Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “load reduction”

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 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

High-Energy-Density Electrolytic Capacitors

Reductions in weight and volume make new application possible. Supercapacitors and improved ultracapacitors advanced electrolytic capacitors developed for use as electric-load-leveling devices in such applications as electric vehicle propulsion systems, portable power tools, and low-voltage pulsed power supplies. One primary advantage: offer power densities much higher than storage batteries. Capacitors used in pulse mode, with short charge and discharge times. Derived from commercially available ultracapacitors. Made of lightweight materials; incorporate electrode/electrolyte material systems capable of operation at voltages higher than previous electrode/electrolyte systems. By use of innovative designs and manufacturing processes, made in wide range of rated capacitances and in rated operating potentials ranging from few to several hundred volts.

Yen, Shiao-Ping S.↗
NASA NTRS1992

Multi-disciplinary optimization of aeroservoelastic systems

The purpose of the research project was to continue the development of new methods for efficient aeroservoelastic analysis and optimization. The main targets were as follows: to complete the development of analytical tools for the investigation of flutter with large stiffness changes; to continue the work on efficient continuous gust response and sensitivity derivatives; and to advance the techniques of calculating dynamic loads with control and unsteady aerodynamic effects. An efficient and highly accurate mathematical model for time-domain analysis of flutter during which large structural changes occur was developed in cooperation with Carol D. Wieseman of NASA LaRC. The model was based on the second-year work 'Modal Coordinates for Aeroelastic Analysis with Large Local Structural Variations'. The work on continuous gust response was completed. An abstract of the paper 'Continuous Gust Response and Sensitivity Derivatives Using State-Space Models' was submitted for presentation in the 33rd Israel Annual Conference on Aviation and Astronautics, Feb. 1993. The abstract is given in Appendix A. The work extends the optimization model to deal with continuous gust objectives in a way that facilitates their inclusion in the efficient multi-disciplinary optimization scheme. Currently under development is a work designed to extend the analysis and optimization capabilities to loads and stress considerations. The work is on aircraft dynamic loads in response to impulsive and non-impulsive excitation. The work extends the formulations of the mode-displacement and summation-of-forces methods to include modes with significant local distortions, and load modes. An abstract of the paper,'Structural Dynamic Loads in Response to Impulsive Excitation' is given in appendix B. Another work performed this year under the Grant was 'Size-Reduction Techniques for the Determination of Efficient Aeroservoelastic Models' given in Appendix C.

Karpel, Mardechay↗
NASA NTRS1998

Mechanical Behavior and Analytical Modeling of Melt-Infiltrated SiC/SiC Woven Composite

The desirable properties in ceramic matrix composites (CMCs), such as high temperature strength, corrosion resistance, high toughness, low density, or good creep resistance have led to increased use of CMCs in high-speed engine structural components and structures that operate in extreme temperature and hostile aero-thermo-chemical environments. Ceramic matrix composites have been chosen for turbine material in the design of 21st century civil propulsion systems to achieve high fuel economy, improved reliability, extended life, and reduced cost. Most commercial CMCs are manufactured using a chemical vapor infiltration (CVI) process. However, a lower cost fabrication known as melt-infiltration process is also providing CMCs marked for use in hot sections of high-speed civil transports. Limited samples of a SiC/SiC melt-infiltrated woven composites are being investigated at room and elevated temperature below and above matrix cracking. These samples show graceful failure and toughness at room temperature with a reduction in strength and modulus at elevated temperatures. A generic finite element model is also being developed to predict monotonic and cyclic loading behavior of the woven composite. Use of the initial test data from the woven composite is being used for the development of the analytical model. This model is the first of a iterative process leading towards the development the model's capability to predict behavior at room and elevated temperature for monotonic and cyclic loading. The purpose of this paper is to report on the material and mechanical findings of the SiC/SiC melt-infiltrated woven composite and progress on the development of the finite element model.

