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At least 73 records · Page 4

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

A new method was developed to extract surface flow vectors from an oilflow visualization image that has oil streaklines. The method is analogous to the PIV processing where the image is divided into interrogation windows. A representative flow direction is obtained for each interrogation window using image processing with a line-detection algorithm. Repeating the process for the entire image, one can find the surface vector field. The Hough transformation, Radon transformation and Machine Learning were used as line-detection algorithms. The obtained vector field is then postprocessed to filter spurious vectors and to apply smoothing. The method was tested on 2D and 3D models with different flow complexities. The method was able to predict surface flow vectors for all cases tested. The predicted surface flow vectors were used in obtaining the surface skin friction. The successful implementation of the surface flow vectors enables interferometric skin friction measurements on surfaces beneath 3D complex flows. In addition, the surface flow vectors can be superimposed on the oilflow visualization images to better explain the surface flow topology.

Surface flow vectors↗

Illustrating Surface Shape in Volume Data via Principal Direction-Driven 3D Line Integral Convolution

The three-dimensional shape and relative depth of a smoothly curving layered transparent surface may be communicated particularly effectively when the surface is artistically enhanced with sparsely distributed opaque detail. This paper describes how the set of principal directions and principal curvatures specified by local geometric operators can be understood to define a natural 'flow' over the surface of an object, and can be used to guide the placement of the lines of a stroke texture that seeks to represent 3D shape information in a perceptually intuitive way. The driving application for this work is the visualization of layered isovalue surfaces in volume data, where the particular identity of an individual surface is not generally known a priori and observers will typically wish to view a variety of different level surfaces from the same distribution, superimposed over underlying opaque structures. By advecting an evenly distributed set of tiny opaque particles, and the empty space between them, via 3D line integral convolution through the vector field defined by the principal directions and principal curvatures of the level surfaces passing through each gridpoint of a 3D volume, it is possible to generate a single scan-converted solid stroke texture that may intuitively represent the essential shape information of any level surface in the volume. To generate longer strokes over more highly curved areas, where the directional information is both most stable and most relevant, and to simultaneously downplay the visual impact of directional information in the flatter regions, one may dynamically redefine the length of the filter kernel according to the magnitude of the maximum principal curvature of the level surface at the point around which it is applied.

Interrante, Victoria↗

The influence of ATC message length and timing on pilot communication

Pilot-controller communication is critical to safe and efficient flight. It is often a challenging component of piloting, which is reflected in the number of incidents and accidents involving miscommunication. Our previous field study identified communication problems that disrupt routine communication between pilots and controllers. The present part-task simulation study followed up the field results with a more controlled investigation of communication problems. Pilots flew a simulation in which they were frequently vectored by Air Traffic Control (ATC), requiring intensive communication with the controller. While flying, pilots also performed a secondary visual monitoring task. We examined the influence of message length (one message with four commands vs. two messages with two commands each) and noncommunication workload on communication accuracy and length. Longer ATC messages appeared to overload pilot working memory, resulting in more incorrect or partial readbacks, as well as more requests to repeat the message. The timing between the two short messages also influenced communication. The second message interfered with memory for or response to the first short message when it was delivered too soon after the first message. Performing the secondary monitoring task did not influence communication. Instead, communication reduced monitoring accuracy.

Morrow, Daniel↗

Colorimetric qualification of shear sensitive liquid crystal coatings

The work that has been done to date on the Shear Sensitive Liquid Crystal Project demonstrated that cholesteric liquid crystal coatings respond to both the direction and magnitude of a shearing force. The response of the coating is to selectively scatter incident white light into a spectrum of colors. Discernible color changes at a fixed angle of observation and illumination are the result of an applied shear stress. The intention was to be able to convert these observable color patterns from a flow visualization technique into a quantitative tool. One of the earlier intentions was to be able to use liquid crystals in dynamic flow fields. This was assumed possible because liquid crystals had made it possible to visualize transients in surface shear forces. Although the transients were visualized by color changes to an order one micro second, the time response of a coating to align to a shearing force is dependent on the magnitude of the change between its initial and final states. Unfortunately, the response is not instantaneous. It is for this reason any future attempt at quantifying the magnitude and directions of a shearing force are limited to surface shear stress vector fields in three dimensional steady state flows. This limitation does not significantly detract from the utility of liquid crystal coatings. The measurement of skin friction in the study of transition on wings, prediction of drag forces, performance assessment, and the investigation of boundary layer behavior is of great importance in aerodynamics. There exist numerous examples of techniques for the measurement of surface shear stress. Most techniques require arduous calibrations and necessitate extensive preparation of the receiving surfaces. However, the main draw back of instruments such as Preston tubes, hot films, buried wire gages, and floating element balances is that they only provide a point measurement. The advantages of capturing global shear data would be appreciable when compared with conventional point measurement sensors. It has yet to be determined if a repeatable correlation exists between the measured color of a liquid crystal coating and the magnitude/directional components of a shear vector imposed onto it.

