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Software for Collaborative Engineering of Launch Rockets

The Rocket Evaluation and Cost Integration for Propulsion and Engineering software enables collaborative computing with automated exchange of information in the design and analysis of launch rockets and other complex systems. RECIPE can interact with and incorporate a variety of programs, including legacy codes, that model aspects of a system from the perspectives of different technological disciplines (e.g., aerodynamics, structures, propulsion, trajectory, aeroheating, controls, and operations) and that are used by different engineers on different computers running different operating systems. RECIPE consists mainly of (1) ISCRM a file-transfer subprogram that makes it possible for legacy codes executed in their original operating systems on their original computers to exchange data and (2) CONES an easy-to-use filewrapper subprogram that enables the integration of legacy codes. RECIPE provides a tightly integrated conceptual framework that emphasizes connectivity among the programs used by the collaborators, linking these programs in a manner that provides some configuration control while facilitating collaborative engineering tradeoff studies, including design to cost studies. In comparison with prior collaborative-engineering schemes, one based on the use of RECIPE enables fewer engineers to do more in less time.

Stanley, Thomas Troy↗

A New Global Regression Analysis Method for the Prediction of Wind Tunnel Model Weight Corrections

A new global regression analysis method is discussed that predicts wind tunnel model weight corrections for strain-gage balance loads during a wind tunnel test. The method determines corrections by combining "wind-on" model attitude measurements with least squares estimates of the model weight and center of gravity coordinates that are obtained from "wind-off" data points. The method treats the least squares fit of the model weight separate from the fit of the center of gravity coordinates. Therefore, it performs two fits of "wind- off" data points and uses the least squares estimator of the model weight as an input for the fit of the center of gravity coordinates. Explicit equations for the least squares estimators of the weight and center of gravity coordinates are derived that simplify the implementation of the method in the data system software of a wind tunnel. In addition, recommendations for sets of "wind-off" data points are made that take typical model support system constraints into account. Explicit equations of the confidence intervals on the model weight and center of gravity coordinates and two different error analyses of the model weight prediction are also discussed in the appendices of the paper.

strain-gage balance↗

Impact of The Protective Renin-Angiotensin System (RAS) on The Vasoreparative Function of CD34+ CACs in Diabetic Retinopathy

Purpose: In diabetes, the impaired vasoreparative function of Circulating Angiogenic Cells (CACs) is believed to contribute to the progression of diabetic retinopathy (DR). Accumulating evidence suggests that the protective arm of renin-angiotensin system (RAS) ACE2 Angiotensin-(1-7) Mas plays an important role in restoring the function of diabetic CACs. We examined the protective RAS in CACs in diabetic individuals with different stages of retinopathy. Methods: Study subjects (n43) were recruited as controls or diabetics with either no DR, mild non-proliferative DR (NPDR), moderate NPDR, severe NPDR or proliferative DR (PDR). Fundus photography and fluorescein angiograms were analyzed using Vessel Generation Analysis (VESGEN) software in a cohort of subjects. CD34+ CACs were isolated from peripheral blood of diabetics and control subjects. RAS gene expressions in CACs were measured by qPCR. The vasoreparative function of CACs was assessed by migration ability toward CXCL12 using the QCM 5M 96-well chemotaxis cell migration assay. Results: ACE2 gene is a key enzyme converting the deleterious Angiotensin II to the beneficial Angiotensin-(1-7). ACE2 expression in CACs from diabetic subjects without DR was increased compared to controls, suggestive of compensation (p0.0437). The expression of Mas (Angiotensin-(1-7) receptor) in CACs was also increased in diabetics without DR, while was reduced in NPDR compared to controls (p0.0002), indicating a possible loss of compensation of the protective RAS at this stage of DR. The presence of even mild NPDR was associated with CD34+ CAC migratory dysfunction. When pretreating CACs of DR subjects with Angiotensin-(1-7), migratory ability to a chemoattractant CXCL12 was restored (p0.0008). By VESGEN analysis, an increase in small vessel density was observed in NPDR subjects when compared with the controls. Conclusions: These data suggest the protective RAS axis within diabetic CACs may help maintain their vasoreparative potential. The VESGEN analysis supports the presence of retinal repair in small vessels. The loss of the protective arm of RAS may predict the progression of DR.

