Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Functional priors”

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 613 records · Page 34

Design and Development of CubeSat Solar Array Deployment Mechanisms Using Shape Memory Alloys

The Advanced eLectrical Bus (ALBus) project is a technology demonstration mission of a 3U CubeSat with an advanced, digitally controlled electrical power system capability and the novel use of Shape Memory Alloy (SMA) technology for reliable solar array (SA) deployable mechanisms. The ALBus CubeSat deploys four SAs in addition to the body-mounted arrays on each side of the CubeSat. A goal of the mission is to utilize the SMAs being developed at the NASA Glenn Research Center to deploy these SAs. The use of SMAs allows for the ability to test and reset the flight deployment mechanism prior to flight, which reduces the risk of in orbit deployment failures common to CubeSats. As a result, an SMA-driven Retention and Release (R&R) mechanism and an SMA-driven hinge were designed, developed, and integrated for flight. This paper summarizes the development of these mechanisms, types and functionalities of the SMAs used, as well as the lessons learned throughout the process.

cubesat↗

A Novel Atmospheric Correction Algorithm to Exploit the Diurnal Variability in Hypertemporal Geostationary Observations

This study developed a new atmospheric correction algorithm, GeoNEX-AC, that is independent from the traditional use of spectral band ratios but dedicated to exploiting information from the diurnal variability in the hypertemporal geostationary observations. The algorithm starts by evaluating smooth segments of the diurnal time series of the top-of-atmosphere (TOA) reflectance to identify clear-sky and snow-free observations. It then attempts to retrieve the Ross-Thick–Li-Sparse (RTLS) surface bi-directional reflectance distribution function (BRDF) parameters and the daily mean atmospheric optical depth (AOD) with an atmospheric radiative transfer model (RTM) to optimally simulate the observed diurnal variability in the clear-sky TOA reflectance. Once the initial RTLS parameters are retrieved after the algorithm’s burn-in period, they serve as the prior information to estimate the AOD levels for the following days and update the surface BRDF information with the new clear-sky observations. This process is iterated through the full time span of the observations, skipping only totally cloudy days or when surface snow is detected. We tested the algorithm over various Aerosol Robotic Network (AERONET) sites and the retrieved results well agree with the ground-based measurements. This study demonstrates that the high-frequency diurnal geostationary observations contain unique information that can help to address the atmospheric correction problem from new directions.

atmospheric correction↗

Strain energy release rate as a function of temperature and preloading history utilizing the edge delamination fatique test method

Static laminate and tension-tension fatigue tests of IM7/8551-7 composite materials was performed. The Edge Delamination Test (EDT) was utilized to evaluate the temperature and preloading history effect on the critical strain energy release rate. Static and fatigue testing was performed at room temperature and 180 F (82 C). Three preloading schemes were used to precondition fatigue test specimens prior to performing the normal tension-tension fatigue EDT testing. Computer software was written to perform all fatigue testing while monitoring the dynamic modulus to detect the onset of delamination and record the test information for later retrieval and reduction.

Zimmerman, Richard S.↗

A simulation of air pollution model parameter estimation using data from a ground-based LIDAR remote sensor

One way to obtain estimates of the unknown parameters in a pollution dispersion model is to compare the model predictions with remotely sensed air quality data. A ground-based LIDAR sensor provides relative pollution concentration measurements as a function of space and time. The measured sensor data are compared with the dispersion model output through a numerical estimation procedure to yield parameter estimates which best fit the data. This overall process is tested in a computer simulation to study the effects of various measurement strategies. Such a simulation is useful prior to a field measurement exercise to maximize the information content in the collected data. Parametric studies of simulated data matched to a Gaussian plume dispersion model indicate the trade offs available between estimation accuracy and data acquisition strategy.

Kibler, J. F.↗

An internal variable constitutive model for the large deformation of metals at high temperatures

The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS.

