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At least 19 records

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DOE OSTI2026

Framework for X-ray mirror surface shape fitting

For accurate characterization of grazing-incidence X-ray mirrors, we present a comprehensive framework to fit measured surface shapes (either slope or height) of X-ray mirrors used in synchrotron radiation and free-electron laser facilities. We summarize the closed-form expressions of some typical surface shapes of X-ray mirrors including elliptic cylinders, hyperbolic cylinders, ellipsoids, hyperboloids, and diaboloids. This framework is composed of four layers: definition of standard shapes with closed-form expressions, generation of theoretical surface with pose parameters (six degrees of freedom defining an object's position and orientation relative to a coordinate system), parameter optimization with the ability to select which parameters are fit and which are held constant, and the development of user-friendly fitting function wrappers for particular fitting tasks. A few practical fitting examples are demonstrated to verify the effectiveness of the proposed fitting framework. We discuss the physical meanings of the fitting parameters, and provide several examples using the elliptic cylinder and ellipsoid shapes to highlight some features of the framework. Moreover, we provide the presented framework as open-source codes (MATLAB and Python codes available at https://github.com/nsls2omf/xmf) to the community to encourage academic collaboration and further improvements.

36 MATERIALS SCIENCE↗

NASA NTRS1985

The Construction of Curves and Surfaces Using Numerical Optimization Techniques

Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions.

Ferguson, D. R.↗

NASA NTRS1984

Fitting Flexible Coverings to Contoured Surfaces

Method using two transparent plastic sheets and polyethylene foam spacer produces flat templates from contoured surfaces. Once prepared, templates laid flat, and insulation inserted between two templates cut to shape to fit contoured surface. Sections of insulation prepared by contour-transferring technique fit contoured surfaces precisely. Procedure used for tailoring protective covers or for installation of vibrationabsorbing material over contoured surfaces.

Helman, D. D.↗

NASA NTRS2018

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

numerical analysi↗

NASA NTRS2018

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

numerical analysis↗

NASA NTRS2018

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least-squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on an in-house object-oriented optimization tool. During the numerical optimization procedure, a design jig-shape is determined by the baseline jig-shape and basis functions. A total of 12 symmetric mode shapes of the cruise-weight configuration, rigid pitch shape, rigid left and right stabilator rotation shapes, and a residual shape are selected as sixteen basis functions. After three optimization runs, the trim shape error distribution is improved, and the maximum trim shape error of 0.9844 inches of the starting configuration becomes 0.00367 inch by the end of the third optimization run.

numerical analysi↗

NASA NTRS1961

A Method of Determining Aerodynamic-Influence Coefficients from Wind-Tunnel Data for Wings at Supersonic Speeds

A method is described for determining aerodynamic-influence coefficients from wind-tunnel data for calculating the steady-state load distribution on a wing with arbitrary angle-of-attack distribution at supersonic speeds. The method combines linearized theory with empirical adjustments in order to give accurate results over a wide range of angles of attack. The experimented data required are pressure distributions measured on a flat wing of the desired planform at the desired Mach number and over the desired range of angles of attack. The method has been tested by applying it to wind-tunnel data measured at Mach numbers of 1.61 and 2.01 on wings of the same planform but of different surface shapes. Influence coefficients adjusted to fit the flat wing gave good predictions of the spanwise and chord-wise distributions of loadings measured on twisted and cambered wings.

Gainer, Patrick A.↗

NASA NTRS1985

Semianalytic modeling of aerodynamic shapes

Equations for the semianalytic representation of a class of surfaces that vary smoothly in cross-sectional shape are presented. Some methods of fitting together and superimposing such surfaces are described. A brief discussion is also included of the application of the theory in various contexts such as computerized lofting of aerodynamic surfaces and grid generation.

Barger, R. L.↗

NASA NTRS2005

Tool Measures Depths of Defects on a Case Tang Joint

A special-purpose tool has been developed for measuring the depths of defects on an O-ring seal surface. The surface lies in a specially shaped ringlike fitting, called a capture feature tang, located on an end of a cylindrical segment of a case that contains a solid-fuel booster rocket motor for launching a space shuttle. The capture feature tang is a part of a tang-and-clevis, O-ring joint between the case segment and a similar, adjacent cylindrical case segment. When the segments are joined, the tang makes an interference fit with the clevis and squeezes the O-ring at the side of the gap.

Ream, M. Bryan↗

NASA NTRS2005

Development of Flexible Multilayer Circuits and Cables

A continuing program addresses the development of flexible multilayer electronic circuits and associated flexible cables. This development is undertaken to help satisfy aerospace-system-engineering requirements for efficient, lightweight electrical and electronic subsystems that can fit within confined spaces, adhere to complexly shaped surfaces, and can be embedded within composite materials. Heretofore, substrate layers for commercial flexible circuitry have been made from sheets of Kapton (or equivalent) polyimide and have been bonded to copper conductors and to other substrate layers by means of adhesives. The substrates for the present developmental flexible circuitry are made from thin films of a polyimide known as LaRC(TM)-SI. This polyimide is thermoplastic and, therefore, offers the potential to eliminate delamination and the need for adhesives. The development work undertaken thus far includes experiments in the use of several techniques of design and fabrication (including computer-aided design and fabrication) of representative flexible circuits. Anticipated future efforts would focus on multilayer bonding, fabrication of prototypes, and overcoming limitations.

