Search NASA⌕ Search

SEARCH · Search NASA

Results for “Dimensional”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Application of a laser scanner to three dimensional visual sensing tasks

The issues are described which are associated with using a laser scanner for visual sensing and the methods developed by the author to address them. A laser scanner is a device that controls the direction of a laser beam by deflecting it through a pair of orthogonal mirrors, the orientations of which are specified by a computer. If a calibrated laser scanner is combined with a calibrated camera, it is possible to perform three dimensional sensing by directing the laser at objects within the field of view of the camera. There are several issues associated with using a laser scanner for three dimensional visual sensing that must be addressed in order to use the laser scanner effectively. First, methods are needed to calibrate the laser scanner and estimate three dimensional points. Second, methods to estimate three dimensional points using a calibrated camera and laser scanner are required. Third, methods are required for locating the laser spot in a cluttered image. Fourth, mathematical models that predict the laser scanner's performance and provide structure for three dimensional data points are necessary. Several methods were developed to address each of these and has evaluated them to determine how and when they should be applied. The theoretical development, implementation, and results when used in a dual arm eighteen degree of freedom robotic system for space assembly is described.

Ryan, Arthur M.↗
NASA NTRS1993

Three-dimensional flow in radial turbomachinery and its impact on design

In the two papers on the 'Theory of Blade Design for Large Deflections' published in 1984, a new inverse design technique was presented for designing the shape of turbomachinery blades in three-dimensional flow. The technique involves the determination of the blade profile from the specification of a distribution of the product of the radius and the pitched averaged tangential velocity (i.e., r bar-V(sub theta), the mean swirl schedule) within the bladed region. This is in contrast to the conventional inverse design technique for turbomachinery blading in two dimensional flow in which the blade surface pressure or velocity distribution is specified and the blade profile determined as a result; this is feasible in two-dimensional flow because the streamlines along the blade surfaces are known a priori. However, in three-dimensional flow, the stream surface is free to deform within the blade passage so that the streamlines on the blade surfaces are not known a priori; thus it is difficult and not so useful to prescribe the blade surface pressure or velocity distribution and determine the resulting blade profile. It therefore seems logical to prescribe the swirl schedule within the bladed region for designing a turbomachinery blade profile in three-dimensional flow. Furthermore, specifying r bar-V(sub theta) has the following advantages: (1) it is related to the circulation around the blade (i.e., it is an aerodynamic quantity); (2) the work done or extracted is approximately proportional to the overall change in r bar-V(sub theta) across a given blade row (Euler turbine equation); and (3) the rate of change of r bar-V(sub theta) along the mean streamline at the blade is related to the pressure jump across the blade and therefore the blade loading. Since the publications of those two papers, the technique has been applied to the design of a low speed as well as a high speed radial inflow turbine (for turbocharger applications) both of which showed definite improvements in performance over that of wheels of conventional designs, the design study of a high pressure ratio radial inflow turbine with and without splitter blades.

Tan, Choon S.↗
NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗
NASA NTRS1993

The three-dimensional evolution of a plane mixing layer - Pairing and transition to turbulence

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Moser, Robert D.↗
NASA NTRS1947

Investigation of Axial-flow Fan and Compressor Rotors Designed for Three-dimensional Flow

An investigation has been conducted to determine whether three-dimensional flows may be utilized in axial-flow fan and compressor rotors so that the spanwise load distribution may be varied to obtain high pressure rise. Two rotors, one with approximately uniform and one with solid-body downstream tangential-velocity distributions, were designed and tested at the design blade angle. Radial surveys of total pressure, static pressure, and flow angle were made upstream and downstream of the test rotors through a quantity-coefficient range. Tests of the solid-body rotor were also conducted at a large value of tip clearance. The results indicated that the three-dimensional flows may be utilized with high efficiency and that the three-dimensional theory used in conjunction with two-dimensional cascade data is sufficiently accurate for design purposes. The tests also showed that the tip-clearance losses of rotors highly loaded at the tips are not excessive. The existing three-dimensional theory in simplified for and an illustrative rotor design are presented in appendixes.

Kahane, A↗
NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗
NASA NTRS1992

Linear stability theory and three-dimensional boundary layer transition

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

Spall, Robert E.↗
NASA NTRS1994

The load separation technique in the elastic-plastic fracture analysis of two- and three-dimensional geometries

Load separation is the representation of the load in the test records of geometries containing cracks as a multiplication of two separate functions: a crack geometry function and a material deformation function. Load separation is demonstrated in the test records of several two-dimensional geometries such as compact tension geometry, single edge notched bend geometry, and center cracked tension geometry and three-dimensional geometries such as semi-elliptical surface crack. The role of load separation in the evaluation of the fracture parameter J-integral and the associated factor eta for two-dimensional geometries is discussed. The paper also discusses the theoretical basis and the procedure for using load separation as a simplified yet accurate approach for plastic J evaluation in semi-elliptical surface crack which is a three-dimensional geometry. The experimental evaluation of J, and particularly J(sub pl), for three-dimensional geometries is very challenging. A few approaches have been developed in this regard and they are either complex or very approximate. The paper also presents the load separation as a mean to identify the blunting and crack growth regions in the experimental test records of precracked specimens. Finally, load separation as a methodology in elastic-plastic fracture mechanics is presented.