Brown, Stuart↗

Simulation of Ground Winds Time Series for the NASA Crew Launch Vehicle (CLV)

Simulation of wind time series based on power spectrum density (PSD) and spectral coherence models for ground wind turbulence is described. The wind models, originally developed for the Shuttle program, are based on wind measurements at the NASA 150-m meteorological tower at Cape Canaveral, FL. The current application is for the design and/or protection of the CLV from wind effects during on-pad exposure during periods from as long as days prior to launch, to seconds or minutes just prior to launch and seconds after launch. The evaluation of vehicle response to wind will influence the design and operation of constraint systems for support of the on-pad vehicle. Longitudinal and lateral wind component time series are simulated at critical vehicle locations. The PSD model for wind turbulence is a function of mean wind speed, elevation and temporal frequency. Integration of the PSD equation over a selected frequency range yields the variance of the time series to be simulated. The square root of the PSD defines a low-pass filter that is applied to adjust the components of the Fast Fourier Transform (FFT) of Gaussian white noise. The first simulated time series near the top of the launch vehicle is the inverse transform of the adjusted FFT. Simulation of the wind component time series at the nearest adjacent location (and all other succeeding next nearest locations) is based on a model for the coherence between winds at two locations as a function of frequency and separation distance, where the adjacent locations are separated vertically and/or horizontally. The coherence function is used to calculate a coherence weighted FFT of the wind at the next nearest location, given the FFT of the simulated time series at the previous location and the essentially incoherent FFT of the wind at the selected location derived a priori from the PSD model. The simulated time series at each adjacent location is the inverse Fourier transform of the coherence weighted FFT. For a selected design case, the equations, the process and the simulated time series at multiple vehicle stations are presented.

Adelfang, Stanley I.↗

Video Mosaicking for Inspection of Gas Pipelines

A vision system that includes a specially designed video camera and an image-data-processing computer is under development as a prototype of robotic systems for visual inspection of the interior surfaces of pipes and especially of gas pipelines. The system is capable of providing both forward views and mosaicked radial views that can be displayed in real time or after inspection. To avoid the complexities associated with moving parts and to provide simultaneous forward and radial views, the video camera is equipped with a wide-angle (>165 ) fish-eye lens aimed along the axis of a pipe to be inspected. Nine white-light-emitting diodes (LEDs) placed just outside the field of view of the lens (see Figure 1) provide ample diffuse illumination for a high-contrast image of the interior pipe wall. The video camera contains a 2/3-in. (1.7-cm) charge-coupled-device (CCD) photodetector array and functions according to the National Television Standards Committee (NTSC) standard. The video output of the camera is sent to an off-the-shelf video capture board (frame grabber) by use of a peripheral component interconnect (PCI) interface in the computer, which is of the 400-MHz, Pentium II (or equivalent) class. Prior video-mosaicking techniques are applicable to narrow-field-of-view (low-distortion) images of evenly illuminated, relatively flat surfaces viewed along approximately perpendicular lines by cameras that do not rotate and that move approximately parallel to the viewed surfaces. One such technique for real-time creation of mosaic images of the ocean floor involves the use of visual correspondences based on area correlation, during both the acquisition of separate images of adjacent areas and the consolidation (equivalently, integration) of the separate images into a mosaic image, in order to insure that there are no gaps in the mosaic image. The data-processing technique used for mosaicking in the present system also involves area correlation, but with several notable differences: Because the wide-angle lens introduces considerable distortion, the image data must be processed to effectively unwarp the images (see Figure 2). The computer executes special software that includes an unwarping algorithm that takes explicit account of the cylindrical pipe geometry. To reduce the processing time needed for unwarping, parameters of the geometric mapping between the circular view of a fisheye lens and pipe wall are determined in advance from calibration images and compiled into an electronic lookup table. The software incorporates the assumption that the optical axis of the camera is parallel (rather than perpendicular) to the direction of motion of the camera. The software also compensates for the decrease in illumination with distance from the ring of LEDs.