Muratore, Joseph J., Jr.↗

The 1999 Hector Mine Earthquake, Southern California: Vector Near-Field Displacements from ERS InSAR

Two components of fault slip are uniquely determined from two line-of-sight (LOS) radar interferograms by assuming that the fault-normal component of displacement is zero. We use this approach with ascending and descending interferograms from the ERS satellites to estimate surface slip along the Hector Mine earthquake rupture. The LOS displacement is determined by visually counting fringes to within 1 km of the outboard ruptures. These LOS estimates and uncertainties are then transformed into strike- and dip-slip estimates and uncertainties; the transformation is singular for a N-S oriented fault and optimal for an E-W oriented fault. In contrast to our previous strike-slip estimates, which were based only on a descending interferogram, we now find good agreement with the geological measurements, except at the ends of the rupture. The ascending interferogram reveals significant west-sidedown dip-slip (approximately 1.0 m) which reduces the strike-slip estimates by 1 to 2 m, especially along the northern half of the rupture. A spike in the strike-slip displacement of 6 m is observed in central part of the rupture. This large offset is confirmed by subpixel cross correlation of features in the before and after amplitude images. In addition to strike slip and dip slip, we identify uplift and subsidence along the fault, related to the restraining and releasing bends in the fault trace, respectively. Our main conclusion is that at least two look directions are required for accurate estimates of surface slip even along a pure strike-slip fault. Models and results based only on a single look direction could have major errors. Our new estimates of strike slip and dip slip along the rupture provide a boundary condition for dislocation modeling. A simple model, which has uniform slip to a depth of 12 km, shows good agreement with the observed ascending and descending interferograms.

Sandwell, David T.↗

Spatial scale of motion segmentation from speed cues

For the accurate perception of multiple, potentially overlapping, surfaces or objects, the visual system must distinguish different local motion vectors and selectively integrate similar motion vectors over space to segment the retinal image properly. We recently showed that large differences in speed are required to yield a percept of motion transparency. In the present study, to investigate the spatial scale of motion segmentation from speed cues alone, we measured the speed-segmentation threshold (the minimum speed difference required for 75% performance accuracy) for 'corrugated' random-dot patterns, i.e. patterns in which dots with two different speeds were alternately placed in adjacent bars of variable width. In a first experiment, we found that, at large bar widths, a smaller speed difference was required to segment and perceive the corrugated pattern of moving dots, while at small bar-widths, a larger speed difference was required to segment the two speeds and perceive two transparent surfaces of moving dots. Both the perceptual and segmentation performance transitions occurred at a bar width of around 0.4 degrees. In a second experiment, speed-segmentation thresholds were found to increase sharply when dots with different speeds were paired within a local pooling area. The critical pairing distance was about 0.2 degrees in the fovea and increased linearly with stimulus eccentricity. However, across the range of eccentricities tested (up to 15 degrees ), the critical pairing distance did not change much and remained close to the receptive field size of neurons within the primate primary visual cortex. In a third experiment, increasing dot density changed the relationship between speed-segmentation thresholds and bar width. Thresholds decreased for large bar widths, but increased for small bar widths. All of these results are well fit by a simple stochastic model, which estimates the probabilities of having identical or different motion vectors within a local pooling area whose size is the same as that of primate V1 neurons. Altogether, these results demonstrate that speed-based segmentation can function well, even at small spatial scales (i.e. high-spatial frequencies of spatial corrugation) and thereby emphasizes the critical role of a local pooling process early in the cortical motion-processing pathway.