Sharobeam, Monir H.↗
NASA NTRS1994

Three-dimensional aspects of radiative transfer in remote sensing of precipitation: Application to the 1986 COHMEX storm

Several multifrequency techniques for passive microwave estimation of precipitation based on the absorption and scattering properties of hydrometers have been proposed in the literature. In the present study, plane-parallel limitations are overcome by using a model based on the discrete-ordinates method to solve the radiative transfer equation in three-dimensional rectangular domains. This effectively accounts for the complexity and variety of radiation problems encountered in the atmosphere. This investigation presents result for plane-parallel and three-dimensional radiative transfer for a precipitating system, discusses differences between these results, and suggests possible explanations for these differences. Microphysical properties were obtained from the Colorado State University Regional Atmospehric Modeling System and represent a hailstorm observed during the 1986 Cooperative Huntsville Meteorological Experiment. These properties are used as input to a three-dimensional radiative transfer model in order to simulate satellite observation of the storm. The model output consists of upwelling brightness temperatures at several of the frequencies on the Special Sensor Microwave/Imager. The radiative transfer model accounts for scattering and emission of atmospheric gases and hydrometers in liquid and ice phases. Brightness temperatures obtained from the three-dimensional model of this investigation indicate that horizontal inhomogeneities give rise to brightness temperature fields that can be quite different from fields obtained using plane-parallel radiative transfer theory. These differences are examined for various resolutions of the satellite sensor field of view. In adddition, the issue of boundary conditions for three-dimensional atmospheric radiative transfer is addressed.

Haferman, J. L.↗
NASA NTRS1994

High dimensional feature reduction via projection pursuit

The recent development of more sophisticated remote sensing systems enables the measurement of radiation in many more spectral intervals than previously possible. An example of that technology is the AVIRIS system, which collects image data in 220 bands. As a result of this, new algorithms must be developed in order to analyze the more complex data effectively. Data in a high dimensional space presents a substantial challenge, since intuitive concepts valid in a 2-3 dimensional space to not necessarily apply in higher dimensional spaces. For example, high dimensional space is mostly empty. This results from the concentration of data in the corners of hypercubes. Other examples may be cited. Such observations suggest the need to project data to a subspace of a much lower dimension on a problem specific basis in such a manner that information is not lost. Projection Pursuit is a technique that will accomplish such a goal. Since it processes data in lower dimensions, it should avoid many of the difficulties of high dimensional spaces. In this paper, we begin the investigation of some of the properties of Projection Pursuit for this purpose.

Jimenez, Luis↗
NASA NTRS1997

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

Montgomery, Matthew D.↗
NASA NTRS2000

Comparison of The Dimensional Stability of Kel-F 81 and Neoflon CTFE M400H Polychlorotrifluoroethylenes Used in Valve Seat Application

The dimensional stability of polychlorotrifluoroethylene (PCTFE) valve seats used in oxygen regulator applications was determined by thermomechanical analysis (TMA). Two traceable grades of PCTFE were tested; Kel-F 81 and Neoflon CTFE M400H. For these particular resins, the effect of percent crystallinity, zero strength time (ZST) molecular weight, resin grade, process history (compression-molded versus extruded) on the dimensional stability and annealing behavior was determined. In addition to the traceable Kel-F 81 and Neoflon CTFE M400H grades, actual PCI'PH valve seats of differing geometry and design were tested by TMA. The PCTFE valve seats were of unspecified resin grade, although certain inferences about the grade could be drawn based on knowledge of the valve seat fabrication date. Results consistently revealed dimensional instability of varying magnitude at temperatures ranging from 40 to 70 degrees Celsius. Furthermore, some of the pre- 1 995 seats appeared to be more dimensionally stable than those fabricated after 1995. The TMA results are discussed in the context of several proposed ignition mechanisms; namely, particle impact, presence of contaminant oils and fibers, and localized heating by flow friction and/or resonance. The effect of metal constraint on the dimensional stability of PCTFE is also discussed. Finally, the effect of percent crystallinity, ZST molecular weight, resin grade, process history (compression-molded versus extruded) on the AIT, delta Hc and impact sensitivity of various types of Neoflon CTFE M400H was determined using Kel-F 81 as a control. Results show that the AIT, delta Hc and impact sensitivity were essentially independent of Neoflon CTFE process history and structure.