Magruder, Darby↗

Design strategies and functionality of the Visual Interface for Virtual Interaction Development (VIVID) tool

Development of interactive virtual environments (VE) has typically consisted of three primary activities: model (object) development, model relationship tree development, and environment behavior definition and coding. The model and relationship tree development activities are accomplished with a variety of well-established graphic library (GL) based programs - most utilizing graphical user interfaces (GUI) with point-and-click interactions. Because of this GUI format, little programming expertise on the part of the developer is necessary to create the 3D graphical models or to establish interrelationships between the models. However, the third VE development activity, environment behavior definition and coding, has generally required the greatest amount of time and programmer expertise. Behaviors, characteristics, and interactions between objects and the user within a VE must be defined via command line C coding prior to rendering the environment scenes. In an effort to simplify this environment behavior definition phase for non-programmers, and to provide easy access to model and tree tools, a graphical interface and development tool has been created. The principal thrust of this research is to effect rapid development and prototyping of virtual environments. This presentation will discuss the 'Visual Interface for Virtual Interaction Development' (VIVID) tool; an X-Windows based system employing drop-down menus for user selection of program access, models, and trees, behavior editing, and code generation. Examples of these selection will be highlighted in this presentation, as will the currently available program interfaces. The functionality of this tool allows non-programming users access to all facets of VE development while providing experienced programmers with a collection of pre-coded behaviors. In conjunction with its existing, interfaces and predefined suite of behaviors, future development plans for VIVID will be described. These include incorporation of dual user virtual environment enhancements, tool expansion, and additional behaviors.

Nguyen, Lac↗

The evolution of prominences and their relationship to active centers /A Review/

A necessary condition for the formation of prominences is established where components of the magnetic field of opposite sign lie juxtaposed. This condition is sometimes recognizable prior to the formation of prominences in active centers and between adjacent active centers in H-alpha by paths of fibrils aligned nearly end to end. Prominences are usually not found in active regions until they are about 4 days old. After this time, the number of prominences appears to be a function of the large-scale complexities in the magnetic field pattern whether these are a result of emerging flux, the merging of adjacent active centers, or the coalescing of remnant fields of active centers. Prominences may disappear by the slow or rapid flow of mass into the chromosphere or by the more violent eruptives. The formation of new active centers has been associated with the eruption of some filaments related to weak chromospheric fields.

Martin, S. F.↗

An analysis of the flow field in the region of the ASRM field joints

The flow field in the region of a solid rocket motor field joint is very important since fluid dynamic and mechanical propellant stresses can couple to cause a motor failure at a joint. Presented here is an examination of the flow field in the region of the Advanced Solid Rocket Motor (ASRM) field joints. The analyses were performed as a first step in assessing the design of the ASRM forward and aft field joints in order to assure the proper operation of the motor prior to further development of test firing. The analyses presented here were performed by employing a two-dimensional axisymmetric assumption. Fluent/BFC, a three dimensional full Navier-Stokes flow field code, was used to make the numerical calculations. This code utilizes a staggered grid formulation along with the SIMPLER numerical algorithm. Wall functions are used to determine the character of the laminar sublayer, and a standard kappa-epsilon turbulence model is used to close the fluid dynamic equations. The analyses performed to this date verify that the ASRM field joint design operates properly. The fluid dynamic stresses at the field joints are small due to the inherent design of the field joints. A problem observed in some other solid rocket motors is that large fluid dynamic stresses are generated at the motor joint on the downstream propellant grain due to forward facing step geometries. The design of the ASRM field joints are such that this is not a problem as shown by the analyses. Also, the analyses of the inhibitor stub left protruding into the port flow from normal propellant burn back show that more information is necessary to complete these analyses. These analyses were performed as parametric analyses in relation to the height of the inhibitor stub left protruding into the motor port. A better estimate of the amount of the inhibitor stub remaining at later burn times must be determined since the height which the inhibitor stub protrudes into the port flow drastically affects the fluid dynamics induced stresses on the propellant grain at the field joints.

Dill, Richard A.↗

Seasonal variation in the structure of red reflectance of leaves from yellow poplar, red oak, and red maple

The light scattered from leaves was measured as a function of view angle in the principal plane for yellow poplar, red oak, and red maple. The source was a parallel-polarized helium-neon laser. Yellow poplar leaves had the highest reflectance of the three species, which may have been due to its shorter palisade cells and more extensive spongy mesophyll. Prior to senescence, there was a significant decrease, but not total extinction, in the reflectance of the beam incident at 60 deg from nadir on the adaxial side of the leaves of all three species. Low-temperature SEM observations showed differences in the surface wax patterns among the three species but did not indicate a cause of the reflectance changes other than possibly the accumulation and aging of the wax.