Barnes, Kevin N.↗

NASA NTRS1993

Robot-friendly connector

Robot friendly connectors, which, in one aspect, are truss joints with two parts, a receptacle and a joint, are presented. The joints have a head which is loosely inserted into the receptacle and is then tightened and aligned. In one aspect, the head is a rounded hammerhead which initially is enclosed in the receptacle with sloppy fit provided by the shape, size, and configuration of surfaces on the head and on the receptacle.

Parma, George F.↗

NASA NTRS1993

Ultrasonic Probing Of Complexly Shaped Joints

Technique developed involves use of ultrasonics to inspect first bond surfaces of solid-rocket-motor joints. By fitting pieces of insulating materials to mate exactly with complicated shapes of affected parts of insulation, complicated shapes redefined into simpler ones probed more easily. When technique used to insonify from insulation side, one readily detects difference between disbond and good bond. Same technique applied to field tang joints, field clevis joints, and aft-dome-to-fixed-nozzle-housing attachment points. Although developed for inspecting joints in solid rocket motors, also applicable to nondestructive evaluation of other complicated joints.

Madaras, Eric I.↗

NASA NTRS2000

Separation of Atmospheric and Surface Spectral Features in Mars Global Surveyor Thermal Emission Spectrometer (TES) Spectra

We present two algorithms for the separation of spectral features caused by atmospheric and surface components in Thermal Emission Spectrometer (TES) data. One algorithm uses radiative transfer and successive least squares fitting to find spectral shapes first for atmospheric dust, then for water-ice aerosols, and then, finally, for surface emissivity. A second independent algorithm uses a combination of factor analysis, target transformation, and deconvolution to simultaneously find dust, water ice, and surface emissivity spectral shapes. Both algorithms have been applied to TES spectra, and both find very similar atmospheric and surface spectral shapes. For TES spectra taken during aerobraking and science phasing periods in nadir-geometry these two algorithms give meaningful and usable surface emissivity spectra that can be used for mineralogical identification.

Smith, Michael D.↗

NASA NTRS1993

The three-dimensional structure of cumulus clouds over the ocean. 1: Structural analysis

Thermal channel (channel 6, 10.4-12.5 micrometers) images of five Landsat thematic mapper cumulus scenes over the ocean are examined. These images are thresholded using the standard International Satellite Cloud Climatology Project (ISCCP) thermal threshold algorithm. The individual clouds in the cloud fields are segmented to obtain their structural statistics which include size distribution, orientation angle, horizontal aspect ratio, and perimeter-to-area (PtA) relationship. The cloud size distributions exhibit a double power law with the smaller clouds having a smaller absolute exponent. The cloud orientation angles, horizontal aspect ratios, and PtA exponents are found in good agreement with earlier studies. A technique also is developed to recognize individual cells within a cloud so that statistics of cloud cellular structure can be obtained. Cell structural statistics are computed for each cloud. Unicellular clouds are generally smaller (less than or equal to 1 km) and have smaller PtA exponents, while multicellular clouds are larger (greater than or equal to 1 km) and have larger PtA exponents. Cell structural statistics are similar to those of the smaller clouds. When each cell is approximated as a quadric surface using a linear least squares fit, most cells have the shape of a hyperboloid of one sheet, but about 15% of the cells are best modeled by a hyperboloid of two sheets. Less than 1% of the clouds are ellipsoidal. The number of cells in a cloud increases slightly faster than linearly with increasing cloud size. The mean nearest neighbor distance between cells in a cloud, however, appears to increase linearly with increasing cloud size and to reach a maximum when the cloud effective diameter is about 10 km; then it decreases with increasing cloud size. Sensitivity studies of threshold and lapse rate show that neither has a significant impact upon the results. A goodness-of-fit ratio is used to provide a quantitative measure of the individual cloud results. Significantly improved results are obtained after applying a smoothing operator, suggesting the eliminating subresolution scale variations with higher spatial resolution may yield even better shape analyses.

Kuo, Kwo-Sen↗

NASA NTRS2008

Spline-Based Smoothing of Airfoil Curvatures

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.↗

NASA NTRS1991

Mean flow and variability in the Kuroshio Extension from Geosat altimetry data

The mean flow and temporal and spatial variations of the Kuroshio Extension in the region of 140-180 deg E and 30-40 deg N are investigated using altimeter data from the Geosat Exact Repeat Mission (ERM). Mean surface height profiles are estimated along individual tracks by assuming the velocity profile of the Kuroshio Extension to be Gaussian-shaped and by successively fitting this synthetic current's height profile to the residual height data. The mean profiles from ascending and descending tracks are used to derive the mean surface height by an inverse method and to obtain the absolute surface height fields for the first 2.5 yr of the Geosat ERM. Both the mean and the instantaneous height fields thus derived compare well with the available hydrographic data and the SST patterns from the NOAA satellites. Effects of deep mean flow and baroclinic shear are found to be important in explaining the observed propagation speeds.