diabetes↗

A Compilation of MATLAB Scripts and Functions for MACGMC Analyses

The primary aim of the current effort is to provide scripts that automate many of the repetitive pre- and post-processing tasks associated with composite materials analyses using the Micromechanics Analysis Code with the Generalized Method of Cells. This document consists of a compilation of hundreds of scripts that were developed in MATLAB (The Mathworks, Inc., Natick, MA) programming language and consolidated into 16 MATLAB functions. (MACGMC). MACGMC is a composite material and laminate analysis software code developed at NASA Glenn Research Center. The software package has been built around the generalized method of cells (GMC) family of micromechanics theories. The computer code is developed with a user-friendly framework, along with a library of local inelastic, damage, and failure models. Further, application of simulated thermo-mechanical loading, generation of output results, and selection of architectures to represent the composite material have been automated to increase the user friendliness, as well as to make it more robust in terms of input preparation and code execution. Finally, classical lamination theory has been implemented within the software, wherein GMC is used to model the composite material response of each ply. Thus, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. The pre-processing tasks include generation of a multitude of different repeating unit cells (RUCs) for CMCs and PMCs, visualization of RUCs from MACGMC input and output files and generation of the RUC section of a MACGMC input file. The post-processing tasks include visualization of the predicted composite response, such as local stress and strain contours, damage initiation and progression, stress-strain behavior, and fatigue response. In addition to the above, several miscellaneous scripts have been developed that can be used to perform repeated Monte-Carlo simulations to enable probabilistic simulations with minimal manual intervention. This document is formatted to provide MATLAB source files and descriptions of how to utilize them. It is assumed that the user has a basic understanding of how MATLAB scripts work and some MATLAB programming experience.

Materials Engineering↗

Unsteady Pressure-Sensitive-Paint Shot Noise Reduction

In the study of unsteady Pressure-Sensitive Paint (uPSP) image data sets, pixel intensity values collected by Phantom cameras from multiple perspectives are used to calculate the surface pressure of an experimental model. This paper focuses on mitigation of shot noise which is introduced into the image data set by the cameras. Shot noise impacts the quality of data collected, increasing the system error in its pressure value calculations. This paper characterises statistical methods to reduce shot noise within experimental data by taking an average or weighted average across an area of pixels of their respective counts. Each combined-pixel has a higher total effective intensity value and therefore exhibits reduced noise throughout its time history. This is demonstrated by calculating the standard deviations of the combined pixel values through time, which decrease as the combined pixel area increases. Finally, these methods are compared across experimental wind tunnel conditions to examine their effectiveness at different Mach numbers. Ultimately, the results are used to recommend a blur filter type and size which will be applied to the raw image data prior to processing, as well as a minimum camera resolution for future experiments. Downstream of the filter application, the software to convert the 2D image data sets into surface pressure readings on a 3D grid use a ratio of decimation that assigns multiple pixels to each 3D grid node. This decimation ratio will also be aligned with the size of the blur filter, resulting in a more manageable data set size and compromised spatial resolution. Combined with the effect of the blur filter, the resulting pixel intensity readings will exhibit significantly reduced shot noise, reducing the magnitude of uncertainty and error in the final calculated pressure. For future tests, the camera spatial resolution must be sufficient to capture small flow and model features even after the recommended blur filter is applied. The image data set is taken from a uPSP experiment of the Space Launch System Block 1 cargo vehicle model in September 2019.

