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The first year of a two year experimental and analytical program is reported. The program is directed at the elastohydrodynamic behavior of sliding elastomeric rod seals for the Stirling engine. During the year, experimental and analytical tools were developed for evaluating seal leakage, seal friction, and the fluid film thickness at the seal/cylinder interface.
Two orbit computation methods were used: (1) numerical method- The solution to the satellite differential equations were solved in a step-by-step manner, using a mathematical algorithm taken from numerical analysis; and (2) analytical method - The solution was expressed by explicit functions of the independent variable. Analytical drag modules, tesseral terms initialization module, second order and long period terms module, and verification testing of the ASOP program were also considered.
A straightforward method for the user of color imagery to determine the spectral analytical density of dyes present in the processed imagery is presented. The method involves exposing a large number of different color patches on the film which span the gamut of the film's imaging capabilities. From integral spectral density measurements at 16 to 19 different wavelengths, the unit spectral dye curves for each of the three dyes present were determined in two different types of color films. A discussion of the use of these spectral dye densities to determine the transformation between integral density measurements and analytical density is presented.
A general analytical theorem developed by van de Hulst (1946) for inverting the convolution integral is reviewed and illustrated both with synthetic data and with experimental data from time-of-flight measurements. If the undesired influence of an instrument used in an experimental measurement can be represented by the convolution integral, the original undistorted or true distribution may sometimes be recovered in postprocessing the data by means of deconvolution. Analytical deconvolution is achieved by using the coefficients from a power series representation of the distorted output distribution and a set of 'solving polynomials' which may be readily derived from the response function of the instrument.
A wind tunnel technique for obtaining gust frequency response functions for use in predicting the response of flexible aircraft to atmospheric turbulence is evaluated. The tunnel test results for a dynamically scaled cable supported aeroelastic model are compared with analytical and flight data. The wind tunnel technique, which employs oscillating vanes in the tunnel throat section to generate a sinusoidally varying flow field around the model, was evaluated by use of a 1/30 scale model of the B-52E airplane. Correlation between the wind tunnel results, flight test results, and analytical predictions for response in the short period and wing first elastic modes of motion are presented.
Mathematical functions commonly used for representing aerosol size distributions are studied parametrically. Methods for obtaining best fit estimates of the parameters are described. A catalog of graphical plots depicting the parametric behavior of the functions is presented along with procedures for obtaining analytical representations of size distribution data by visual matching of the data with one of the plots. Examples of fitting the same data with equal accuracy by more than one analytic model are also given.
Flight tests for verifying an analytical aerodynamic derivative model of a CH-47 helicopter were conducted for low cruise speeds and transition to hover portions of curved, decelerating landing approach trajectories. All testing was performed on a closed loop basis with the stability augmentation system of the helicopter operating, and response data were obtained using both manual and computer generated input maneuvers. The results indicate some differences between the measured response time histories and those predicted by both analytical and flight test identified derivatives. With some exceptions the discrepancies are not severe, and the overall agreement between the measured and computed time histories is reasonably good. No adverse effects attributable to closed loop testing were noted, and the use of computer generated inputs proved to be superior to manual ones.
This report presents the results from an experimental and analytical investigation of the stress distributions occurring in a rail shear test. The effects of non-uniform stresses induced by differential thermal expansion, rail flexibility and specimen aspect ratio on measured shear modulus and ultimate strength of composite laminates are shown. A two-dimensional linearly elastic finite element model was used to analytically determine how various geometric parameters influenced the magnitude and distribution of inplane normal and shear stresses in a tensile rail shear specimen. Rail shear tests were conducted at room temperature and 589 K (600 F) on selected graphite-polyimide composite laminates using two titanium rail configurations. The analysis and test methods are discussed, and the results of the effects of the various parameters on shear modulus and ultimate strength are presented.
A method developed to determine maximum changes in analytical mass and stiffness matrices to make them consistent with a set of measured normal modes and natural frequencies is presented. The corrected model will be an improved base for studies of physical changes, boundary condition changes, and for prediction of forced responses. The method features efficient procedures not requiring solutions of the eigenvalue problem, and the ability to have more degrees of freedom than the test data. In addition, modal displacements are obtained for all analytical degrees of freedom, and the frequency dependence of the coordinate transformations is properly treated.
The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.
