On the figure of the planet Mercury
Mercury shape estimated with isostatic form of equilibrium controlled by situation near perihelion passage at 3-2 resonance spin rate, discussing solidification thermal effects
Liu, H.-S.↗
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The size and shape of equilibrium capillary surfaces
The classical theory of capillary is concerned largely with size and shape estimates in symmetric asymptotic configurations. Recent developments leading to global results for all symmetric cases, and to qualitative information on asymptotic properties are discussed. Additional stability criteria are described. Asymmetric situations leading to behavior that differs strikingly from the symmetric case are discussed. When gravity vanishes, capillary surfaces in the accustomed sense may not appear. The question of characterizing those tubes in which surfaces can be found has partially been settled. Progress toward determining the effects of contact angle hysteresis in cases of particular interest is reported.
Finn, R.↗
Shape Determination for Large Static Structures
Parameter and shape estimates updated from new measurements. Involves statistical structural analysis, statistical electromagneticfield analysis, filtering, measurement modeling, and iterative prediction/correction procedures. Estimating algorithms result from generalizations of Kalman statistical-filter theory.
Rodriguez, G.↗
Table mountain observatory support to other programs
The Table Mountain Observatory (TMO) facilities include well equipped 24 inch and 16 inch telescopes with a 40 inch telescope (owned by Pomona College) due for completion during FY 89. This proposal is to provide operational support (equipment maintenance, setup, and observing assistnce) at TMO to other programs. The program currently most heavily supported by this grant is the asteroid photometry program directed by A. W. Harris. During 1987, about 20 asteroids were observed, including a near-earth asteroid, 1951 Midas. The photometric observations are used to derive rotation periods, estimate shapes and pole orientations, and to define the phase relations of asteroids. The E class asteroid 64 Angelina was observed, and showed the same opposition spike observed of 44 Jysa, last year. Comet observations are made with the narrow band camera system of David Rees, University College London. Observational support and training was provided to students and faculty from Claremont Colleges for variable star observing programs. Researchers propose to continue the asteroid program, with emphasis on measuring phase relations of low and high albedo asteroids at very low phase angles, and supporting collaborative studies of asteroid shapes.
Harris, Alan W.↗
Adaptive Strategies for Controls of Flexible Arms
An adaptive controller for a modern manipulator has been designed based on asymptotical stability via the Lyapunov criterion with the output error between the system and a reference model used as the actuating control signal. Computer simulations were carried out to test the design. The combination of the adaptive controller and a system vibration and mode shape estimator show that the flexible arm should move along a pre-defined trajectory with high-speed motion and fast vibration setting time. An existing computer-controlled prototype two link manipulator, RALF (Robotic Arm, Large Flexible), with a parallel mechanism driven by hydraulic actuators was used to verify the mathematical analysis. The experimental results illustrate that assumed modes found from finite element techniques can be used to derive the equations of motion with acceptable accuracy. The robust adaptive (modal) control is implemented to compensate for unmodelled modes and nonlinearities and is compared with the joint feedback control in additional experiments. Preliminary results show promise for the experimental control algorithm.
Yuan, Bau-San↗
Sonoluminescence Bubble Measurements using Vision-Based Algorithms
Vision-based measurement methods were used to measure bubble sizes in this sonoluminescence experiment. Bubble imaging was accomplished by placing the bubble between a bright light source and a microscope-CCD camera system. A collimated light-emitting diode was operated in a pulsed model with an adjustable time delay with respect to the piezo-electric transducer drive signal. The light-emitting diode produced a bubble shadowgraph consisting of a multiple exposure made by numerous light pulses imaged onto a charge-couple device camera. Each image was transferred from the camera to a computer-controlled machine vision system via a frame grabber. The frame grabber was equipped with on-board memory to accomodate sequential image buffering while images were transferred to the host processor and analyzed. This configuration allowed the host computer to perform diameter measurements, centroid position measurements and shape estimation in "real-time" as the next image was being acquired. Bubble size measurement accuracy with an uncertainty of 3 microns was achieved using standard lenses and machine vision algorithms. Bubble centroid position accuracy was also within the 3 micron tolerance of the vision system. This uncertainty estimation accounted for the optical spatial resolution, digitization errors and the edge detection algorithm accuracy. The vision algorithms include camera calibration, thresholding, edge detection, edge position determination, distance between two edges computations and centroid position computations.