Lucy Tang↗

Unsteady Pressure-Sensitive Paint (UPSP) Shot Noise Reduction

In the study of unsteady Pressure-Sensitive Paint (uPSP) image data sets, pixel intensity values collected by Phantom cameras from multiple perspectives are used to calculate the surface pressure of an experimental model. This paper focuses on mitigation of shot noise which is introduced into the image data set by the cameras. Shot noise impacts the quality of data collected, increasing the system error in its pressure value calculations. This paper characterises statistical methods to reduce shot noise within experimental data by taking an average or weighted average across an area of pixels of their respective counts. Each combined-pixel has a higher total effective intensity value and therefore exhibits reduced noise throughout its time history. This is demonstrated by calculating the standard deviations of the combined pixel values through time, which decrease as the combined pixel area increases. Finally, these methods are compared across experimental wind tunnel conditions to examine their effectiveness at different Mach numbers. Ultimately, the results are used to recommend a blur filter type and size which will be applied to the raw image data prior to processing, as well as a minimum camera resolution for future experiments. Downstream of the filter application, the software to convert the 2D image data sets into surface pressure readings on a 3D grid use a ratio of decimation that assigns multiple pixels to each 3D grid node. This decimation ratio will also be aligned with the size of the blur filter, resulting in a more manageable data set size and compromised spatial resolution. Combined with the effect of the blur filter, the resulting pixel intensity readings will exhibit significantly reduced shot noise, reducing the magnitude of uncertainty and error in the final calculated pressure. For future tests, the camera spatial resolution must be sufficient to capture small flow and model features even after the recommended blur filter is applied. The image data set is taken from a uPSP experiment of the Space Launch System Block 1 cargo vehicle model in September 2019.

Lucy Tang↗

An Approach to Building a Traceability Tool for Software Development

It is difficult in a large, complex computer program to ensure that it meets the specified requirements. As the program evolves over time, a11 program constraints originally elicited during the requirements phase must be maintained. In addition, during the life cycle of the program, requirements typically change and the program must consistently reflect those changes. Imagine the following scenario. Company X wants to develop a system to automate its assembly line. With such a large system, there are many different stakeholders, e.g., managers, experts such as industrial and mechanical engineers, and end-users. Requirements would be elicited from all of the stake holders involved in the system with each stakeholder contributing their point of view to the requirements. For example, some of the requirements provided by an industrial engineer may concern the movement of parts through the assembly line. A point of view provided by the electrical engineer may be reflected in constraints concerning maximum power usage. End-users may be concerned with comfort and safety issues, whereas managers are concerned with the efficiency of the operation. With so many points of view affecting the requirements, it is difficult to manage them, communicate information to relevant stakeholders. and it is likely that conflicts in the requirements will arise. In the coding process, the implementors will make additional assumptions and interpretations on the design and the requirements of the system. During any stage of development, stakeholders may request that a requirement be added or changed. In such a dynamic environment, it is difficult to guarantee that the system will preserve the current set of requirements. Tracing, the mapping between objects in the artifacts of the system being developed, addresses this issue. Artifacts encompass documents such as the system definition, interview transcripts, memoranda, the software requirements specification, user's manuals, the functional specifications, design reports, and system code. Tracing helps 1) validate system features against, the requirement specification, 2) identify error sources and, most importantly, 3) manage change. With so many people involved in the development of the system, it becomes necessary to identify the reasons behind the design requirements or the implementation decisions. This paper is concerned with an approach that maps documents to constraints that capture properties of and relationships between the objects being modeled by the program. Section 2 provides the reader with a background on traceability tools. Section 3 gives a brief description of the context monitoring system on which the approach suggested in this paper is based. Section 4 presents an overview of our approach to providing traceability. The last section presents our future direction of research.