Lang, J.↗
NASA NTRS2003

Modeling Aircraft Wing Loads from Flight Data Using Neural Networks

Neural networks were used to model wing bending-moment loads, torsion loads, and control surface hinge-moments of the Active Aeroelastic Wing (AAW) aircraft. Accurate loads models are required for the development of control laws designed to increase roll performance through wing twist while not exceeding load limits. Inputs to the model include aircraft rates, accelerations, and control surface positions. Neural networks were chosen to model aircraft loads because they can account for uncharacterized nonlinear effects while retaining the capability to generalize. The accuracy of the neural network models was improved by first developing linear loads models to use as starting points for network training. Neural networks were then trained with flight data for rolls, loaded reversals, wind-up-turns, and individual control surface doublets for load excitation. Generalization was improved by using gain weighting and early stopping. Results are presented for neural network loads models of four wing loads and four control surface hinge moments at Mach 0.90 and an altitude of 15,000 ft. An average model prediction error reduction of 18.6 percent was calculated for the neural network models when compared to the linear models. This paper documents the input data conditioning, input parameter selection, structure, training, and validation of the neural network models.

Allen, Michael J.↗
NASA NTRS2011

Climatic Effects of Regional Nuclear War

We use a modern climate model and new estimates of smoke generated by fires in contemporary cities to calculate the response of the climate system to a regional nuclear war between emerging third world nuclear powers using 100 Hiroshima-size bombs (less than 0.03% of the explosive yield of the current global nuclear arsenal) on cities in the subtropics. We find significant cooling and reductions of precipitation lasting years, which would impact the global food supply. The climate changes are large and longlasting because the fuel loadings in modern cities are quite high and the subtropical solar insolation heats the resulting smoke cloud and lofts it into the high stratosphere, where removal mechanisms are slow. While the climate changes are less dramatic than found in previous "nuclear winter" simulations of a massive nuclear exchange between the superpowers, because less smoke is emitted, the changes seem to be more persistent because of improvements in representing aerosol processes and microphysical/dynamical interactions, including radiative heating effects, in newer global climate system models. The assumptions and calculations that go into these conclusions will be described.

Oman, Luke D.↗
NASA NTRSDate not supplied

Transonic Cruise Slotted Wing Design for Commercial Transport Aircraft using CDISC

A knowledge-based aerodynamic design method, CDISC, has been extended to enable the computational design of transonic cruise slotted wings for commercial transport aircraft. The cruise slotted wing is a multielement wing concept with a forward main element and an aft flap element, separated to form an intermediate slot. This slot favorably redirects airflow from the main element lower surface toward the low-momentum, upper-surface boundary layer of the flap. Relative to the supercritical wing, the cruise slotted wing enables greater aft loading that helps to reduce shock strength and transonic pressure drag. The cruise slotted wing may be considered a passive drag-reduction technology with potential fuel burn savings and increased vehicle range for next-generation aircraft. The current paper seeks to quantify the drag-saving benefits of cruise slotted wing technology in application to single-aisle commercial transport aircraft. A series of multielement design constraints were developed within CDISC for the design of a partial-span, cruise slotted wing for a Mach-0.8 variant of the Common Research Model. To mitigate the skin-friction drag penalty associated with cruise slotted wings, the design features a flap with natural laminar flow over approximately 75% of the flap surface area. Cruise drag estimates from the NASA USM3D flow solver between a supercritical wing and the partial-span, cruise slotted wing design were within one drag count. Near-cruise, off-design analyses showed limited laminar flow sensitivity to angle of attack and a more gradual drag rise compared to a supercritical wing. Based on this demonstrated benefit, future work is motivated to design a cruise slotted wing with natural laminar flow on both wing elements to achieve a significant reduction in cruise drag while providing delayed drag divergence.

CDISC↗
DOE OSTI2021

Economic Analysis of a Novel Thermal Energy Storage System Using Solid Particles for Grid Electricity Storage: Preprint

