Search NASA⌕ Search

SEARCH · Search NASA

Results for “digital coordination”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY↗
NASA NTRS1977

Digital technique for generating synthetic aperture radar images

This paper describes a digital processing method applicable to a synthetic aperture radar, to be carried by the space shuttle or by satellites. The method uses an earth-fixed coordinate system in which corrective procedures are invoked to compensate for errors introduced by the satellite motion, earth curvature, and wavefront curvature. Among the compensations discussed are those of the coordinate system, skewness, roll, pitch, yaw, earth rotation, and others. The application of a Fast Fourier Transform in the numerical processing of the two-dimensional convolution is discussed in detail.

Van De Lindt, W. J.↗
NASA NTRS1972

Coordination and establishment of centralized facilities and services for the University of Alaska ERTS survey of the Alaskan environment

The author has identified the following significant results. Specifications have been prepared for the engineering design and construction of a digital color display unit which will be used for automatic processing of ERTS data. The color display unit is a disk refresh memory with computer interfaced input and a color cathode ray tube output display. The system features both analog and digital post disk data manipulation and a versatile color coding device suitable for displaying not only images, but also computer generated graphics such as diagrams, maps, and overlays. Input is from IBM compatible 9 track, 800 BPI tapes, as generated by an IBM 360 computer. ERTS digital tapes are read into the 360, where various analyses such as maximum likelihood classification are performed and the results are written on a magnetic tape which is the input to the color display unit. The greatest versatility in the data manipulation area is provided by the minicomputer built into the color display unit, which is off-line from the main 360 computer. The minicomputer is able to read any line from the refresh disk and place it in its 4K-16 bit memory. Considerable flexibility is available for post-processing enhancement of images by the investigator.

Belon, A. E.↗
NASA NTRS1985

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.↗
NASA NTRS1987

AVIRIS onboard data handling and control

The timing and flow of detector and ancillary data for the Airborne Visible/Infrared imaging spectrometer (AVIRIS) are controlled within the instrument by its digital electronics assembly. In addition to providing detector and signal chain timing, the digital electronics receives, formats, and rate-buffers digitized science data; collects and formats ancillary (calibration and engineering) data; and merges both into a single tape record. Overall AVIRIS data handling is effected by a combination of dedicated digital electronics to control instrument timing, image data flow, and data rate buffering and a microcomputer programmed to handle real-time control of instrument mechanisms and the coordinated preparation of ancillary data.

Steinkraus, Ronald E.↗
NASA NTRS1988

AVIRIS onboard data handling and control

The timing and flow of detector and ancillary data for the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) are controlled within the instrument by its digital electronics assembly. In addition to providing detector and signal chain timing, the digital electronics receives, formats, and rate-buffers digitized science data; collects and formats ancillary (calibration and engineering) data; and merges both into a single tape record. Overall AVIRIS data handling is effected by a combination of dedicated digital electronics to control instrument timing, image data flow, and data rate buffering and a microcomputer programmed to handle real-time control of instrument mechanisms and the coordinated preparation of ancillary data.

Steinkraus, Ronald E.↗
NASA NTRS2009

Lunar Pole Illumination and Communications Maps Computed from GSSR Elevation Data

A Digital Elevation Model of the lunar south pole was produced using Goldstone Solar System RADAR (GSSR) data obtained in 2006.12 This model has 40-meter horizontal resolution and about 5-meter relative vertical accuracy. This Digital Elevation Model was used to compute average solar illumination and Earth visibility with 100 kilometers of the lunar south pole. The elevation data were converted into local terrain horizon masks, then converted into lunar-centric latitude and longitude coordinates. The horizon masks were compared to latitude, longitude regions bounding the maximum Sun and Earth motions relative to the moon. Estimates of Earth visibility were computed by integrating the area of the region bounding the Earth's motion that was below the horizon mask. Solar illumination and other metrics were computed similarly. Proposed lunar south pole base sites were examined in detail, with the best site showing yearly solar power availability of 92 percent and Direct-To-Earth (DTE) communication availability of about 50 percent. Similar analysis of the lunar south pole used an older GSSR Digital Elevation Model with 600-meter horizontal resolution. The paper also explores using a heliostat to reduce the photovoltaic power system mass and complexity.