NASA Discipline Neuroscience↗

Solar physics applications of computer graphics and image processing

Computer graphics devices coupled with computers and carefully developed software provide new opportunities to achieve insight into the geometry and time evolution of scalar, vector, and tensor fields and to extract more information quickly and cheaply from the same image data. Two or more different fields which overlay in space can be calculated from the data (and the physics), then displayed from any perspective, and compared visually. The maximum regions of one field can be compared with the gradients of another. Time changing fields can also be compared. Images can be added, subtracted, transformed, noise filtered, frequency filtered, contrast enhanced, color coded, enlarged, compressed, parameterized, and histogrammed, in whole or section by section. Today it is possible to process multiple digital images to reveal spatial and temporal correlations and cross correlations. Data from different observatories taken at different times can be processed, interpolated, and transformed to a common coordinate system.

Altschuler, M. D.↗

High-Resolution Mapping of Lunar Crustal Magnetic Fields: Correlations with Albedo Markings of the Reiner Gamma Class

During the last eight months of the Lunar Prospector mission (December 1999-July 1999), the spacecraft was placed in a relatively low-altitude (15-30-km perapsis), near-polar orbit that allowed high-resolution mapping of crustal magnetic fields. We report here initial studies of the correlation of locally strong magnetic anomalies with unusual, swirl-like albedo markings of the Reiner Gamma class. Based on this correlation, which is known from earlier studies of Apollo subsatellite magnetometer data, it has been proposed that the swirls represent regions whose higher albedos have been preserved via deflection of the solar-wind ion bombardment by strong crustal fields. This model in turn depends on the hypothesis that solar-wind implanted H is at least one component of the process that optically matures exposed silicate surfaces in the inner solar system . Specifically, it is hypothesized that implanted H acts as an effective reducing agent to enhance the rate of production of nanophase metallic Fe particles from preexisting silicates during micrometeoroid impacts. According to the model, the curvilinear shapes of these albedo markings are caused, at least in part, by the geometry of ion deflections in a magnetic field. The improved resolution and coverage of the Prospector data allow more detailed mapping of the fields, especially on the lunar farside. This permits a more quantitative test of whether all albedo markings of this class are associated with strong local magnetic fields.Only if the latter condition is met can the solar-wind deflection hypothesis he valid. The basic procedure for mapping crustal magnetic fields using Lunar Prospector magnetometer data follows that developed for analysis of Apollo subsatellite magnetometer data. The specific mapping steps are (1) selection of mission time intervals suitable for mapping crustal fields; these are limited essentially either to times when the Moon is in a lobe of the geomagnetic tail or to times when the Moon is in the solar wind but the spacecraft is in the lunar wake; the data are transformed to a radial, east, and north coordinate system with measurements given as a function of spacecraft latitude, longitude, and altitude; (2) visual editing of individual orbit segments selected for minimal external field disturbances; (3) minimization of remaining low-frequency external fields for individual orbit data segments by quadratic detrending; and (4) two-dimensional filtering of individual orbit segments to produce a vector field map along the slightly curved surface defined by the spacecraft altitude; maps of the three field components (radial, east, and north), the field magnitude, and the spacecraft altitude are constructed. For data obtained at low to middle latitudes, the horizontal resolution of the field maps is limited by the orbit-track separation (about 30 km at the equator). Maps of the field magnitude have been constructed within limited selenographic regions based mainly on data acquired in March, April, and May of 1999. This was a time period when the orbit plane was nearly aligned with the Sun-Moon line so that field mapping was possible at times when the Moon was in the solar wind as well as when the Moon was in the geomagnetic tail. Most of the coverage is across the lunar farside. However, a shows an example of a field map produced from solar-wind wake data for a region including Reiner Gamm on western Oceanus Procellarum (location: 58.5W, 7.5N). The contour interval is 3 nT and the mean spacecraft altitude is 18 km to within the accuracy allowed by the resolution of the map (30 km or about 1 deg.); strong magnetic anomalies correlate closely with swirl locations. Individual orbit profiles (whose resolution along the orbit track is comparable to the spacecraft altitude of 18 km) also demonstrate a good correlation of field magnitude with surface albedo. In order to investigate the correlation of magnetic fields with the location of swirl features, we have reexamined available lunar imagery (Lunar Orbiter, Apollo, and Clementine) to identify and map swirl locations within regions where swirls have previously been mapped. In these images, swirls were distinguished from other high-albedo features such as crater rays by their curvilinear shapes and increased visibility in forward-scattered light. Digital maps of swirls identified by all available imagery were then superposed on maps of the field magnitude at the spacecraft altitude. Based upon analysis of these composite magnetic/geologic maps, we draw the preliminary conclusion that swirl features are associated with magnetic anomalies revealed by Lunar Prospector. Detailed maps of these swirl features are currently being constructed for the magnetically strong regions antipodal to the Imbrium, Serenitatis, and Crisium Basins. Additional information contained in the original,