As renewable power generation becomes the mainstream new-built energy source, energy storage will become an indispensable need to complement the uncertainty of renewable resources to firm the power supply. When phasing out fossil-fuel power plants to meet the carbon neutral utility target in the midcentury around the world, large capacity of energy storage will be needed to provide reliable grid power. The integration of renewable power and storage to support future carbon-free utility has several significant and positive impacts including expanding the renewable generation into the grid, improving the peak-load response, and balancing the electricity supply and demand. Long-duration energy storage (10–100 hours duration) can potentially complement the reduction of fossil-fuel baseload generation that otherwise would risk grid security when a large portion of grid power comes from variable renewable sources. Current energy storage methods based on pumped storage hydropower or batteries have many limitations. Thermal energy storage (TES) has unique advantages in scale and siting flexibility to provide grid-scale storage capacity. A particle-based TES system has promising cost and performance for the future growing energy storage needs. This paper introduces the system and components required for the particle TES to be technically and economically competitive. A technoeconomic analysis based on preliminary component designs and performance shows that the particle TES integrated with an efficient air-Brayton combined cycle power system can provide power for several days by low-cost, high-performance storage cycles. It addresses grid storage needs by enabling large-scale grid integration of intermittent renewables like wind and solar, thereby increasing their grid value. The design specifications and cost estimations of major components in a commercial scale system are presented in this paper. The cost model provides insights for further development and cost comparison with competing technologies.

27 ARPA - Advanced Research Projects Agency-Energy↗
DOE OSTI2024

Synthetic methods for crystallite size control of bimetallic polyanionic battery compositions

Bimetallic polyanionic materials, such as silver vanadium phosphorus oxide (Ag 2 VO 2 PO 4 , SVOP), are promising cathode materials for Li batteries due in part to their large capacity and high current capability. A new synthesis of Ag 2 VO 2 PO 4 based on microwave heating is disclosed, where the reaction time is reduced by approximately 100 times relative to other reported methods, and the crystallite size is controlled via synthesis temperature, showing a linear positive correlation of crystallite size with temperature. Reaction times of an hour or less are sufficient to render phase-pure material after reaction at 50° C. to 180° C., significantly lower than the temperatures reported for other methods. Crystallite sizes between 42 nm and 60 nm are achieved by the novel method, smaller than by other methods. Silver/vanadium atomic ratios of 1.96 to 2.04 in the as-synthesized SVOP result and appear temperature-dependent. Notably, under galvanostatic reduction, the Ag 2 VO 2 PO 4 sample with the smallest crystallite size delivers the highest capacity and shows the highest loaded voltage.

Takeuchi, Kenneth J.↗
DOE OSTI2024

Thermally anisotropic building envelope for thermal management: finite element model calibration using field evaluation data

The thermally anisotropic building envelope (TABE) is an active building envelope that redistributes thermal loads in response to weather conditions and building energy demand. Conductive layers throughout the TABE distribute low-grade heat among hydronic loops, altering heat flow direction and intensity. Finite element models of TABE roof and wall panels were developed and calibrated using field evaluation data. The calibration results showed that heat flux differences between the experimental data and finite element models averaged –0.42% and 3.57%, with a maximum mean square error of 1.78 and 3.96 for roof and wall panels, respectively. A reduction in heat flux from the environment to the building living space over the entire testing period (weeks in July/August) was found to be 85% for roof panels and 335% (load reversed) for wall panels. Finally, these results indicate TABE can effectively harness low-grade thermal energy sources to achieve high energy efficiency and promote demand-side management.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1992

Vibration reduction in helicopter rotors using an active control surface located on the blade

A feasibility study of vibration reduction in a four-bladed helicopter rotor using individual blade control (IBC), which is implemented by an individually controlled aerodynamic surface located on each blade, is presented. For this exploratory study, a simple offset-hinged spring restrained model of the blade is used with fully coupled flap-lag-torsional dynamics for each blade. Deterministic controllers based on local and global system models are implemented to reduce 4/rev hub loads using both an actively controlled aerodynamic surface on each blade as well as conventional IBC, where the complete blade undergoes cyclic pitch change. The effectiveness of the two approaches for simultaneous reduction of the 4/rev hub shears and hub moments is compared. Conventional IBC requires considerably more power to achieve approximately the same level of vibration reduction as that obtained by implementing IBC using an active control surface located on the outboard segment of the blade. The effect of blade torsional flexibility on the vibration reduction effectiveness of the actively controlled surface was also considered and it was found that this parameter has a very substantial influence.