Waller, Jess M.↗
NASA NTRS1996

Experimental and Computational Boundary-Layer Studies in a Supersonic Two-Dimensional Nozzle

Calculations have been carried out on the adiabatic laminar boundary layer developing on the surface of a two-dimensional supersonic nozzle, consisting of contoured nozzle blocks and flat sidewalls. Two- and three-dimensional Navier-Stokes codes, as well as two-dimensional boundary-layer codes have been employed. Thee codes have been adapted to the characteristics of a specific wind tunnel nozzle, so that their numerical results could be directly compared with experimental data obtained in the same nozzle. Such comparisons have been made for the boundary-layer growth on the contoured nozzle, and for the boundary-layer growth, surface streamlines and surface shear on the sidewalls. The three-dimensional Navier-Stokes code was found to be the only one to correctly predict the mean boundary-layer flow on both the sidewalls and the contoured nozzle. Theory and experiment both indicate that the sidewall flow is highly three-dimensional, with non-uniform shear, comer vortices and a boundary layer strongly distorted by cross flows induced by lateral pressure gradients.

Brogan, Torence P.↗
NASA NTRS1998

Experimental and Computational Boundary-Layer Studies In a Supersonic Two-Dimensional Nozzle

Experiments and computations were carried out on the adiabatic laminar boundary layer developing along the surfaces of a two-dimensional supersonic nozzle, consisting of upper and lower contoured nozzle blocks and flat sidewalls. Two- and three-dimensional Navier-Stokes codes, as well as two-dimensional boundary-layer codes were employed. These codes were adapted to the characteristics of a specific wind tunnel nozzle, so that their numerical results could be directly compared with experimental data obtained in the same nozzle. Such comparisons were made for the boundary-layer growth on the nozzle contoured surfaces, and for the boundary-layer growth, surface streamlines and surface shear on the sidewalls. The three-dimensional Navier-Stokes code was found to be the only one to correctly predict the mean laminar boundary-layer flow on both the sidewalls and the contoured surfaces. Theory and experiment both indicated that the sidewall flow is highly three-dimensional, with non-uniform shear, corner vortices and a boundary layer strongly distorted by cross flows induced by lateral pressure gradients.

Demetriades, Anthony↗
NASA NTRS2001

Hippocampal place-cell firing during movement in three-dimensional space

"Place" cells of the rat hippocampus are coupled to "head direction" cells of the thalamus and limbic cortex. Head direction cells are sensitive to head direction in the horizontal plane only, which leads to the question of whether place cells similarly encode locations in the horizontal plane only, ignoring the z axis, or whether they encode locations in three dimensions. This question was addressed by recording from ensembles of CA1 pyramidal cells while rats traversed a rectangular track that could be tilted and rotated to different three-dimensional orientations. Cells were analyzed to determine whether their firing was bound to the external, three-dimensional cues of the environment, to the two-dimensional rectangular surface, or to some combination of these cues. Tilting the track 45 degrees generally provoked a partial remapping of the rectangular surface in that some cells maintained their place fields, whereas other cells either gained new place fields, lost existing fields, or changed their firing locations arbitrarily. When the tilted track was rotated relative to the distal landmarks, most place fields remapped, but a number of cells maintained the same place field relative to the x-y coordinate frame of the laboratory, ignoring the z axis. No more cells were bound to the local reference frame of the recording apparatus than would be predicted by chance. The partial remapping demonstrated that the place cell system was sensitive to the three-dimensional manipulations of the recording apparatus. Nonetheless the results were not consistent with an explicit three-dimensional tuning of individual hippocampal neurons nor were they consistent with a model in which different sets of cells are tightly coupled to different sets of environmental cues. The results are most consistent with the statement that hippocampal neurons can change their "tuning functions" in arbitrary ways when features of the sensory input or behavioral context are altered. Understanding the rules that govern the remapping phenomenon holds promise for deciphering the neural circuitry underlying hippocampal function.

