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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A high resolution electro-optical displacement measurement system

An improved electrooptical system has been developed to sense wind tunnel model position. The original system using 25.6 mm, 1024-element linear photodiode arrays (PDAs) is being successfully used at a NASA wind tunnel but has a limited range. A new two-channel system using 61.44 mm, 4096-element PDAs has been developed to double the range of vertical and pitch measurement and increase the resolution by 60 percent. The PDAs are illuminated by expanding the beam of a single low power helium neon laser into a collimated sheet of light. An object placed in front of the two parallel PDAs produces a shadow on the array apertures which determines the object's position or size. The system has an overall precision of 12.7 microns and + or - 0.015 degrees in linear and angular measurements.

Schott, Timothy D.↗
DOE OSTI2024

Low-cost sensor-based damage localization for large-area monitoring of FRP composites

Abstract In recent years, there has been growing interest in self-sensing structural materials across research and industry sectors. Detecting and locating structural damage typically requires numerous sensors wired to a data acquisition (DAQ) circuit, rendering implementation impractical in real structures. This paper proposes an innovative, cost-effective sensor network for damage detection and localization in fiber-reinforced polymer composites. The innovation encompasses three key elements: (1) utilizing carbon fiber tows within the composite as piezoresistive sensors, eliminating the need for additional foreign sensor devices; (2) introducing a novel sensor layout wherein sensor tow branches with varied resistance values are connected in parallel, reducing the number of connections to the DAQ circuit and cutting manufacturing costs significantly; (3) developing a practical sensor terminal fabrication technique to minimize manufacturing expenses. The proposed design methodology for the branch resistance values is first validated using a demonstration panel. Subsequently, the overall strategy is assessed by conducting impact tests on carbon and glass fiber-reinforced composite specimens. Results validate the sensor’s ability to accurately detect and locate structural damage.

Demo, Luke B. (ORCID:0000000208806522)↗
NASA NTRS2023

Radiative interaction of atmosphere and surface: write up with elements of code

In passive satellite remote sensing of the Earth, separation of the path radiance (atmosphere-only contribution) from the surface reflection remains a “significant challenge”. Recent literature names it among the gaps in radiative transfer (RT) topics that “require continued research in the near future”. The challenge comes from multiple reflections (bouncing) between the atmosphere and surface – radiative interaction. In this paper we use a known RT technique, the matrix-operator method (MOM), and a new modification of the monochromatic vector RT (vRT) code IPOL (Intensity and POLarization) to simulate the interaction of a plane-parallel atmosphere and a few widely used surface reflection models. Following the idea of the Green’s function method, IPOL no longer takes the surface model parameters on input. Instead, it provides the path radiance, and the atmospheric reflection and transmission matrices as output. Despite many RT codes use the MOM formalism, this output does not seem common. The surface reflection matrix is computed externally. Therefore, this paper extends the Green’s function atmospheric correction technique to the case of polarized light. Aiming clarity rather than performance, we explain in Python the structure of the surface matrices for the isotropic (Lambertian), directional unpolarized, and polarized ocean reflection models. We then combine these surface matrices and the precomputed IPOL output to get numerically accurate signal at the top of atmosphere (TOA) and test it vs. published benchmarks. Then, for each benchmark scenario we show how to get the surface from the TOA signal, i.e. perform the RT-based atmospheric correction.

radiative transfer↗
NASA NTRS1998

High Performance Database Management for Earth Sciences

The High Performance Database Research Center at Florida International University is completing the development of a highly parallel database system based on the semantic/object-oriented approach. This system provides exceptional usability and flexibility. It allows shorter application design and programming cycles and gives the user control via an intuitive information structure. It empowers the end-user to pose complex ad hoc decision support queries. Superior efficiency is provided through a high level of optimization, which is transparent to the user. Manifold reduction in storage size is allowed for many applications. This system allows for operability via internet browsers. The system will be used for the NASA Applications Center program to store remote sensing data, as well as for Earth Science applications.

