thrust real time is described. A comparison was made between the actual results and those predicted by an engine model simulation. The percent difference between the two methods was compared to the predicted uncertainty based on instrumentation and model uncertainty and agreed closely with the results found during altitude facility testing. Data was obtained from acceleration runs of various altitudes at maximum power settings with and without afterburner. Real time in-flight thrust measurement was a major advancement to flight test productivity and was accomplished with no loss in accuracy over previous post flight methods.
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.