Brakke, Thomas W.↗

A Solution Methodology and Computer Program to Efficiently Model Thermodynamic and Transport Coefficients of Mixtures

A solution methodology has been developed to efficiently model multi-specie, chemically frozen, thermally perfect gas mixtures. The method relies on the ability to generate a single (composite) set of thermodynamic and transport coefficients prior to beginning a CFD solution. While not fundamentally a new concept, many applied CFD users are not aware of this capability nor have a mechanism to easily and confidently generate new coefficients. A database of individual specie property coefficients has been created for 48 species. The seven coefficient form of the thermodynamic functions is currently used rather then the ten coefficient form due to the similarity of the calculated properties, low temperature behavior and reduced CPU requirements. Sutherland laminar viscosity and thermal conductivity coefficients were computed in a consistent manner from available reference curves. A computer program has been written to provide CFD users with a convenient method to generate composite specie coefficients for any mixture. Mach 7 forebody/inlet calculations demonstrated nearly equivalent results and significant CPU time savings compared to a multi-specie solution approach. Results from high-speed combustor analysis also illustrate the ability to model inert test gas contaminants without additional computational expense.

Ferlemann, Paul G.↗

Advanced Polymers Containing the Phenyltrifluoroethylidene Connecting Group

A new, lower cost fluorinated dianhydride based on the phenyltrifluoroethylidene (3F) connecting linkage was invented by the principal author in the early 1980's. New 3F condensation and addition cured polyimides were synthesized with the newly discovered 3F dianhydride and the previously known 3F diamine. As controls, polyimides based on the somewhat analogous higher cost hexafluoroisopropylidene (6F) linkage were also prepared. The short term thermal oxidative stability (TOS), determined by thermal gravimetric analysis (TGA), and the glass transition temperatures (Tg) of 3F dianhydride polyimides were found to be similar to 6F dianhydride polyimides, but the Tg was slightly higher for 3F diamine polyimides than 6F diamine polyimides. Unfortunately, in real time testing, long term TOS of 3F polymers was clearly inferior to 6F polymers. This was due to a 3 to 5 fold greater rate of loss of trifluoromethyl group from 3F versus 6F linkages. However, at shorter times or lower temperatures, 3F TOS was almost comparable to 6F TOS. The wide scope of the 3F technology was also demonstrated to have distinct unique advantages over 6F technology through the use of the 3F pendant phenyl ring as a synthetic site to introduce other functional groups. These groups have been used for the control or modification of polymer properties; an advantage lacking within 6F technology. The synthetic ease by which 3F can be introduced into various types of monomers has lead to the explosion of advanced 3F polyimides and other high performance advanced 3F polymers in the prior decade of 3F polymer literature as cited herein; covering polyimides, substituted polyimides, at least ten types of nonpolyimide 3F polymer modifications, and also the government's nine 3F U.S. patents and corporations' nine 3F U.S. patents.

Alstron, William B.↗

Multi-System Effects of Daily Artificial Gravity Exposures in Humans Deconditioned by Bed Rest

We have begun to explore the utility of intermittent artificial gravity (AG) as a multi-system countermeasure to the untoward health and performance effects of adaptation to decreased gravity during prolonged space flight. The first study in this exploration was jointly designed by an international, multi-disciplinary team of scientists interested in standardizing an approach so that comparable data could be obtained from follow-on studies performed in multiple international locations. Fifteen rigorously screened male volunteers participated in the study after providing written informed consent. All were subjected to 21 days of 6deg head-down-tilt (HDT) bed rest. Eight were treated with daily 1hr AG exposures (2.5g at the feet decreasing to 1.0g at the heart) aboard a short radius (3m) centrifuge, while the other seven served as controls. Multiple observations were made of dependent measures in the bone, muscle, cardiovascular, sensory-motor, immune, and behavioral systems during a 10 day acclimatization period prior to HDT bed rest and again during an 8 day recovery period after the bed rest period. Comparisons between the treatment and control subjects demonstrated salutary effects of the AG exposure on aspects of the muscle and cardiovascular systems, with no untoward effects on the vestibular system, the immune system, or cognitive function. Bone deconditioning was similar between the treatment and control groups, suggesting that the loading provided by this specific AG paradigm was insufficient to protect that system from deconditioning. Future work will be devoted to varying the loading duty cycle and/or coupling the AG loading with exercise to provide maximum physiological protection across all systems. Testing will also be extended to female subjects. The results of this study suggest that intermittent AG could be an effective multi-system countermeasure.