Rishe, Naphtali↗
NASA NTRS2012

Development of Field Excavator with Embedded Force Measurement

A semi-intelligent excavation mechanism was developed for use with the NASA-built Centaur 2 rover prototype. The excavator features a continuously rotatable large bucket supported between two parallel arms, both of which share a single pivot axis near the excavator base attached to the rover. The excavator is designed to simulate the collection of regolith, such as on the Moon, and to dump the collected soil into a hopper up to one meter tall for processing to extract oxygen. Because the vehicle can be autonomous and the terrain is generally unknown, there is risk of damaging equipment or using excessive power when attempting to extract soil from dense or rocky terrain. To minimize these risks, it is critical for the rover to sense the digging forces and adjust accordingly. It is also important to understand the digging capabilities and limitations of the excavator. This paper discusses the implementation of multiple strain gages as an embedded force measurement system in the excavator's arms. These strain gages can accurately measure and resolve multi-axial forces on the excavator. In order to validate these sensors and characterize the load capabilities, a series of controlled excavation tests were performed at Glenn Research Center with the excavator at various depths and cut angles while supported by a six axis load cell. The results of these tests are both compared to a force estimation model and used for calibration of the embedded strain gages. In addition, excavation forces generated using two different types of bucket edge (straight vs. with teeth) were compared.

Soils↗
NASA NTRS1991

Lunar rovers and local positioning system

Telerobotic rovers equipped with adequate actuators and sensors are clearly necessary for extraterrestrial construction. They will be employed as substitutes for humans, to perform jobs like surveying, sensing, signaling, manipulating, and the handling of small materials. Important design criteria for these rovers include versatility and robustness. They must be easily programmed and reprogrammed to perform a wide variety of different functions, and they must be robust so that construction work will not be jeopardized by parts failures. The key qualities and functions necessary for these rovers to achieve the required versatility and robustness are modularity, redundancy, and coordination. Three robotic rovers are being built by CSC as a test bed to implement the concepts of modularity and coordination. The specific goal of the design and construction of these robots is to demonstrate the software modularity and multirobot control algorithms required for the physical manipulation of constructible elements. Each rover consists of a transporter platform, bus manager, simple manipulator, and positioning receivers. These robots will be controlled from a central control console via a radio-frequency local area network (LAN). To date, one prototype transporter platform frame was built with batteries, motors, a prototype single-motor controller, and two prototype internal LAN boards. Software modules were developed in C language for monitor functions, i/o, and parallel port usage in each computer board. Also completed are the fabrication of half of the required number of computer boards, the procurement of 19.2 Kbaud RF modems for inter-robot communications, and the simulation of processing requirements for positioning receivers. In addition to the robotic platform, the fabrication of a local positioning system based on infrared signals is nearly completed. This positioning system will make the rovers into a moving reference system capable of performing site surveys. In addition, a four degree mechanical manipulator especially suited for coordinated teleoperation was conceptually designed and is currently being analyzed. This manipulator will be integrated into the rovers as their end effector. Twenty internal LAN cards fabricated by a commercial firm are being used, a prototype manipulator and a range finder for a positioning system were built, a prototype two-motor controller was designed, and one of the robots is performing its first telerobotic motion. In addition, the robots' internal LAN's were coordinated and tested, hardware design upgrades based on fabrication and fit experience were completed, and the positioning system is running. The rover system is able to perform simple tasks such as sensing and signaling; coordination systems which allow construction tasks to begin were established, and soon coordinated teams of robots in the laboratory will be able to manipulate common objects.