Delgado, Nelly↗

Thomas Leps Internship Abstract

An optical navigation system is being flown as the backup system to the primary Deep Space Network telemetry for navigation and guidance purposes on Orion. This is required to ensure Orion can recover from a loss of communication, which would simultaneously cause a loss of DSN telemetry. Images taken of the Moon and Earth are used to give range and position information to the navigation computer for trajectory calculations and maneuver execution. To get telemetry data from these images, the size and location of the moon need to be calculated with high accuracy and precision. The reentry envelope for the Orion EM-1 mission requires the centroid and radius of the moon images to be determined within 1/3 of a pixel 3 sigma. In order to ensure this accuracy and precision can be attained, I was tasked with building precise dot grid images for camera calibration as well as building a hardware in the loop test stand for flight software and hardware proofing. To calibrate the Op-Nav camera a dot grid is imaged with the camera, the error between the image dot location and the actual dot location can be used to build a distortion map of the camera and lens system so that images can be fixed to display truth locations. To build the dot grid images I used the Electro Optics Lab optical bench Bright Object Simulator System, and gimbal. The gimbal was slewed to a series of elevations and azimuths. An image of the collimated single point light source was then taken at each position. After a series of 99 images were taken at different locations the single light spots were extracted from each image and added to a composite image containing all 99 points. During the development of these grids it was noticed that an intermittent error in the artificial "star" locations occurred. Prior to the summer this error was attributed to the gimbal having glitches in it's pointing direction and was going to be replaced, however after further examining the issue I determined it to be a software issue. I have since narrowed the likely source of the error down to a Software Development Kit released by the camera supplier PixeLink. I have since developed a workaround in order to build star grids for calibration until the software bug can be isolated and fixed. I was also tasked with building a Hardware in the Loop test stand in order to test the full Op-Nav system. A 4k screen displays simulated Lunar and Terrestrial images from a possible Orion trajectory. These images are then projected through a collimator and then captured with an Op-Nav camera controlled by an Intel NUC computer running flight software. The flight software then analyzes the images to determine attitude and position, this data is then reconstructed into a trajectory and matched to the simulated trajectory in order to determine the accuracy of the attitude and position estimates. In order for the system to work it needs to be precisely and accurately aligned. I developed an alignment procedure that allows the screen, collimator and camera to be squared, centered and collinear with each other within a micron spatially and 5 arcseconds in rotation. I also designed a rigid mount for the screen that was machined on site in Building 10 by another intern. While I was working in the EOL we received a $500k Orion startracker for alignment procedure testing. Due to my prior experience in electronics development, as an ancillary duty, I was tasked with building the cables required to operate and power the startracker. If any errors are made building these cables the startracker would be destroyed, I was honored that the director of the lab entrusted such a critical component with me. This internship has cemented my view on public space exploration. I always preferred public sector to privatization because, as a scientist, the most interesting aspects of space for me are not necessarily the most profitable. I was concerned that the public sector was faltering however, and that in order to improve human space exploration I would be forced into private sector. I now know that, at least at JSC, human spaceflight is still progressing, and exciting work is still being done. I am now actively seeking employment at JSC after I complete my Ph.D and have met with my branch chiefs and mentor to discuss transitioning to a grad Co-op position.

Leps, Thomas↗

Snow cover monitoring by machine processing of multitemporal LANDSAT MSS data

LANDSAT frames were geometrically corrected and data sets from six different dates were overlaid to produce a 24 channel (six dates and four wavelength bands) data tape. Changes in the extent of the snowpack could be accurately and easily determined using a change detection technique on data which had previously been classified by the LARSYS software system. A second phase of the analysis involved determination of the relationship between spatial resolution or data sampling frequency and accuracy of measuring the area of the snowpack.

Luther, S. G.↗

NASA's spacecraft data system

The NASA Small Explorer Data System (SEDS), a space flight data system developed to support the Small Explorer (SMEX) project, is addressed. The system was flown on the Solar Anomalous Magnetospheric Particle Explorer (SAMPEX) SMEX mission, and with reconfiguration for different requirements will fly on the X-ray Timing Explorer (XTE) and the Tropical Rainfall Measuring Mission (TRMM). SEDS is also foreseen for the Hubble repair mission. Its name was changed to Spacecraft Data System (SDS) in view of expansions. Objectives, SDS hardware, and software are described. Each SDS box contains two computers, data storage memory, uplink (command) reception circuitry, downlink (telemetry) encoding circuitry, Instrument Telemetry Controller (ITC), and spacecraft timing circuitry. The SDS communicates with other subsystems over the MIL-STD-1773 data bus. The SDS software uses a real time Operating System (OS) and the C language. The OS layer, communications and scheduling layer, application task layer, and diagnostic software, are described. Decisions on the use of advanced technologies, such as ASIC's (Application Specific Integrated Circuits) and fiber optics, led to technical improvements, such as lower power and weight, without increasing the risk associated with the data system. The result was a successful SAMPEX development, integration and test, and mission using SEDS, and the upgrading of that system to SDS for TRMM and XTE.

Cudmore, Alan↗

The Right Amount of Glue: Technologies and Standards Relevant to a Future Solar-Terrestrial Data Environment

In order to meet the challenge of developing a new system science, we will need to employ technology that enables researchers to access data from fields with which they are at least initially unfamiliar as well as from sources they use more regularly. At the same time, the quantity of data to be obtained by missions such as the Solar Dynamics Observatory demands ease and simplicity of data access. These competing demands must in turn fit within severely constrained funding for data analysis in such projects. Based on experience in only a single discipline but with a diversity of data types and sources, we will give examples of technology that have made a significant difference in the way people do science. Similarly, we will show how adoption of a well-documented data format has made it easier for one community to search, reduce, and analyze data. We will also describe a community-supported data reduction and analysis software tree with useful features. We will attempt to generalize the lessons learned in these instances to features the broader, solar-terrestrial community might find compelling, while avoiding overdesign of a common data environment.