lunar base↗
NASA NTRS1978

A computer program for analyzing unresolved Mossbauer hyperfine spectra

The program for analyzing unresolved Mossbauer hyperfine spectra was written in FORTRAN 4 language for the Control Data CYBER 170 series digital computer system with network operating system 1.1. With the present dimensions, the program requires approximately 36,000 octal locations of core storage. A typical case involving two innermost coordination shells in which the amplitudes and the peak positions of all three components were estimated in 25 iterations requires 30 seconds on CYBER 173. The program was applied to determine the effects of various near neighbor impurity shells on hyperfine fields in dilute FeAl alloys.

Schiess, J. R.↗
NASA NTRS2002

Operational Limitations of the High Rate Frame Multiplexer (HRFM) Onboard the International Space Station(ISS)-and How These Limitations Affect Payload Developers (PDs) and International Partners (IPs)

The data system onboard the United States Operating Segment (USOS) of the ISS is currently used to capture, route, record and downlink high-rate science data from experiments inside the US Lab. Once NASDA's Japanese Experiment Module (JEM) and ESA's Attached Pressurized Module (APM) are launched - in the 2004 to 2005 timeframe - data from these facilities will also be routed to the ground using the USOS data system. A critical component of the USOS data system is the High Rate Frame Multiplexer (HRFM). The HRFM combines multiple data/video inputs and combines them into one data stream. This Ku-band data stream is then routed through the Tracking and Data Relay Satellite (TDRS) system to the ground. The Data Management Coordinator (DMC) - located at the Marshall Space Flight Center's Payload Operations Center (POC) - is responsible for commanding and controlling the HRFM. The HRFM can multiplex a maximum of eight digital data sources and four digital video sources. Thus far, this limitation has not been constraining to operations. However, once the JEM and APM are integrated, the HRFM limitations will become a major constraint to science operations onboard. The purpose of this paper is to characterize the limitations of the HRFM and to explain how these limitations can be successfully managed. With this information, Payload Developers and International Partners will be able to more effectively utilize the data systems onboard the ISS. Ultimately, more science data can be captured and downlinked to Flight Controllers and Scientists on the ground.

Mixson, Charles D.↗
NASA NTRS2004

Fourth Integrated Communications, Navigation, and Surveillance (ICNS) Conference and Workshop 2004: Conclusions and Recommendations

The NASA Glenn Research Center organized and hosted the Fourth Integrated Communications, Navigation, and Surveillance (ICNS) Technologies Conference and Workshop, which took place April 26-30, 2004 at the Hyatt Fair Lakes Hotel in Fairfax, Virginia. This fourth conference of the annual series followed the very successful first ICNS Conference (May 1-3, 2001 in Cleveland, Ohio), second ICNS conference (April 29-May 2, 2002 in Vienna, Virginia), and third ICNS conference (May 19-22, 2003 in Annapolis, Maryland). The purpose of the Fourth ICNS Conference was to assemble government, industry and academic communities performing research and development for advanced digital communications, surveillance and navigation systems and associated applications supporting the national and global air transportation systems to: 1) Understand current efforts and recent results in near- and far-term R&D and technology demonstration; 2) Identify integrated digital communications, navigation and surveillance R&D requirements necessary for a safe, secure and reliable, high-capacity, advanced air transportation system; 3) Provide a forum for fostering collaboration and coordination; and 4) Discuss critical issues and develop recommendations to achieve the future integrated CNS vision for national and global air transportation. The workshop attracted 316 attendees from government, industry and academia to address these purposes through technical presentations, breakout sessions, and individual and group discussions during the workshop and after-hours events, and included 16 international attendees. An Executive Committee consisting of representatives of several key segments of the aviation community concerned with CNS issues met on the day following the workshop to consider the primary outcomes and recommendations of the workshop. This report presents an overview of the conference, workshop breakout session results, and the findings of the Executive Committee.