Qiu, BO↗

NASA NTRS2010

Nearly Seamless Vacuum-Insulated Boxes

A design concept, and a fabrication process that would implement the design concept, have been proposed for nearly seamless vacuum-insulated boxes that could be the main structural components of a variety of controlled-temperature containers, including common household refrigerators and insulating containers for shipping foods. In a typical case, a vacuum-insulated box would be shaped like a rectangular parallelepiped conventional refrigerator box having five fully closed sides and a hinged door on the sixth side. Although it is possible to construct the five-closed-side portion of the box as an assembly of five unitary vacuum-insulated panels, it is not desirable to do so because the relatively high thermal conductances of the seams between the panels would contribute significant amounts of heat leakage, relative to the leakage through the panels themselves. In contrast, the proposal would make it possible to reduce heat leakage by constructing the five-closed-side portion of the box plus the stationary portion (if any) of the sixth side as a single, seamless unit; the only remaining seam would be the edge seal around the door. The basic cross-sectional configuration of each side of a vacuum-insulated box according to the proposal would be that of a conventional vacuum-insulated panel: a low-density, porous core material filling a partially evacuated space between face sheets. However, neither the face sheets nor the core would be conventional. The face sheets would be opposite sides of a vacuum bag. The core material would be a flexible polymer-modified silica aerogel of the type described in Silica/Polymer and Silica/Polymer/Fiber Composite Aero - gels (MSC-23736) in this issue of NASA Tech Briefs. As noted in that article, the stiffness of this core material against compression is greater than that of prior aerogels. This is an important advantage because it translates to greater retention of thickness and, hence, of insulation performance when pressure is applied across the thickness, in particular, when the space between the face sheets is evacuated, causing the core material to be squeezed between the face sheets by atmospheric pressure. Fabrication of a typical vacuum-insulated box according to the proposal would begin with fabrication of a cross-shaped polymer-modified aerogel blanket. The dimensions of the cross would be chosen so that (1) the central rectangular portion of the cross would form the core for the back of the box and (2) the arms of the cross could be folded 90 from the back plane to form the cores of the adjacent four sides of the box. Optionally, the blanket could include tabs for joining the folded sides of the blanket along mating edges and tabs that could serve as hinges for the door. Vacuum bags in the form of similar five-sided boxes would be made of a suitable polymeric film, one bag to fit the outer core surface, the other to fit the inner core surface. By use of commercially available film-sealing equipment, these box-shaped bags would be seamed together to form a single vacuum bag encasing the box-shaped core. Also, a one-way valve would be sealed to the bag. Through this valve, the interior of the bag would be evacuated to a pressure between 1 and 10 torr (approximately between 0.13 and 1.3 kPa). The polymer-modified aerogel core material is known to perform well as a thermal insulator in such a partial vacuum.

Stepanian, Christopher J.↗

NASA NTRS1996

Spatial orientation of semicircular canals and afferent sensitivity vectors in pigeons

Rotational head motion in vertebrates is detected by the semicircular canal system, whose innervating primary afferent fibers carry information about movement in specific head planes. The semicircular canals have been qualitatively examined over a number of years, and the canal planes have been quantitatively characterized in several animal species. The present study first determined the geometric relationship between individual semicircular canals and between the canals and the stereotactic head planes in pigeons. Stereotactic measurements of multiple points along the circumference of the bony canals were taken, and the measured points fitted with a three-dimensional planar surface. Direction normals to the plane's surface were calculated and used to define angles between semicircular canal pairs. Because of the unusual shape of the anterior semicircular canals in pigeons, two planes, a major and a minor, were fitted to the canal's course. Calculated angle values for all canals indicated that the horizontal and posterior semicircular canals are nearly orthogonal, but the anterior canals have substantial deviations from orthogonality with other canal planes. Next, the responses of the afferent fibers that innervate each of the semicircular canals to 0.5 Hz sinusoidal rotation about an earth-vertical axis were obtained. The head orientation relative to the rotation axis was systematically varied so that directions of maximum sensitivity for each canal afferent could be determined. These sensitivity vectors were then compared with the canal plane direction normals. The afferents that innervated specific semicircular canals formed homogeneous clusters of sensitivity vectors in different head planes. The horizontal and posterior afferents had average sensitivity vectors that were largely co-incident with the innervated canal plane direction normals. Anterior canal afferents, however, appeared to synthesize contributions from the major and minor plane components of the bony canal structure to produce a resultant sensitivity vector that was positioned between the canal planes. Calculated angles between the average canal afferent sensitivity vectors revealed that direction orthogonality is preserved at the afferent signal level, even though deviations from canal plane orthogonality exist.

NASA Discipline Neuroscience↗