Gurman, J. B.↗

Low-Loss, High-Isolation Microwave Microelectromechanical Systems (MEMS) Switches Being Developed

Switches, electrical components that either permit or prevent the flow of electricity, are the most important and widely used electrical devices in integrated circuits. In microwave systems, switches are required for switching between the transmitter and receiver; in communication systems, they are needed for phase shifters in phased-array antennas, for radar and communication systems, and for the new class of digital or software definable radios. Ideally, switches would be lossless devices that did not depend on the electrical signal's frequency or power, and they would not consume electrical power to change from OFF to ON or to maintain one of these two states. Reality is quite different, especially at microwave frequencies. Typical switches in microwave integrated circuits are pin diodes or gallium arsenide (GaAs) field-effect transistors that are nonlinear, with characteristics that depend on the power of the signal. In addition, they are frequency-dependent, lossy, and require electrical power to maintain a certain state. A new type of component has been developed that overcomes most of these technical difficulties. Microelectromechanical (MEMS) switches rely on mechanical movement as a response to an applied electrical force to either transmit or reflect electrical signal power. The NASA Glenn Research Center has been actively developing MEMS for microwave applications for over the last 5 years. Complete fabrication procedures have been developed so that the moving parts of the switch can be released with near 100-percent yield. Moreover, the switches fabricated at Glenn have demonstrated state-of-the-art performance. A typical MEMS switch is shown. The switch extends over the signal and ground lines of a finite ground coplanar waveguide, a commonly used microwave transmission line. In the state shown, the switch is in the UP state and all the microwave power traveling along the transmission line proceeds unimpeded. When a potential difference is applied between the cantilever and the transmission line, the cantilever is pulled downward until it connects the signal line to the ground planes, creating a short circuit. In this state, all the microwave power is reflected. The graph shows the measured performance of the switch, which has less than 0.1 dB of insertion loss and greater than 30dB of isolation. These switches consume negligible electrical power and are extremely linear. Additional research is required to address reliability and to increase the switching speed.

Ponchak, George E.↗

Software Development and Testing Support for the Avionics Systems Telemetry Tool Suite

The Customer Avionics Interface Development and Analysis (CAIDA) team provides modeling and simulation software for the verification of the Launch Control System (LCS). In late 2015, CAIDA began development of the Data Exchange Message (DEM) Generator (DEMGen) and development of the DEM Modifier (DEMMod) in early 2017. DEMGen is able to mimic the telemetry streams normally sent by different simulators allowing increased user control and more telemetry instances. DEMMod takes in a telemetry stream and allows the modification of entire packets or simple measurement values. Together, these tools provide the capabilities to simulate and test complex launch scenarios to ensure LCS is fully prepared for any anomalous behavior during an actual launch. In early 2018, CAIDA began a new project called the CAIDA Advanced Telemetry Tool (CATT), which combined the code and documentation of DEMGen and DEMMod. CATT now allows the integration of new tools into a singular program providing compact and easy access. In the fall of 2018, the author worked with another intern, Antonio Negron, to develop several new CATT features along with proper documentation and unit testing. In the following spring, the author continued that work by integrating the features into CATT, solidifying the documentation, and expanding the testing to cover more cases. The outcome of both semesters includes an inspection engine for automated packet analysis, a packet-masking feature, and a multi-measurement sequencing feature.

Thomas, Taylor Walter↗

Meteoroid Engineering Model (MEM) 3: NASA’s Newest Meteoroid Model

Meteoroid impacts threaten spacecraft and astronauts at all locations within the Solar System. At certain altitudes in low-Earth orbit, orbital debris dominates the risk, but meteoroids are more significant within 250 km of the Earth’s surface and above 4000 km [1]. In interplanetary space, orbital debris is nonexistent and meteoroids constitute the entire population of potentially dangerous impactors. The NASA Meteoroid Environment Office (MEO) produces the Meteoroid Engineering Model (MEM) to support meteoroid impact risk assessments [2]; MEM is a stand-alone piece of software that describes the flux, speed, directionality, and bulk density of meteoroids striking a spacecraft on a user-supplied trajectory. The MEO released version 3 of MEM in 2019 [3]. This proceeding describes the orbital populations that form the core of MEM, highlights key differences between MEM 3 and its predecessors, discusses the implications of these changes for spacecraft, summarizes our validation against meteor and in-situ data, and delineates the model’s limitations.