Hood, L. L.↗

Hot gas ingestion test results of a two-poster vectored thrust concept with flow visualization in the NASA Lewis 9- x 15-foot low speed wind tunnel

A 9.2 percent scale Short Takeoff and Vertical Landing (STOVL) hot gas ingestion model was designed and built by McDonnell Douglas Corporation (MCAIR) and tested in the Lewis Research Center 9 x 15 foot Low Speed Wind Tunnel (LSWT). Hot gas ingestion, the entrainment of heated engine exhaust into the inlet flow field, is a key development issure for advanced short takeoff and vertical landing aircraft. Flow visualization from the Phase 1 test program, which evaluated the hot ingestion phenomena and control techniques, is covered. The Phase 2 test program evaluated the hot gas ingestion phenomena at higher temperatures and used a laser sheet to investigate the flow field. Hot gas ingestion levels were measured for the several forward nozzle splay configurations and with flow control/life improvement devices (LIDs) which reduced the hot gas ingestion. The model support system had four degrees of freedom - pitch, roll, yaw, and vertical height variation. The model support system also provided heated high-pressure air for nozzle flow and a suction system exhaust for inlet flow. The test was conducted at full scale nozzle pressure ratios and inlet Mach numbers. Test and data analysis results from Phase 2 and flow visualization from both Phase 1 and 2 are documented. A description of the model and facility modifications is also provided. Headwind velocity was varied from 10 to 23 kn. Results are presented over a range of nozzle pressure ratios at a 10 kn headwind velocity. The Phase 2 program was conducted at exhaust nozzle temperatures up to 1460 R and utilized a sheet laser system for flow visualization of the model flow field in and out of ground effects. The results reported are for nozzle exhaust temperatures up to 1160 R. These results will contain the compressor face pressure and temperature distortions, the total pressure recovery, the inlet temperature rise, and the environmental effects of the hot gas. The environmental effects include the ground plane contours, the model airframe heating, and the location of the ground flow separation.

Johns, Albert L.↗

Large field-of-view KD*P modulator

This paper describes how FOV errors have affected the polarization measurements of the NASA Marshall vector magnetograph and how a polarimeter has been modified to minimize these errors. The design of a large-FOV (LFOV) KD*P modulator is discussed. The Poincare sphere is used to visualize the function of the different optical elements that make up the LFOV modulator.

West, E. A.↗

Spatially Resolved Mapping of Three-Dimensional Molecular Orientations with ~2 nm Spatial Resolution through Tip-Enhanced Raman Scattering

We record local optical field images of silver nanocubes (75 nm) using tip-enhanced Raman (TER) spectral imaging. The images that we observe are consistent with several recent reports from our group, but here, we demonstrate sub-2 nm spatial resolution in local optical field nanoimaging under ambient laboratory conditions. This is achieved by scanning the substrate (nanocube on Si) relative to a 4-thiobenzonitrile (TBN)-functionalized Ag-coated TER probe. The spatial resolution that we obtain necessitates that only a few molecules govern the recorded optical response; molecular orientation becomes an important consideration in such measurements. We model the orientation through geometry optimization of a TBN molecule chemisorbed onto an Ag79 cluster (sphere with a ~1 nm diameter). Using the computed orientation of the cluster-bound molecule, we then model the optical response using formalism that accounts for the orientation of the molecule relative to vector components of the local optical fields. We find optimal agreement between experiment and theory. In effect, this work reveals the parallels between single-molecule Raman scattering and high-spatial-resolution TER spectroscopy, even when the images themselves cannot be used to visualize a single molecule in real space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface Tension Driven Convection Experiment (STDCE)