Non-NASA Center↗
NASA NTRS2000

Three-Dimensional Electron Optics Model Developed for Traveling-Wave Tubes

A three-dimensional traveling-wave tube (TWT) electron beam optics model including periodic permanent magnet (PPM) focusing has been developed at the NASA Glenn Research Center at Lewis Field. This accurate model allows a TWT designer to develop a focusing structure while reducing the expensive and time-consuming task of building the TWT and hot-testing it (with the electron beam). In addition, the model allows, for the first time, an investigation of the effect on TWT operation of the important azimuthally asymmetric features of the focusing stack. The TWT is a vacuum device that amplifies signals by transferring energy from an electron beam to a radiofrequency (RF) signal. A critically important component is the focusing structure, which keeps the electron beam from diverging and intercepting the RF slow wave circuit. Such an interception can result in excessive circuit heating and decreased efficiency, whereas excessive growth in the beam diameter can lead to backward wave oscillations and premature saturation, indicating a serious reduction in tube performance. The most commonly used focusing structure is the PPM stack, which consists of a sequence of cylindrical iron pole pieces and opposite-polarity magnets. Typically, two-dimensional electron optics codes are used in the design of magnetic focusing devices. In general, these codes track the beam from the gun downstream by solving equations of motion for the electron beam in static-electric and magnetic fields in an azimuthally symmetric structure. Because these two-dimensional codes cannot adequately simulate a number of important effects, the simulation code MAFIA (solution of Maxwell's equations by the Finite-Integration-Algorithm) was used at Glenn to develop a three-dimensional electron optics model. First, a PPM stack was modeled in three dimensions. Then, the fields obtained using the magnetostatic solver were loaded into a particle-in-cell solver where the fully three-dimensional behavior of the beam was simulated in the magnetic focusing field. For the first time, the effects of azimuthally asymmetric designs and critical azimuthally asymmetric characteristics of the focusing stack (such as shunts, C-magnets, or magnet misalignment) on electron beam behavior have been investigated. A cutaway portion of a simulated electron beam focused by a PPM stack is illustrated.

Kory, Carol L.↗
NASA NTRS2010

Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids

The quality of simulated hypersonic stagnation region heating with tetrahedral meshes is investigated by using an updated three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. An earlier implementation of this algorithm provided improved symmetry characteristics on tetrahedral grids compared to conventional reconstruction methods. The original formulation however displayed quantitative differences in heating and shear that were as large as 25% compared to a benchmark, structured-grid solution. The primary cause of this discrepancy is found to be an inherent inconsistency in the formulation of the flux limiter. The inconsistency is removed by employing a Green-Gauss formulation of primitive gradients at nodes to replace the previous Gram-Schmidt algorithm. Current results are now in good agreement with benchmark solutions for two challenge problems: (1) hypersonic flow over a three-dimensional cylindrical section with special attention to the uniformity of the solution in the spanwise direction and (2) hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problems provide a sensitive indicator for algorithmic effects on heating. Additional simulations on a sharp, double cone and the shuttle orbiter are then presented to demonstrate the capabilities of the new algorithm on more geometrically complex flows with tetrahedral grids. These results provide the first indication that pure tetrahedral elements utilizing the updated, three-dimensional, upwind reconstruction algorithm may be used for the simulation of heating and shear in hypersonic flows in upwind, finite volume formulations.

Gnoffo, Peter A.↗
NASA NTRS2002

Impact of left ventricular outflow tract area on systolic outflow velocity in hypertrophic cardiomyopathy: a real-time three-dimensional echocardiographic study

OBJECTIVES: The aim of this study was to use real-time three-dimensional echocardiography (3DE) to investigate the quantitative relation between minimal left ventricular (LV) outflow tract area (A(LVOT)) and maximal LV outflow tract (LVOT) velocity in patients with hypertrophic obstructive cardiomyopathy (HCM). BACKGROUND: In patients with HCM, LVOT velocity should change inversely with minimal A(LVOT) unless LVOT obstruction reduces the pumping capacity of the ventricle. METHODS: A total of 25 patients with HCM with systolic anterior motion (SAM) of the mitral valve leaflets underwent real-time 3DE. The smallest A(LVOT) during systole was measured using anatomically oriented two-dimensional "C-planes" within the pyramidal 3DE volume. Maximal velocity across LVOT was evaluated by two-dimensional Doppler echocardiography (2DE). For comparison with 3DE A(LVOT), the SAM-septal distance was determined by 2DE. RESULTS: Real-time 3DE provided unique information about the dynamic SAM-septal relation during systole, with A(LVOT) ranging from 0.6 to 5.2 cm(2) (mean: 2.2 +/- 1.4 cm(2)). Maximal velocity (v) correlated inversely with A(LVOT) (v = 496 A(LVOT)(-0.80), r = -0.95, p < 0.001), but the exponent (-0.80) was significantly different from -1.0 (95% confidence interval: -0.67 to -0.92), indicating a significant impact of small A(LVOT) on the peak LVOT flow rate. By comparison, the best correlation between velocity and 2DE SAM-septal distance was significantly (p < 0.01) poorer at -0.83, indicating the superiority of 3DE for assessing A(LVOT). CONCLUSIONS: Three-dimensional echocardiography-measured A(LVOT) provides an assessment of HCM geometry that is superior to 2DE methods. These data indicate that the peak LVOT flow rate appears to be significantly decreased by reduced A(LVOT). Real-time 3DE is a potentially valuable clinical tool for assessing patients with HCM.

NASA Discipline Cardiopulmonary↗