Phillips, Brent↗
NASA NTRS2005

New Applications for the Testing and Visualization of Wireless Networks

Traditional techniques for examining wireless networks use physical link characteristics such as Signal-to-Noise (SNR) ratios to assess the performance of wireless networks. Such measurements may not be reliable indicators of available bandwidth. This work describes two new software applications developed at NASA Glenn Research Center for the investigation of wireless networks. GPSIPerf combines measurements of Transmission Control Protocol (TCP) throughput with Global Positioning System (GPS) coordinates to give users a map of wireless bandwidth for outdoor environments where a wireless infrastructure has been deployed. GPSIPerfView combines the data provided by GPSIPerf with high-resolution digital elevation maps (DEM) to help users visualize and assess the impact of elevation features on wireless networks in a given sample area. These applications were used to examine TCP throughput in several wireless network configurations at desert field sites near Hanksville, Utah during May of 2004. Use of GPSIPerf and GPSIPerfView provides a geographically referenced picture of the extent and deterioration of TCP throughput in tested wireless network configurations. GPSIPerf results from field-testing in Utah suggest that it can be useful in assessing other wireless network architectures, and may be useful to future human-robotic exploration missions.

Griffin, Robert I.↗
NASA NTRS1979

A Digital Program for Calculating the Interaction Between Flexible Structures, Unsteady Aerodynamics and Active Controls

A computer program, ISAC, is described which calculates the stability and response of a flexible airplane equipped with active controls. The equations of motion relative to a fixed inertial coordinate system are formulated in terms of the airplane's rigid body motion and its unrestrained normal vibration modes. Unsteady aerodynamic forces are derived from a doublet lattice lifting surface theory. The theoretical basis for the program is briefly explained together with a description of input data and output results.

Peele, E. L.↗
NASA NTRS2014

Clearance Analysis of CTC2 (on ELC4) to S-TRRJ HRS Radiator Rotation Envelope

In response to the planned retirement of the Space Shuttle Program, International Space Station (ISS) management began stockpiling spare parts on the ISS. Many of the larger orbital replacement units were stored on the Expedite the Processing of Experiments to Space Station (EXPRESS) Logistics Carriers (ELCs) mounted on the end of the S3 and P3 truss segments, immediately outboard of the Thermal Radiator Rotary Joints (TRRJs) and their attached radiators. In an August 2009 computer-aided design (CAD) assessment, it was determined that mounting the Cargo Transport Container (CTC) 2 on the inboard face of ELC4 as planned would create insufficient clearance between the CTC2 and the rotational envelope of the radiators when the TRRJs were rotated to a gamma angle of 35.0 degrees. The true clearance would depend on how the Unpressurized Cargo Carrier Attachment System (UCCAS) was mounted to the S3 truss and how the ELC4 was attached to it. If the plane of the UCCAS attachment points were tilted even slightly inboard, it would significantly change the clearance between CTC2 and the Starboard TRRJ (S-TRRJ) radiators. Additionally, since CTC2 would be covered in multilayer insulation (MLI), the true outer profile of CTC2 was not captured in the CAD models used for the clearance assessment. It was possible that, even if the S-TRRJ radiators cleared CTC2, they could snag the MLI covering. In the fall of 2010, the Image Science and Analysis Group (ISAG) was asked to perform an on-orbit clearance analysis to determine the location of CTC2 on ELC4 and the S-TRRJ radiators at the angle of closest approach so that a positive clearance could be assured. To provide the measurements as quickly as possible to aid in the assessment, it was decided that the clearance analysis would be broken into two phases. Phase I: The location and orientation of the UCCAS fittings, which support and hold the ELC4 in place, would be measured relative to the ISS Analytical Coordinate System (ISSACS) as defined by nine preexisting Space Vision System (SVS) targets affixed to the forward/zenith side of the S1 and S3 truss segments. The location of the outboard edge of the S-TRRJ radiator would also be measured when positioned at the angle of closest approach to CTC2 (gamma = 35.0 degrees). This data would allow the Digital Pre-Assembly Group to predict how the ELC4 would sit on the UCCAS and how that would translate into the clearance between CTC2 and the S-TRRJ radiators. Phase II: After the ELC4 was delivered and installed into the UCCAS, the position of the CTC2 mounting plate on the inboard face of ELC4, would be measured in the ISSACS coordinate system relative to the SVS control points used in Phase I. Although CTC2 would not yet be mounted on ELC4, the working envelope of CTC2 could be mathematically added to the measured position of ELC4 to produce a best estimate for CTC2's mounted location. Comparing CTC2's best estimated location to the S-TRRJ radiator (measured in Phase I); relative to the ISSACS coordinate system, would provide a direct measurement of the expected clearance. Due to the impending delivery of ELC4 (scheduled for January 2011), planning for the Phase I clearance analysis began immediately. Using the Dynamic Onboard Ubiquitous Graphics (DOUG) program, ISAG designed a way to acquire images of the SVS control points on truss segments S1 and S3, the aft facing edge of the S-TRRJ Heat Rejection Subsystem (HRS) radiator, and the three UCCAS latch mechanisms mounted on the zenith face of the S3 truss using the Space Station Remote Manipulator System (SSRMS). To minimize the number of SSRMS movements, the Special Purpose Dexterous Manipulator (SPDM) would be attached to the SSRMS. This would make it possible to park the SPDM in one position and acquire multiple images by changing the viewing orientation of the SPDM body cameras using the pan/tilt units on which they are mounted. Using this implementation concept, ISAG identified four SSRMS/SPDM positions from which the majority of the needed imagery could be acquired. Five additional images would be acquired using the CP-3 external ISS camera mounted on the S1 truss immediately inboard of ELC4. Based on a photogrammetric simulation, it was estimated that the measured location of the HRS radiator and UCCAS latch points would be accurate to about 0.3 in. in each of the three axes relative to ISSACS. Working with ROBO, ISAG collected 78 images of the ISS December 29, 2010. From this imagery, the best 40 were selected for use in the analysis process. The images were radiometrically enhanced to improve color and contrast and loaded into the FotoG analysis software along with the camera parameters and control data, which consisted of the coordinates for the nine SVS targets on the S1 and S3 trusses in the ISSACS coordinate system.