This document reports the results obtained from the Surface Tension Driven Convection Experiment (STDCE) conducted aboard the USML-1 Spacelab in 1992. The experiments used 10 cSt silicone oil placed in an open circular container that was 10 cm wide and 5 cm deep. Thermocapillary flow was induced by using either a cylindrical heater placed along the container centerline or by a CO2 laser. The tests were conducted under various power settings, laser beam diameters, and free surface shapes. Thermistors located at various positions in the test section recorded the temperature of the fluid, heater, walls, and air. An infrared imager was used to measure the free surface temperature. The flow field was studied by flow visualization and the data was analyzed by a PTV technique. The results from the flow visualization and the temperature measurements are compared with the numerical analysis that was conducted in conjunction with the experiment. The compared results include the experimental and numerical velocity vector plots, the streamline plots, the fluid temperature, and the surface temperature distribution.

Ostrach, S.↗

Acoustic Calibration of the Exterior Effects Room at the NASA Langley Research Center

The Exterior Effects Room (EER) at the NASA Langley Research Center is a 39-seat auditorium built for psychoacoustic studies of aircraft community noise. The original reproduction system employed monaural playback and hence lacked sound localization capability. In an effort to more closely recreate field test conditions, a significant upgrade was undertaken to allow simulation of a three-dimensional audio and visual environment. The 3D audio system consists of 27 mid and high frequency satellite speakers and 4 subwoofers, driven by a real-time audio server running an implementation of Vector Base Amplitude Panning. The audio server is part of a larger simulation system, which controls the audio and visual presentation of recorded and synthesized aircraft flyovers. The focus of this work is on the calibration of the 3D audio system, including gains used in the amplitude panning algorithm, speaker equalization, and absolute gain control. Because the speakers are installed in an irregularly shaped room, the speaker equalization includes time delay and gain compensation due to different mounting distances from the focal point, filtering for color compensation due to different installations (half space, corner, baffled/unbaffled), and cross-over filtering.

Faller, Kenneth J., II↗

Numerical Flow Visualization in Basic- and Hyper-Cluster Spheres

Packed spherical particle beds have wide applications throughout the process industry and are usually analyzed using an appropriate combination of laminar and turbulent flows with empirically derived coefficients of which the Ergun (1952) relation is probably the best known. The 3-D complexity of the void distribution within the beds has precluded detailed studies of sphere clusters. Numerical modeling and flow vector visualization for the basic tetra- and hexa-sphere clusters and two hyper-sphere clusters are presented at two Reynolds numbers, 400 and 1200. Cutting planes are used to enable visualization of the complex flows generated within the sphere clusters and are discussed herein. The boundary conditions and flow fields for the simple clusters are also compared to the hyper-clusters with larger variations found for hexa-clusters.

Hendricks, R. C.↗

Integrated Computational System for Aerodynamic Steering and Visualization

In February of 1994, an effort from the Fluid Dynamics and Information Sciences Divisions at NASA Ames Research Center with McDonnel Douglas Aerospace Company and Stanford University was initiated to develop, demonstrate, validate and disseminate automated software for numerical aerodynamic simulation. The goal of the initiative was to develop a tri-discipline approach encompassing CFD, Intelligent Systems, and Automated Flow Feature Recognition to improve the utility of CFD in the design cycle. This approach would then be represented through an intelligent computational system which could accept an engineer's definition of a problem and construct an optimal and reliable CFD solution. Stanford University's role focused on developing technologies that advance visualization capabilities for analysis of CFD data, extract specific flow features useful for the design process, and compare CFD data with experimental data. During the years 1995-1997, Stanford University focused on developing techniques in the area of tensor visualization and flow feature extraction. Software libraries were created enabling feature extraction and exploration of tensor fields. As a proof of concept, a prototype system called the Integrated Computational System (ICS) was developed to demonstrate CFD design cycle. The current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will (1) briefly review the technologies developed during 1995-1997 (2) describe current technologies in the area of comparison techniques, (4) describe the theory of our new method researched during the grant year (5) summarize a few of the results and finally (6) discuss work within the last 6 months that are direct extensions from the grant.