Paloski, William H.↗

Safe2Ditch Steer-To-Clear Development and Flight Testing

This paper describes a series of small unmanned aerial system (sUAS) flights performed at NASA Langley Research Center in April and May of 2019 to test a newly added Steer-to-Clear feature for the Safe2Ditch (S2D) prototype system. S2D is an autonomous crash management system for sUAS. Its function is to detect the onset of an emergency for an autonomous vehicle, and to enable that vehicle in distress to execute safe landings to avoid injuring people on the ground or damaging property. Flight tests were conducted at the City Environment Range for Testing Autonomous Integrated Navigation (CERTAIN) range at NASA Langley. Prior testing of S2D focused on rerouting to an alternate ditch site when an occupant was detected in the primary ditch site. For Steer-to-Clear testing, S2D was limited to a single ditch site option to force engagement of the Steer-to-Clear mode. The implementation of Steer-to-Clear for the flight prototype used a simple method to divide the target ditch site into four quadrants. An RC car was driven in circles in one quadrant to simulate an occupant in that ditch site. A simple implementation of Steer-to- Clear was programmed to land in the opposite quadrant to maximize distance to the occupant’s quadrant. A successful mission was tallied when this occurred. Out of nineteen flights, thirteen resulted in successful missions. Data logs from the flight vehicle and the RC car indicated that unsuccessful missions were due to geolocation error between the actual location of the RC car and the derived location of it by the Vision Assisted Landing component of S2D on the flight vehicle. Video data indicated that while the Vision Assisted Landing component reliably identified the location of the ditch site occupant in the image frame, the conversion of the occupant’s location to earth coordinates was sometimes adversely impacted by errors in sensor data needed to perform the transformation. Logged sensor data was analyzed to attempt to identify the primary error sources and their impact on the geolocation accuracy. Three trends were observed in the data evaluation phase. In one trend, errors in geolocation were relatively large at the flight vehicle’s cruise altitude, but reduced as the vehicle descended. This was the expected behavior and was attributed to sensor errors of the inertial measurement unit (IMU). The second trend showed distinct sinusoidal error for the entire descent that did not always reduce with altitude. The third trend showed high scatter in the data, which did not correlate well with altitude. Possible sources of observed error and compensation techniques are discussed.

Petty, Bryan J.↗

Supervisory manipulation based on the concepts of absolute vs relative and fixed vs moving tasks

If a machine is to perform a given subtask autonomously, it will require an internal model which, combined with operator and environmental inputs, can be used to generate the manipulator functions necessary to complete the task. This paper will advance a technique based on linear transformations by which short, supervised periods of manipulation can be accomplished. To achieve this end a distinction will be made between tasks which can be completely defined during the training period, and tasks which can be only partially defined prior to the moment of execution. A further distinction will be made between tasks which have a fixed relationship to the manipulator base throughout the execution period, and tasks which have a continuously changing task/base relationship during execution. Finally, through a rudimentary analysis of the methods developed in this paper, some of the practical aspects of implementing a supervisory system will be illustrated

Brooks, T. L.↗

Flare Emission Onset in the Slow-Rise and Fast-Rise Phases of an Erupting Solar Filament Observed with TRACE