Liddle, Donn↗
NASA NTRS2016

Hybrid Reality Lab Capabilities - Video 2

Our Hybrid Reality and Advanced Operations Lab is developing incredibly realistic and immersive systems that could be used to provide training, support engineering analysis, and augment data collection for various human performance metrics at NASA. To get a better understanding of what Hybrid Reality is, let's go through the two most commonly known types of immersive realities: Virtual Reality, and Augmented Reality. Virtual Reality creates immersive scenes that are completely made up of digital information. This technology has been used to train astronauts at NASA, used during teleoperation of remote assets (arms, rovers, robots, etc.) and other activities. One challenge with Virtual Reality is that if you are using it for real time-applications (like landing an airplane) then the information used to create the virtual scenes can be old (i.e. visualized long after physical objects moved in the scene) and not accurate enough to land the airplane safely. This is where Augmented Reality comes in. Augmented Reality takes real-time environment information (from a camera, or see through window, and places digitally created information into the scene so that it matches with the video/glass information). Augmented Reality enhances real environment information collected with a live sensor or viewport (e.g. camera, window, etc.) with the information-rich visualization provided by Virtual Reality. Hybrid Reality takes Augmented Reality even further, by creating a higher level of immersion where interactivity can take place. Hybrid Reality takes Virtual Reality objects and a trackable, physical representation of those objects, places them in the same coordinate system, and allows people to interact with both objects' representations (virtual and physical) simultaneously. After a short period of adjustment, the individuals begin to interact with all the objects in the scene as if they were real-life objects. The ability to physically touch and interact with digitally created objects that have the same shape, size, location to their physical object counterpart in virtual reality environment can be a game changer when it comes to training, planning, engineering analysis, science, entertainment, etc. Our Project is developing such capabilities for various types of environments. The video outlined with this abstract is a representation of an ISS Hybrid Reality experience. In the video you can see various Hybrid Reality elements that provide immersion beyond just standard Virtual Reality or Augmented Reality.