Hall, Nancy R.↗
Adaptive Load Control of Flexible Aircraft Wings Using Fiber Optic Sensing
Over the past century aircraft wing design has transformed from the morphing wing used on the Wright Flyer to rigid wings with little to no shape-tailoring abilities. Modern day wings are designed to fly at a single trim condition and optimized to have a maximum aerodynamic efficiency at only this condition. Shape morphing wings on the other hand have the potential to undergo geometric changes allowing them to adapt to their mission profiles. Several flight demonstrations have been conducted over the decades using morphing-wing technologies. Active wing-twist control was demonstrated on the X-53 Active Aeroelastic Wing (AAW) research project by utilizing multiple leading- and trailing-edge control surfaces. Passive morphing technology has been demonstrated on the Rockwell RPRV-870 Highly Maneuverable Aircraft Technology (HiMAT) aircraft. In the current study, the wings of a small unmanned aerial system (sUAS) were modified to have segmented control surfaces (SCS). The modifications include segmenting the original wing control surfaces (one flap and one aileron per wing) into 44 individual sections, each section having its own independent servo control motor. The wings were also instrumented with a network of over 1800 fiber-optic strain sensors (on four sensing fibers distributed over the top and bottom surfaces of the wing) monitoring the strain response of the wing to aerodynamic loading. The SCS positions were manipulated in real time to modify the spanwise lift distribution of the wings on the sUAS. The change in the structural response of the wings caused by load redistribution was quantified by measuring the bending strains on the upper and lower wing surfaces using an on-board compact fiber-optic strain sensing (cFOSS) system. A feedback controller was developed to control the SCS positions using strain-based shape estimations from the Displacement Transfer Function (DTF). Post-processing of the strain data allowed for the transverse displacement distributions and load distributions to be compared for the conventional and segmented control surface cases using displacements and loads algorithms developed by Richards and Ko at AFRC (refs. 5-10). While the current study focused on the shifting of the spanwise aerodynamic loads as quantified by displacements, future applications for loads or displacement control might include active gust alleviation and flutter suppression.
Pena, Francisco↗
Application of Radon Transform to Multi-Angle Measurements Made by the Research Scanning Polarimeter: A New Approach to Cloud Tomography. Part I: Theory and Tests on Simulated Data.
The Research Scanning Polarimeter (RSP) is an airborne along-track scanner measuring the polarized and total reflectances in 9 spectral channels. The RSP was a prototype for the Aerosol Polarimetry Sensor (APS) launched on-board the NASA Glory satellite. Currently the retrieval algorithms developed for the RSP are being adopted for the measurements of the space-borne polarimeters on the upcoming NASA’s Plankton, Aerosol, Cloud Ocean Ecosystem (PACE)satellite mission. The RSP’s uniquely high angular resolution coupled with the high frequency of measurements allows for characterization of liquid water cloud droplet sizes using the polarized rainbow structure. It also provides geometric constraints on the cumulus cloud’s 2D cross section yielding the cloud’s geometric shape estimates. In this study we further build on the latter technique to develop a new tomographic approach to retrieval of cloud internal structure from remote sensing measurements. While tomography in the strict definition is a technique based on active measurements yielding a tomogram (directional optical thickness as a function of angle and offset of the view ray), we developed a “semi-tomographic” approach in which tomogram of the cloud is estimated from passive observations instead of being measured directly. This tomogram is then converted into 2D spatial distribution of the extinction coefficient using inverse Radon transform (filtered back projection) which is the standard tomographic procedure used e.g., in medical CT scans. This algorithm is computationally inexpensive compared to techniques relying on highly-multi-dimensional least-square fitting; it does not require iterative 3D RT simulations. The resulting extinction distribution is defined up to an unknown constant factor, so we discuss the ways to calibrate it using additional independent measurements. In the next step we use the profile of the droplet size distribution parameters from the cloud’s side (derived by fitting the polarized rainbows) to convert the 2D extinction distribution into that of the droplet number concentration. We illustrate and validate the proposed technique using 3D-RT-simulatedRSP observations of a LES-generated Cu cloud. Quantitative comparisons between the retrieved and the original optical and microphysical parameters are presented.
clouds↗
Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
Huang, Zhaofeng↗
Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
Huang, Zhaofeng↗
Modeling, estimation and identification methods for static shape determination of flexible structures
This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.
