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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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This paper addresses the problem of determiining an analytical stochastic controller for achieving docking between two vehicles. With the use of simplifying assumptions, analytical RMS docking errors are determined. The analytical approach presented is considered to be a powerful preliminary design tool in assessing the effects of sensor errors and plant disturbances on docking errors.
Mode matching and segmented duct analytical models have been developed to take advantage of relative placement of liner segments in the design of optimal duct acoustic liners of one, two, and three segments. This paper presents experimental results which were obtained for liners installed in a rectangular duct for the case with no mean airflow through the duct. Excellent correlation is shown between the analytical and experimental data, thus verifying the analytical procedures used to design the optimum segmented lining configurations.
Various analytical approaches to predicting the performance of film cooled turbine blades are reviewed. A two-dimensional cascade flow solution is developed for calculating the effects of the coolant injection on the total flow field. This solution is used with an available analytical performance predicting method to provide an improved method. Comparisons are made with experimental data and other analytical results.
Line-focusing acrylic Fresnel lenses with application potential in the 200 to 370 C range are being analytically and experimentally evaluated. Investigations previously conducted with a 56 cm wide lens have been extended by the present study to experimentation/analyses with a 1.8 by 3.7 m lens. A measured peak concentration ratio of 64 with 90 percent of the transmitted energy focused into a 5.0 cm width was achieved. A peak concentration of 61 and a 90 percent target width of 4.5 cm were analytically computed. The experimental and analytical lens transmittance was 81 percent and 86 percent, respectively. The lens also was interfaced with a receiver assembly and operated in the collection mode. The collection efficiency ranged from 42 percent at 100 C to 26 percent at 300 C.
The basic form of a model representation for systems of n interacting biological species is a set of essentially nonlinear autonomous ordinary differential equations. A generic canonical expression for the rate functions in the equations is reported which permits the analytical general solution to be obtained by elementary computation. It is shown that a general analytical solution is directly obtainable for models where the rate functions are prescribed by the generic canonical expression from the outset. Some illustrative examples are given which demonstrate that the generic canonical expression can be used to construct analytically solvable models for two interacting species with limit-cycle dynamics as well as for a three-species interdependence.
Plastic Fresnel lenses for solar concentration are attractive because of potential for low-cost mass production. An analytical and experimental evaluation of line-focusing Fresnel lenses with application potential in the 200 to 370 C range is reported. Analytical techniques were formulated to assess the solar transmission and imaging properties of a grooves-down lens. Experimentation was based primarily on a 56 cm-wide lens with f-number 1.0. A sun-tracking heliostat provided a non-moving solar source. Measured data indicated more spreading at the profile base than analytically predicted. The measured and computed transmittances were 85 and 87% respectively. Preliminary testing with a second lens (1.85 m) indicated that modified manufacturing techniques corrected the profile spreading problem.
A linear perturbation method developed by White (1972) to improve the correlation between analytical models and experimental data is applied to modeling of the Viking Propulsion Subsystem (VPS), flown successfully as part of the Viking Spacecraft launch of 1975. Analytical models and modal test data developed for the VPS are employed in the application; a set of mathematically generated data and a corresponding perturbed analytical model, representative of actual flight hardware, are also subjected to the White method. It is found that the linear perturbation method does not yield a single unique improved model.
Consideration is given to analytical inversions in the remote sensing of particle size distributions, noting multispectral extinctions in anomalous diffraction approximation and angular and spectral scattering in diffraction approximation. A closed-form analytical inverse solution is derived in order to reconstruct the size distribution of atmospheric aerosols. The anomalous diffraction approximation to Mie's solution is used to describe the particles. Experimental data yield the geometrical area of aerosol polydispersion. Size distribution is thus found from a set of multispectral extinction measurements. In terms of the angular and spectral scattering of light in a narrow forward cone, it is shown that an analytical inverse solution may also be found for the Fraunhofer approximation to the Kirchhoff diffraction, and for an improved expression of this approximation due to Penndorf (1962) and Shifrin-Punina (1968).
Tabulated surface pressure data for a series of four forebodies which have analytically defined cross sections and which are based on a parabolic arc profile having a 20 deg half angle at the nose are presented without analysis. The first forebody has a circular cross section, and the second has a cross section which is an ellipse with an axis ratio of 2/1. The third has a cross section defined by a lobed analytic curve. The fourth forebody has cross sections which develop smoothly from circular at the pointed nose through the lobed analytic curve and back to circular at the aft end. The data generally cover angles of attack from -5 deg to 20 deg at angles of sideslip from 0 deg to 5 deg for Mach numbers of 1.70, 2.50, 3.95, and 4.50 at a constant Reynolds number.
It is known that dynamic rotor inflow has a substantial effect on rotor dynamic loads. Despite the complexity of the unsteady flow problem, simple analytical models can be made useful by identifying their parameters from transient response tests without performing flow measurements. Two analytical inflow models are studied: the first is based on an equivalent blade Lock number, the second is based on a time delayed unsteady momentum inflow. In preparation for the experimental data analysis, identifications from simulated test data and an eigenvalue analysis are performed. The experimental results show that the first analytical inflow model is accurate for rotor advance ratios of 0.4 and above. For lower advance ratios, the second inflow model provides better accuracy. Prediction studies with experimental data not used for the identification are performed to determine the accuracy of the mathematical models.
Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant-density asteroid belt. The derivations include extensions and adaptations of Plakhov's (1968) analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness, and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus. The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained by using the analytic expressions and those obtained by numerical integration are discussed. The effects of the asteroid belt on earth-based ranging to Mars are also demonstrated.
A systematic analytical approach to the determination of helicopter IFR precision approach requirements is formulated. The approach is based upon the hypothesis that pilot acceptance level or opinion rating of a given system is inversely related to the degree of pilot involvement in the control task. A nonlinear simulation of the helicopter approach to landing task incorporating appropriate models for UH-1H aircraft, the environmental disturbances and the human pilot was developed as a tool for evaluating the pilot acceptance hypothesis. The simulated pilot model is generic in nature and includes analytical representation of the human information acquisition, processing, and control strategies. Simulation analyses in the flight director mode indicate that the pilot model used is reasonable. Results of the simulation are used to identify candidate pilot workload metrics and to test the well known performance-work-load relationship. A pilot acceptance analytical methodology is formulated as a basis for further investigation, development and validation.
An analytical procedure has been developed to predict rime ice growth on unprotected airfoil sections and to evaluate the aerodynamic performance. A time stepping method is used in which: (1) water droplet trajectories are calculated, (2) a rime ice shape determined, (3) the flowfield around the iced airfoil is recalculated, and (4) the build-up process iterated upon until the desired icing time is reached. The performance of the iced airfoil shapes are then determined from existing analytic methods. Rime ice shapes determined in the NASA Lewis Icing Research Tunnel on a modified NACA 64 series airfoil agree well with the shapes predicted by the analytical method. Measured and predicted increases in drag due to the rime ice also agree favorably. A simplified scaling analysis is also presented and verified which provides the duplication of full scale results of rime ice accretions in small scale model tests.
A combined experimental and analytical investigation was performed to understand the various fluid processes associated with the conversion of flow energy into electric power in a fluidic generator. Experiments were performed under flight-simulated laboratory conditions and results were compared with those obtained in the free-flight conditions. It is concluded that the mean mass flow critically controlled the output of the fluidic generator. Cross-correlation of the outputs of transducer data indicate the presence of a standing wave in the tube; the mechanism of oscillation is an acoustic resonance tube phenomenon. A linearized model was constructed coupling the flow behavior of the jet, the jet-layer, the tube, the cavity, and the holes of the fluidic generator. The analytical results also show that the mode of the fluidic power generator is an acoustical resonance phenomenon with the frequency of operation given by f approx = a/4L, where f is the frequency of jet swallowing, a is the average speed of sound in the tube, and L is the length of the tube. Analytical results further indicated that oscillations in the fluidic generator are always damped and consequently there is a forcing of the system in operation.
An alternative to rectification is proposed for detection of an ultrasonic signal. This method is especially useful in medical and non-destructive evaluation (nde) applications. With this method, the magnitude of the complex analytic signal is used to define the envelope of the ultrasonic waveform. The square of this quantity has been shown elsewhere to be equal to the true rate-of-arrival of energy. An earlier study, using digital data processing, has already demonstrated the superior resolvability of closely spaced interfaces obtained with the analytic signal magnitude, as compared to conventional rectification. Here, an analogue implementation is presented which utilizes single-sideband techniques to obtain both quadrature components of the analytic signal and its magnitude. A conventional transducer, pulser, and receiver are used.
It is noted that performance predictions for nonlinear digital satellite channels are usually obtained by either purely analytical methods or Monte Carlo simulations. When used with other than very simple channel models, however, they become extremely costly. It is shown that, through analytical modeling of the effect of the nonlinearity on the uplink waveform, it is possible to obtain approximate performance predictions with a minimum of computer time. It is also demonstrated that the results agree quite well with Monte Carlo simulations and that significant trade-offs can be performed with this tool. An analytical simulation based on Blachman's (1968) definition of signal x signal, signal x noise, and noise x noise terms is shown to provide the required flexibility for modeling the effect of signal distortions on the link performance and to produce good results over a wide range of nonlinearities and channel conditions.
A method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure. The method directly identifies, without iteration, a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements. An application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure. The resulting changes in the model are judged to be small compared to expectations of errors in the analysis. Thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics. In addition, it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structures.
A theoretical method by which the energy dependence of the radial diffusion coefficient may be deduced from spectral observations of the particle population at the inner edge of the earth's radiation belts is presented. This region has previously been analyzed with numerical techniques; in this report an analytical treatment that illustrates characteristic limiting cases in the L shell range where the time scale of Coulomb losses is substantially shorter than that of radial diffusion (L approximately 1-2) is given. It is demonstrated both analytically and numerically that the particle spectra there are shaped by the energy dependence of the radial diffusion coefficient regardless of the spectral shapes of the particle populations diffusing inward from the outer radiation zone, so that from observed spectra the energy dependence of the diffusion coefficient can be determined. To insure realistic simulations, inner zone data obtained from experiments on the DIAL, AZUR, and ESRO 2 spacecraft have been used as boundary conditions. Excellent agreement between analytic and numerical results is reported.