Hesselink, Lambertus↗

Orientation of human optokinetic nystagmus to gravity: a model-based approach

Optokinetic nystagmus (OKN) was induced by having subjects watch a moving display in a binocular, head-fixed apparatus. The display was composed of 3.3 degrees stripes moving at 35 degrees/s for 45 s. It subtended 88 degrees horizontally by 72 degrees vertically of the central visual field and could be oriented to rotate about axes that were upright or tilted 45 degrees or 90 degrees. The head was held upright or was tilted 45 degrees left or right on the body during stimulation. Head-horizontal (yaw axis) and head-vertical (pitch axis) components of OKN were recorded with electro-oculography (EOG). Slow phase velocity vectors were determined and compared with the axis of stimulation and the spatial vertical (gravity axis). With the head upright, the axis of eye rotation during yaw axis OKN was coincident with the stimulus axis and the spatial vertical. With the head tilted, a significant vertical component of eye velocity appeared during yaw axis stimulation. As a result the axis of eye rotation shifted from the stimulus axis toward the spatial vertical. Vertical components developed within 1-2 s of stimulus onset and persisted until the end of stimulation. In the six subjects there was a mean shift of the axis of eye rotation during yaw axis stimulation of approximately 18 degrees with the head tilted 45 degrees on the body. Oblique optokinetic stimulation with the head upright was associated with a mean shift of the axis of eye rotation toward the spatial vertical of 9.2 degrees. When the head was tilted and the same oblique stimulation was given, the axis of eye rotation rotated to the other side of the spatial vertical by 5.4 degrees. This counterrotation of the axis of eye rotation is similar to the "Muller (E) effect," in which the perception of the upright is counterrotated to the opposite side of the spatial vertical when subjects are tilted in darkness. The data were simulated by a model of OKN with a "direct" and "indirect" pathway. It was assumed that the direct visual pathway is oriented in a body, not a spatial frame of reference. Despite the short optokinetic after-nystagmus time constants, strong horizontal to vertical cross-coupling could be produced if the horizontal and vertical time constants were in proper ratio and there were no suppression of nystagmus in directions orthogonal to the stimulus direction. The model demonstrates that the spatial orientation of OKN can be achieved by restructuring the system matrix of velocity storage. We conclude that an important function of velocity storage is to orient slow-phase velocity toward the spatial vertical during movement in a terrestrial environment.

Non-NASA Center↗

Three-dimensional vortical structures of transition in plane channel flow

Three-dimensional visualization of flwo field structures in transitional plane channel flow obtained from a numerical simulation are presented at two Reynolds numbers. It is revealed that at the one-spike stage, independent of Reynolds number, the flow is characterized by a multi-layer vortex system. In the upper layer, total vorticity vector plots indicate a high-shear layer dominated by spanwise vorticity, whereas the middle layer (corresponding approximately to the critical layer) forms a vortex loop (alpha-vortex) consisting of strong streamwise and spanwise vorticity components. At the three-spike stage, the breakdown of the vortical structure proceeds in a manner similar to frontal relaminarization of turbulent spots. This process is accompanied by intense vortex lift-up activity near the wall which seems to originate at the legs of the vortex loop trailing the high-shear layer. Finally, at the five-spike stage, it is shown that high-vorticity regions (vortical structures) develop into horseshow eddies in planes inclined to the main flow direction.

Biringen, S.↗

Qualitative evaluation of a conformal velocity vector display for use at high angles-of-attack in fighter aircraft

A piloted simulation study was conducted to evaluate the utility of a display device designed to illustrate graphically and conformally the approximate location of a fighter aircraft's velocity vector. The display device consisted of two vertical rows of light emitting diodes (LED's) located toward the center of the cockpit instrument panel to each side of the control stick. The light strings provided a logical extension of the head up display (HUD) velocity vector symbol at flight path angles which exceeded the HUD field-of-view. Four test subjects flew a modified F/A-18 model with this display in an air-to-air engagement task against an equally capable opponent. Their responses to a questionnaire indicated that the conformal velocity vector information could not be used during the scenarios investigated due to the inability to visually track a target and view the lights simultaneously.

Jones, Denise R.↗