Delgado, Francisco J.↗
NASA NTRS1974

Geometric stiffness characteristics of a rotating elastic appendage

Previous work by Likins (1972 and 1973) on finite element appendage equations for hybrid coordinate dynamic analysis and on the dynamic analysis of a system of hinge-connected rigid bodies with nonrigid appendages is extended to the establishment of a basis for a generic digital computer program to be developed for the simulation of nonrigid spacecraft. A subtle but significant generalization of that previous work as well as a correction and elaboration accomplish this purpose.

Likins, P. W.↗
NASA NTRS1974

Skylab Medical Data Center and Archives

The founding of the Skylab medical data center and archives as a central area to house medical data from space flights is described. Skylab program strip charts, various daily reports and summaries, experiment reports and logs, status report on Skylab data quality, raw data digital tapes, processed data microfilm, and other Skylab documents are housed in the data center. In addition, this memorandum describes how the data center acted as a central point for the coordination of preflight and postflight baseline data and how it served as coordinator for all data processing through computation and analysis. Also described is a catalog identifying Skylab medical experiments and all related data currently archived in the data center.

Spross, F. R.↗
NASA NTRS2003

Terrain Portrayal for Head-Down Displays Flight Test

The Synthetic Vision Systems General Aviation (SVS-GA) element of NASA's Aviation Safety Program is developing technology to eliminate low visibility induced General Aviation (GA) accidents through the application of synthetic vision techniques. SVS displays present computer generated 3-dimensional imagery of the surrounding terrain to greatly enhance pilot's situation awareness (SA), reducing or eliminating Controlled Flight into Terrain (CFIT), as well as Low-Visibility Loss of Control (LVLOC) accidents. In addition to substantial safety benefits, SVS displays have many potential operational benefits that can lead to flight in instrument meteorological conditions (IMC) resembling those conducted in visual meteorological conditions (VMC). Potential benefits could include lower landing minimums, more approach options, reduced training time, etc. SVS conducted research will develop display concepts providing the pilot with an unobstructed view of the outside terrain, regardless of weather conditions and time of day. A critical component of SVS displays is the appropriate presentation of terrain to the pilot. The relationship between the realism of the terrain presentation and resulting enhancements of pilot SA and pilot performance has been largely undefined. Comprised of coordinated simulation and flight test efforts, the terrain portrayal for head-down displays (TP-HDD) test series examined the effects of two primary elements of terrain portrayal: variations of digital elevation model (DEM) resolution and terrain texturing. Variations in DEM resolution ranged from sparsely spaced (30 arc-sec/2,953ft) to very closely spaced data (1 arc-sec/98 ft). Variations in texture involved three primary methods: constant color, elevation-based generic, and photo-realistic, along with a secondary depth cue enhancer in the form of a fishnet grid overlay. The TP-HDD test series was designed to provide comprehensive data to enable design trades to optimize all SVS applications, as well as develop requirements and recommendations to facilitate the implementation and certification of SVS displays. The TP-HDD flight experiment utilized the NASA LaRC Cessna 206 Stationaire and evaluated eight terrain portrayal concepts in an effort to confirm and extend results from the previously conducted TP-HDD simulation experiment. A total of 15 evaluation pilots, of various qualifications, accumulated over 75 hours of dedicated research flight time at Newport News (PHF) and Roanoke (ROA), VA, airports from August through October, 2002. This report will present results from the portion of testing conducted at Roanoke, VA.

Hughes, Monica F.↗
NASA NTRS1983

Stability experiments in rotating-disk flow

An experimental study of the transitional flow on a flat disk, rotating in still air, has been conducted. Using digitized hot-wire data, the axes of the stationary spiral vortices, which are the primary instability mechanism for the disk flow, have been mapped-out in terms of both spatial coordinates and velocity fluctuations. Data are presented for a clean disk and for a disk with a single, isolated roughness element. The data show that the disk vortices are generated at discrete roughness disturbance sites on the disk and that they propagate and grow as wave packets. The familiar vortex pattern of 30 or so vortices results only when these wave packets have merged and filled the entire circumference. The appearance of stationary, secondary vortices prior to turbulent breakdown has also been observed. Comparisons with linear stability theory show reasonable agreement with measured growth rate data.

Wilkinson, S. P.↗