We observe the eruption of an active-region solar filament of 1998 July 11 using high time cadence and high spatial resolution EUV observations from the TRACE sareiii'ce, along with soft X-ray images from the soft X-ray telescope (SXT) on the Yohkoh satellite, hard X-ray fluxes from the BATSE instrument on the (CGRO) satellite and from the hard X-ray telescope (HXT) on Yohkoh, and ground-based magnetograms. We concentrate on the initiation of the eruption in an effort to understand the eruption mechanism. First the filament undergoes slow upward movement in a "slow rise" phase with an approximately constant velocity of approximately 15 km/s that lasts about 10-min, and then it erupts in a "fast-rise" phase, reaching a velocity of about 200 km/s in about 5-min, followed by a period of deceleration. EUV brightenings begin just before the start of the filament's slow rise, and remain immediately beneath the rising filament during the slow rise; initial soft X-ray brightenings occur at about the same time and location. Strong hard X-ray emission begins after the onset of the fast rise, and does not peak until the filament has traveled a substantial altitude (to a height about equal to the initial length of the erupting filament) beyond its initial location. Our observations are consistent with the slow-rise phase of the eruption resulting from the onset of "tether cutting" reconnection between magnetic fields beneath the filament, and the fast rise resulting from an explosive increase in the reconnection rate or by catastrophic destabilization of the overlying filament-carrying fields. About two days prior to the event new flux emerged near the location of the initial brightenings, and this recently- emerged flux could have been a catalyst for initiating the tether-cutting reconnection. With the exception of the initial slow rise, our findings qualitatively agree with the prediction for erupting-flux-rope height as a function of time in a model discussed by Chen & Shibata (2000) based on reconnection between emerging flux and a flux rope.

Sterling, A. C.↗

Toward an IMU-based Space Suit Motion Capture System

Spacesuits are complex engineering systems that sustain human health and enable performance outside of Earth-like environments. These systems must support human mobility and physical workload demands while minimizing injury risk during extravehicular activity (EVA). Future EVA on the lunar surface during the Artemis program is expected to be more frequent and require higher physical workloads than previous EVAs during the ISS, Shuttle, or Apollo programs. Hence it is important to optimize future as well as current spacesuits to be efficient and comfortable for the success of space and planetary missions. To enable this, an efficient method is needed to test these spacesuits on the ground.When testing spacesuits in ground environments, it is often necessary to understand the kinematics of the suit to validate the design against relevant requirements or characterize the physical workload necessary to operate the suit. This is a challenging task for traditional optical motion capture (OMC) approaches: suit-mounted OMC markers are easily occluded by the subject or environment and may become detached during testing. Controlling lighting and reflectivity of objects in the motion capture volume is also difficult. Fixed-position OMC cameras also constrain testing to a small and contrived laboratory environment, disallowing kinematics capture in field environments.One promising alternative is the use of suit-mounted inertial measurement units (IMUs). These sensors are small, unobtrusive, and portable, but come at the cost of increased sensor noise and complexity of the software and mathematics to analyze the collected data. To this end, engineers at NASA are developing the Augmented Suit Inverse Kinematics (ASIK) system, a complete motion capture methodand inverse kinematics solver which relies solely on a network of wireless IMUs attached to the major kinematic segments of the spacesuit. The ASIK modeling language allows for the simple inclusion of probabilistic priors such as suit size and shape or IMU positions and rotations. Furthermore, to increase accuracy and reduce operational overhead to use this motion capture approach, the developed inverse kinematics solver exploits so-called self-calibratingalgorithmic techniques, which reduce the need for precise alignment of the sensors on the segments or scripted functional calibration procedures. The ASIK system was tested in a 7-subject pilot study. Each subject donned NASA’s new prototype exploration spacesuit in the Active Response Gravity Offload System (ARGOS) facility at the NASA Johnson Space Center. The subjects were outfitted with a set of 14 APDM (Portland, OR, USA) Opal IMUs, 12 of which were used in the ASIK model to estimate lower body and trunk kinematics. The subjects were also outfitted with a set of reflective OMC markers and traditional OMC data was collected and processed. Presented results will include characterization of ASIK-derived suit joint angles accuracy against an optical motion capture datum. Discussion of these results, as well as discussion of system calibration and nuances of mathematical observability, will be included.If successful, IMU-based motion capture will enable testing and validation of spacesuits more frequently, with less overhead, in more extreme environments. Future work will apply these techniques to common spacesuit testing tasks, such as gait, mobility, and balance assessment, physical workload characterization, and ergonomics evaluations.

Timothy Mcgrath↗