Millott, T. A.↗
DOE OSTI2026

Transformation of CeO 2 Nanoparticles into Atomically Dispersed Ce Cations Leads to Enhanced Reactivity for Automotive Emissions Control

Nanosized cerium oxide (CeO 2 ) has been extensively used as the oxygen storage component in automotive emission control systems. However, the possible influence of atomically dispersed Ce in these catalysts has not been recognized. Here, in this study, we demonstrate the controllable transformation of ceria nanoparticles into isolated cerium cations on γ-Al 2 O 3 via reductive atom trapping in 10% H 2 at 800 °C, achieving over half-monolayer coverage. Dispersed Ce 1 ions anchored by surface penta- and octa-coordinated Al sites exhibit outstanding thermal stability in air up to 500 °C, enabling further loading of active metals with well-defined catalyst structures. With this strategy, supported single-atom Rh 1 surrounded by dispersed Ce 1 is confirmed to exhibit much superior performance to Rh 1 on bare Al 2 O 3 or nanocrystalline CeO 2 in catalyzing NO reduction by CO, exhibiting a striking one-order-of-magnitude increase in activity. Dispersed Ce 1 exhibits greatly enhanced oxygen transfer capability compared to ceria nanoparticles and introduces a modified reaction mechanism that involves an adjacent Rh 1 –Ce 1 motif, resulting in a greatly decreased activation barrier (from 192 to 96 kJ/mol). The reactivity enhancements are also seen with Ce 1 -promoted Pt nanoparticles for oxidation of CO and hydrocarbons.

Jiang, Dong [Washington State Univ., Pullman, WA (↗
DOE OSTI2024

Tailoring Interfaces for Enhanced Methanol Production from Photoelectrochemical CO 2 Reduction

Efficient and stable photoelectrochemical reduction of CO 2 into highly reduced liquid fuels remains a formidable challenge, which requires an innovative semiconductor/catalyst interface to tackle. In this study, we introduce a strategy involving the fabrication of a silicon micropillar array structure coated with a superhydrophobic fluorinated carbon layer for the photoelectrochemical conversion of CO 2 into methanol. The pillars increase the electrode surface area, improve catalyst loading and adhesion without compromising light absorption, and help confine gaseous intermediates near the catalyst surface. The superhydrophobic coating passivates parasitic side reactions and further enhances local accumulation of reaction intermediates. Upon one-electron reduction of the molecular catalyst, the semiconductor–catalyst interface changes from adaptive to buried junctions, providing a sufficient thermodynamic driving force for CO 2 reduction. These structures together create a unique microenvironment for effective reduction of CO 2 to methanol, leading to a remarkable Faradaic efficiency reaching 20% together with a partial current density of 3.4 mA cm –2 , surpassing the previous record based on planar silicon photoelectrodes by a notable factor of 17. Furthermore, this work demonstrates a new pathway for enhancing photoelectrocatalytic CO 2 reduction through meticulous interface and microenvironment tailoring and sets a benchmark for both Faradaic efficiency and current density in solar liquid fuel production.

14 SOLAR ENERGY↗
NASA NTRS2023

Subsonic Ultra Green Aircraft Research: Phase IV Final Report – Volume I Mach 0.80 Transonic Truss-Braced Wing High-Speed Design Report