Rodriguez, G.↗
Simulation study of geometric shape factor approach to estimating earth emitted flux densities from wide field-of-view radiation measurements
A study was performed on the use of geometric shape factors to estimate earth-emitted flux densities from radiation measurements with wide field-of-view flat-plate radiometers on satellites. Sets of simulated irradiance measurements were computed for unrestricted and restricted field-of-view detectors. In these simulations, the earth radiation field was modeled using data from Nimbus 2 and 3. Geometric shape factors were derived and applied to these data to estimate flux densities on global and zonal scales. For measurements at a satellite altitude of 600 km, estimates of zonal flux density were in error 1.0 to 1.2%, and global flux density errors were less than 0.2%. Estimates with unrestricted field-of-view detectors were about the same for Lambertian and non-Lambertian radiation models, but were affected by satellite altitude. The opposite was found for the restricted field-of-view detectors.
Weaver, W. L.↗
Simulation study of a geometric shape factor technique for estimating earth-emitted radiant flux densities from wide-field-of-view radiation measurements
Geometric shape factors were computed and applied to satellite simulated irradiance measurements to estimate Earth emitted flux densities for global and zonal scales and for areas smaller than the detector field of view (FOV). Wide field of view flat plate detectors were emphasized, but spherical detectors were also studied. The radiation field was modeled after data from the Nimbus 2 and 3 satellites. At a satellite altitude of 600 km, zonal estimates were in error 1.0 to 1.2 percent and global estimates were in error less than 0.2 percent. Estimates with unrestricted field of view (UFOV) detectors were about the same for Lambertian and limb darkening radiation models. The opposite was found for restricted field of view detectors. The UFOV detectors are found to be poor estimators of flux density from the total FOV and are shown to be much better as estimators of flux density from a circle centered at the FOV with an area significantly smaller than that for the total FOV.
Weaver, W. L.↗
Aerial measurement error with a dot planimeter: Some experimental estimates
A shape analysis is presented which utilizes a computer to simulate a multiplicity of dot grids mathematically. Results indicate that the number of dots placed over an area to be measured provides the entire correlation with accuracy of measurement, the indices of shape being of little significance. Equations and graphs are provided from which the average expected error, and the maximum range of error, for various numbers of dot points can be read.
Yuill, R. S.↗
Three-Dimensional Shapes and Impactor Size Estimation of Stardust Impact
Impact tracks formed by cometary dust capture in silica aerogel collectors in the Stardust mission [1] have a variety of shapes, showing diversity of the cometary dust [2]. We have investigated 3-D structures and elemental distributions of three impact tracks using synchrotron radiation x-ray analyses (microtomography and XRF) as one of the preliminary examination [3]. In this study, additional five tracks were investigated by the same analytical method. Impactor sizes of the tracks were estimated from the track entrance sizes and Fe abundances. Size parameters, such as length, of the tracks were normalized by the impactor size to compare track shape
Iida, Y.↗
Suppression of Soot Formation and Shapes of Laminar Jet Diffusion Flames
Laminar nonpremixed (diffusion) flames are of interest because they provide model flame systems that are far more tractable for analysis and experiments than practical turbulent flames. In addition, many properties of laminar diffusion flames are directly relevant to turbulent diffusion flames using laminar flamelet concepts. Finally, laminar diffusion flame shapes have been of interest since the classical study of Burke and Schumann because they involve a simple nonintrusive measurement that is convenient for evaluating flame shape predictions. Motivated by these observations, the shapes of round hydrocarbon-fueled laminar jet diffusion flames were considered, emphasizing conditions where effects of buoyancy are small because most practical flames are not buoyant. Earlier studies of shapes of hydrocarbon-fueled nonbuoyant laminar jet diffusion flames considered combustion in still air and have shown that flames at the laminar smoke point are roughly twice as long as corresponding soot-free (blue) flames and have developed simple ways to estimate their shapes. Corresponding studies of hydrocarbon-fueled weakly-buoyant laminar jet diffusion flames in coflowing air have also been reported. These studies were limited to soot-containing flames at laminar smoke point conditions and also developed simple ways to estimate their shapes but the behavior of corresponding soot-free flames has not been addressed. This is unfortunate because ways of selecting flame flow properties to reduce soot concentrations are of great interest; in addition, soot-free flames are fundamentally important because they are much more computationally tractable than corresponding soot-containing flames. Thus, the objectives of the present investigation were to observe the shapes of weakly-buoyant laminar jet diffusion flames at both soot-free and smoke point conditions and to use the results to evaluate simplified flame shape models. The present discussion is brief.
Xu, F.↗
Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics
The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.
Pai, Shantaram S.↗
Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics
The calculation of shape and scale parametes of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by using the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.
Shantaram, S. Pai↗