A method is developed and illustrated which finds minimum changes in analytical mass and stiffness matrices to make them consistent with a set of measured normal modes and natural frequencies. The corrected model is an improved base for studies of physical changes, changes in boundary conditions, and for prediction of forced responses. Features of the method are: efficient procedures not requiring solutions of the eigenproblem; the model may have more degrees of freedom than the test data; modal displacements at all the analytical degrees of freedom are obtained; the frequency dependence of the coordinate transformations are properly treated.
Estimation of the impact of jet noise requires analytical modeling not only of the noise source mechanism, but also of the propagation of noise from the source to receiver. One factor which influences the jet noise path is shielding of one jet by another in a twin jet configuration. An analytical model is developed to investigate the shielding phenomenon. The two-dimensional wave equation is solved for a stationary line source impinging upon a cylinder of heated flow. The solution estimates the diffraction and scattering of the incident sound wave by the shielding jet in a plane normal to the jet axis. The frequency dependence of the normalized sound pressure estimated by the model is found to agree in form with empirical data. The azimuthal redistribution of the incident sound shows that, as the frequency of maximum shielding is approached, the scattered sound becomes more highly concentrated into lobes adjacent to the shielding zone.
An analytical method was developed to predict pilot ratings for highly elastic aircraft subject to severe mode interactions between rigid body and elastic dynamics. An extension of the standard optimal control model of pilot response was made to include the hypothesis that the pilot controls the system with an internal model consisting of the slowly varying part of the aircraft dynamics. This modified optimal control model was analytically evaluated for a longitudinal pitch tracking task on a large flexible aircraft. Parametric variations in the undamped natural frequencies of two symmetric elastic modes were made to induce varying amounts of mode interaction. The model proved successful in discriminating when the pilot can or cannot visually separate rigid from elastic pitch response in the turbulence excited tracking task. This method shows considerable promise in making it possible to investigate such mode interaction effects on handling qualities in the preliminary design stage of new aircraft.
A broad survey of possible orbiter landing configurations was made with specific goals of defining boundaries for the landing task. The results suggest that the center of the corridors between marginal and routine represents a more or less optimal preflare condition for regular operations. Various constraints used to define the boundaries are based largely on qualitative judgements from earlier flight experience with the X-15 and lifting body research aircraft. The results should serve as useful background for expanding and validating landing simulation programs. The analytic approach offers a particular advantage in identifying trends due to the systematic variation of factors such as vehicle weight, load factor, approach speed, and aim point. Limitations such as a constant load factor during the flare and using a fixed gear deployment time interval, can be removed by increasing the flexibility of the computer program. This analytic definition of landing profiles of the orbiter may suggest additional studies, includin more configurations or more comparisons of landing profiles within and beyond the corridor boundaries.
Progress in the refinement and evaluation of an analytical jet shielding model are summarized. The model consists of a point noise source impinging on a cylinder of heated flow in which the temperature and velocity are uniform across the cross section of the jet. The shielding jet is infinite in extent along the jet axis and the radius of the jet is constant. The analytical model was compared to experimental data for a point noise source impinging on an ambient temperature, subsonic jet and on a subsonic simulated hot jet using helium as the flow medium. Results of these comparisons are discussed.
Development of jet noise source model, and comparison to experiments with a point noise source are summarized. The refinement of the noise source is expected to resolve discrepancies noted between previous analytical results with a point noise source model and experimental results for twin-jet shielding. Comparison of the analytical model with experimental program which include shielding of a point noise source by a jet and twin jet shielding are also made. The comparisons should serve to define more completely the mechanisms of shielding
Utilizing an optical model potential approximation to the exact nucleus-nucleus multiple-scattering series, optical potentials for nucleon-nucleus and nucleus-nucleus collisions are analytically derived. These expressions are applicable to light and medium cosmic ray nuclei as their single-particle density distributions are analytically determined, without approximation, from their actual harmonic well charge density distributions. Pauli correlation effects are included through the use of a simple Gaussian function to replace the usual expression obtained in the infinite nuclear matter approximation.
An analytical analysis of conditions producing pilot induced oscillations (PIO's) was made for the space shuttle orbiter in a landing approach configuration for the task of milling the elevation angle of the line of sight to a target vehicle. The analysis yielded a value of PIO frequency and a value for the amount of total system time delay (pilot + control system) that can be tolerated before instability results. Calculations were performed showing the effect of varying the range to the target and of varying the handling qualities of the orbiter vehicle. Analytical predictions were compared with simulation results obtained using a visual motion simulator.