This design report summarizes work performed by the Boeing Subsonic Ultra-Green Aircraft Research (SUGAR) team from December 2016 through June 2018. In Phase IV of the SUGAR program, Boeing is working to improve the productivity of a TTBW configuration by updating the Mach 0.745 vehicle concept to operate efficiently at Mach 0.80. Due to the aerodynamic and structural design challenges associated with adapting the design to a higher speed, design tasks have been broken into several subtasks. The information in this report (Volume I) documents the development of a Mach 0.80 vehicle outer mold line, maturation of TTBW structural concepts, and presents a preliminary high-liftsystem assessment. Results from these studies were integrated into an aircraft-level performance code that estimates the benefits of TTBW technology, both on its own and as a part of the SUGAR integrated technology suite. The aerodynamic performance results presented herein detail the high cruise efficiency of the TTBW concept operating at M=0.80. Results from the RANS code OVERFLOW indicate that the TTBW is aerodynamically well suited for operation at the design M=0.80 transonic cruise Mach number. Aircraft-level performance predictions show that the TTBW offers a 7.2% improvement in fuel burn (per seat) for an economic mission of 900nm, and a 9.0% improvement in fuel burn (per seat) for a 3500nm mission with full passenger payload, relative to an aspect ratio 13 conventional tube and wing configuration of equivalent technology. Integration of the TTBW performance benefits into the SUGAR technology suite shows a 55.9% reduction in fuel burn (for the economic mission) relative to the reference (SUGAR Free) aircraft, which is a consistently sized traditional cantilever wing, single-aisle transport typical of the 2008 fleet. This benefit does not include the performance improvement potential of hybrid-electric systems studied in earlier phases of the SUGAR program Structural concept development work completed in Phase IV has identified several strut attachment concepts that are worth additional development activity – an inboard strut attachment swivel joint concept (which enables the strut to carry axial loads while avoiding strut bending induced by wing twist during flight) significantly simplifies the construction of the main strut. An outboard offset strut attachment concept holds significant potential for further reductions in wing-strut interference drag. Based on work performed to date on Phase IV and the previous phases of the SUGAR program, the TTBW concept continues to remain a viable concept for significantly improving the performance of future aircraft. High-fidelity aerodynamic analysis of the Mach 0.80 TTBW aircraft has shown fuel burn improvement that has exceeded initial expectations despite the increase in cruise Mach number. Structural concept maturation has continued to refine the TTBW structure, and has found no obvious ‘show-stoppers’ to date. Therefore, the potential benefit of improved performance through the use of a very high aspect ratio strut-braced wing continues to warrant additional study

SUGAR↗
NASA NTRS1998

Load Distribution in Transmissions "Split"

The transmission system of a helicopter must meet particularly critical requirements. It must transmit engine power to the rotor, at the same time ensuring a typical speed reduction of 60 to 1. It must also be safe, reliable, light, and reach a high level of performance while, at the same time, it must produce few vibrations and little noise. Helicopter transmissions have achieved high-level performances thanks to the combination of analyses, experiments, and the application of practical field experience. However, the new generation of helicopters will require transmission systems that are even safer, lighter, less noisy, and more reliable.

Krantz, Timothy L.↗
NASA NTRS1997

Experimental Characterization of Hysteresis in a Revolute Joint for Precision Deployable Structures

Recent studies of the micro-dynamic behavior of a deployable telescope metering truss have identified instabilities in the equilibrium shape of the truss in response to low-energy dynamic loading. Analyses indicate that these micro-dynamic instabilities arise from stick-slip friction within the truss joints (e.g., hinges and latches). The present study characterizes the low-magnitude quasi-static load cycle response of the precision revolute joints incorporated in the deployable telescope metering truss, and specifically, the hysteretic response of these joints caused by stick-slip friction within the joint. Detailed descriptions are presented of the test setup and data reduction algorithms, including discussions of data-error sources and data-filtering techniques. Test results are presented from thirteen specimens, and the effects of joint preload and manufacturing tolerances are investigated. Using a simplified model of stick-slip friction, a relationship is made between joint load-cycle behavior and micro-dynamic dimensional instabilities in the deployable telescope metering truss.

Lake, Mark S.↗
NASA NTRS1995

Traction Drives for Zero Stick-Slip Robots, and Reaction Free, Momentum Balanced Systems