Moorhead, Althea V.↗

The Effect of a Potentially Low Solar Cycle #24 on Orbital Lifetimes of Fengyun 1-C Debris

The magnitude of Solar Cycle #24 will have a non-trivial impact on the lifetimes of debris pieces that resulted from the intentional hypervelocity impact of the Fengyun 1-C satellite in January 2007. Recent solar flux measurements indicate Solar Cycle #24 has begun in the last few months, and will continue until approximately 2019. While there have been differing opinions on whether the intensity of this solar cycle will be higher or lower than usual, the Space Weather Prediction Center within the National Oceanic Atmospheric Administration (NOAA/SWPC) has recently forecast unusually low solar activity, which would result in longer orbital lifetimes. Using models for both the breakup of Fengyun 1-C and the propagation of the resultant debris cloud, the Orbital Debris Program Office at NASA Johnson Space Center conducted a study to better understand the impact of the solar cycle on lifetimes for pieces as small as 1 mm. Using a modified collision breakup model and PROP3D propagation software, the orbits of nearly 2 million objects 1 mm and larger were propagated for up to 200 years. By comparing a normal solar cycle with that of the NOAA/SWPC forecast low cycle, the effect of the solar flux on the lifetimes of the debris pieces is evaluated. The modeling of the low solar cycle shows an additional debris count of 12% for pieces larger than 10 cm by 2019 when compared to the resultant debris count using a normal cycle. The difference becomes more exaggerated (over 15%) for debris count in the smaller size regimes. However, in 50 years, the models predict the differences in debris count from differing models of Solar Cycle #24 to be less than 10% for all size regimes, with less variance in the smaller sizes. Understanding the longevity of the debris cloud will affect collision probabilities for both operational spacecraft and large derelict objects over the next century and beyond.

Whitlock, David↗

Ensuring fault tolerance of phase-locked clocks

Processors within a real-time multiprocessor system must be synchronized with as little overhead as possible. Although synchronization can be achieved via both software (e.g., interactive convergence and interactive consistency algorithms) and hardware (e.g., multistage synchronizers and phase-locked clocks), phase-locked clocks are most attractive due to their small overheads. Despite the fact that synchronization of the multiprocessor system with phase-locked clocks is totally different in nature from the interactive consistency algorithm, it is presently proven that it must satisfy the same condition, N equal to or greater than 3m + 1, where N is the total number of clocks in the multiprocessor system and m is the maximum number of faults tolerable. Also presented are results showing how to design phase-locked clocks so as to be impervious up to a given arbitrary number of malicious failures.

Krishna, C. M.↗

The Watchdog Task: Concurrent error detection using assertions

The Watchdog Task, a software abstraction of the Watchdog-processor, is shown to be a powerful error detection tool with a great deal of flexibility and the advantages of watchdog techniques. A Watchdog Task system in Ada is presented; issues of recovery, latency, efficiency (communication) and preprocessing are discussed. Different applications, one of which is error detection on a single processor, are examined.

Ersoz, A.↗

Synchronized computational architecture for generalized bilateral control of robot arms

A master six degree of freedom Force Reflecting Hand Controller (FRHC) is available at a master site where a received image displays, in essentially real time, a remote robotic manipulator which is being controlled in the corresponding six degree freedom by command signals which are transmitted to the remote site in accordance with the movement of the FRHC at the master site. Software is user-initiated at the master site in order to establish the basic system conditions, and then a physical movement of the FRHC in Cartesean space is reflected at the master site by six absolute numbers that are sensed, translated and computed as a difference signal relative to the earlier position. The change in position is then transmitted in that differential signal form over a high speed synchronized bilateral communication channel which simultaneously returns robot-sensed response information to the master site as forces applied to the FRHC so that the FRHC reflects the feel of what is taking place at the remote site. A system wide clock rate is selected at a sufficiently high rate that the operator at the master site experiences the Force Reflecting operation in real time.

Szakaly, Zoltan F.↗