Two differential (dual input, single output) drives (a roller-gear and a pure roller), and a momentum balanced (single input, dual output) drive (pure roller ) were designed, fabricated, and tested. The differential drives are each rated at 295 rad/sec (2800 rpm) input speed, 450 N-m (4,000 in-lbf) output torque. The momentum balanced drive is rated at 302 rad/sec (2880 rpm) input speed, and dual output torques of 434N-m (3840 in-lbf). The Dual Input Differential Roller-Gear Drive (DC-700) has a planetary roller-gear system with a reduction ratio (one input driving the output with the second input fixed) of 29.23: 1. The Dual Input Differential Roller Drive (DC-500) has a planetary roller system with a reduction ratio of approximately 24:1. Each of the differential drives features dual roller-gear or roller arrangements consisting of a sun, four first row planets, four second row planets, and a ring. The Momentum Balanced (Grounded Ring) Drive (DC-400) has a planetary roller system with a reduction ratio of 24:1 with both outputs counterrotating at equal speed. Its single roller cluster consists of a sun, five first and five second row planets, a roller cage or spider and a ring. Outputs are taken from both the roller cage and the ring which counterrotate. Test results reported for all three drives include angular and torque ripple (linearity and cogging), viscous and Coulomb friction, and forward and reverse power efficiency. Of the two differential drives, the Differential Roller Drive had better linearity and less cogging than did the Differential Roller-Gear Drive, but it had higher friction and lower efficiency (particularly at low power throughput levels). Use of full preloading rather than a variable preload system in the Differential Roller Drive assessed a heavy penalty in part load efficiency. Maximum measured efficiency (ratio of power out to power in) was 95% for the Differential Roller-Gear Drive and 86% for the Differential Roller Drive. The Momentum Balanced (Grounded Ring) Drive performed as expected kinematically. Reduction r-atios to the two counterrotating outputs (design nominal=24:1) were measured to be 23.98:1 and 24.12:1 at zero load.. At 25ONm (2200 in-lbf) output torque the ratio changed 2% due to roller creep. This drive was the smoothest of all three as determined from linearity and cogging tests, and maximum measured efficiency (ratio of power out to power in) was 95%. The disadvantages of full preloading as comvared to variable preload were apparent in this drive as in the Differential Roller Drive. Efficiencies at part load were low, but improved dramatically with increases in torque. These were consistent with friction measurements which indicated losses primarily from Coulomb friction. The initial preload level setting was low so roller slip was encountered at higher torques during testing.

Anderson, William J.↗
DOE OSTI2020

Room Temperature Quasi-static Characterization and Constitutive Model Parametrization of Flexible Polyurethane Foams of Different Densities Loaded in Different Orientations

This report describes the efforts to characterize and model General Plastics TF6070 and EF4000 flexible polyurethane foams under room temperature, large deformation quasi-static cyclic mechanical loading conditions. Densities from three to fifteen pound per cubic foot (PCF) are examined, which correspond to relative densities of approximately 4 to 20%. These foams are open cell structured and flexible at room temperature with a glass transition transition less than -30°C, and they fully recover their original shape when unloaded (at room temperature). Uniaxial compression tests were conducted with accompanying lateral image series for Digital Image Correlation (DIC) analysis with the goal of extracting transverse strain responses. Due to difficulties with DIC analysis at large strains, lateral strains were instead extracted for each test via edge tracking. The experimental results exhibit a nonlinear elastic response and anisotropic material behavior (particularly for the lower densities). Some hysteresis is observed that is different between the first and subsequent cycles of deformation indicating both a small degree of permanent damage (reduced stiffness during reloading) and viscoelasticity. These inelastic mechanisms are not considered in the modeling and calibration in this report. This work considers only the rate independent, room temperature foam behavior. Individual foam densities were calibrated for loading in two directions, parallel and perpendicular to the foam bubble rise direction, since the mechanical behavior is different in these two directions. The Flex Foam constitutive model was used for all parameterizations despite the fact that the model is isotropic. A review of the constitutive model is given as well as necessary data reduction procedures to parameterize it for each foam density and orientation are discussed. Finally, two different parameterizations are developed that take the undeformed foam density as an input that span all densities considered. These two parameterized models represent foams loaded in the rise and transverse directions respectively. We summarize the assumptions and limitations of the parameterizations provided in this report to guide analysis choices with them. All parameterizations presented herein have the following traits, room temperature, rate independent, damage-free, and non-dissipative . Isotropy (even if they are representing anisotropic data). Supplied Sierra Solid Mechanics Flex Foam Model Inputs are in units: pounds, inches, Celsius, and seconds

36 MATERIALS SCIENCE↗
DOE OSTI2023

Open Water Blade Strain Measurements on a Vertical-Axis Tidal Turbine

Open-water testing of marine renewable energy devices represents a significant milestone and hurdle for research teams and companies that seek to reduce the levelized cost of energy to allow these devices to compete in the open electrical generation market. For open-water testing of tidal energy converters (TECs), accurate measurements of loading characteristics on the blades and other structural components correlated with power performance metrics can be invaluable to further refine design principles and models, allowing continued improvement and cost reductions of new turbine designs. This paper will describe the modifications and additions made to a TEC system to achieve time-correlated blade strain measurements during full turbine operation along with a discussion on the overall impacts the required modifications had on the unmodified turbine.

mechanical loads↗