Avery, James↗
DOE OSTI2025

Wellbore Fracture Imaging Using Inflow Detection Measurements

One of the most striking measurements taken during DOE’s EGS Collab project at the 4850-foot depth location was the so-called ‘sewer cam’, which enabled direct visualization of the flow of water into the production well through fractures during the stimulation. The ability to see directly which fractures were flowing and (roughly) how much was a breakthrough in understanding the topology of the created fracture network. Achieving this kind of fracture flow imaging at FORGE would be more challenging because of the 225°C temperature, but equally or even more valuable if it could be achieved. In 2017, a joint project between Sandia and Stanford developed a downhole tool concept to measure the enthalpy of multiphase fluid entering a geothermal well from individual fractures (Gao et al., 2017). For the FORGE project, measuring enthalpy is of less interest because the fluid is expected to be single-phase liquid water. However, the foundation of the device was the measurement of chloride ion concentration, which could form the basis for a direct measurement of inflow from fractures. During the 2017 project, this novel chloride sensing system was implemented into a laboratory test instrument, and we confirmed the capability of the system to measure the ion concentration of fluid entering a model wellbore through a small entry port. The wellbore was a 6-inch diameter model well, and the port was approximately 0.08 inch (2mm) in diameter. The device could measure the chloride concentration accurately even when the well was flowing in a bubbly flow. Given its accuracy, the tool should be able to identify locations of water entering the wellbore even if the ion concentration differs only slightly from that of the water in the well. It is likely that different fractures may flow slightly different chloride concentrations, which would make it feasible to detect individual fractures as well as to estimate the volume of their flow. Ultimately, we could also recognize different fractures flowing back significantly different ion concentrations after fracturing in the FORGE wells. This could be realized by adding different ions in the fracturing fluids in different fractures created at different stages of stimulation (and modifying the tool to include different ion specificity). Sandia’s tool was shown during the study to have the capability to withstand the 225°C temperature, and the electrochemical sensing elements were tested in the laboratory to 225°C at 1500 psia for 24 hours. An early implementation of the fully integrated downhole electrochemical tool, including high-temperature electronics, robust housing, and wireline truck interface, had previously been constructed and tested successfully at Sandia; thus, hardware development tasks focused on advancing the technology readiness level (TRL) of this promising technology for FORGE deployment, rather than on developing a new scientific basis for its operation. The data collection electronics in this tool allowed for several other sensors (pressure, temperature, flow spinner) to be implemented in parallel as well. The research was a new collaboration between Stanford and Sandia to modify and refine the tool for FORGE deployment, to make the downhole measurements, and to characterize the evolving fractures.

15 GEOTHERMAL ENERGY↗
NASA NTRS1988

Single-Mode Projection Filters for Modal Parameter Identification for Flexible Structures

Single-mode projection filters are developed for eigensystem parameter identification from both analytical results and test data. Explicit formulations of these projection filters are derived using the orthogonal matrices of the controllability and observability matrices in the general sense. A global minimum optimization algorithm is applied to update the filter parameters by using the interval analysis method. The updated modal parameters represent the characteristics of the test data. For illustration of this new approach, a numerical simulation for the MAST beam structure is shown by using a one-dimensional global optimization algorithm to identify modal frequencies and damping. Another numerical simulation of a ten-mode structure is also presented by using a two-dimensional global optimization algorithm to illustrate the feasibility of the new method. The projection filters are practical for parallel processing implementation.

Huang, Jen-Kuang↗
NASA NTRS1990

Design of optimal correlation filters for hybrid vision systems

Research is underway at the NASA Johnson Space Center on the development of vision systems that recognize objects and estimate their position by processing their images. This is a crucial task in many space applications such as autonomous landing on Mars sites, satellite inspection and repair, and docking of space shuttle and space station. Currently available algorithms and hardware are too slow to be suitable for these tasks. Electronic digital hardware exhibits superior performance in computing and control; however, they take too much time to carry out important signal processing operations such as Fourier transformation of image data and calculation of correlation between two images. Fortunately, because of the inherent parallelism, optical devices can carry out these operations very fast, although they are not quite suitable for computation and control type operations. Hence, investigations are currently being conducted on the development of hybrid vision systems that utilize both optical techniques and digital processing jointly to carry out the object recognition tasks in real time. Algorithms for the design of optimal filters for use in hybrid vision systems were developed. Specifically, an algorithm was developed for the design of real-valued frequency plane correlation filters. Furthermore, research was also conducted on designing correlation filters optimal in the sense of providing maximum signal-to-nose ratio when noise is present in the detectors in the correlation plane. Algorithms were developed for the design of different types of optimal filters: complex filters, real-value filters, phase-only filters, ternary-valued filters, coupled filters. This report presents some of these algorithms in detail along with their derivations.

Rajan, Periasamy K.↗
NASA NTRS2009

NASA Tech Briefs, April 2009

Topics covered include: Direct-Solve Image-Based Wavefront Sensing; Use of UV Sources for Detection and Identification of Explosives; Using Fluorescent Viruses for Detecting Bacteria in Water; Gradiometer Using Middle Loops as Sensing Elements in a Low-Field SQUID MRI System; Volcano Monitor: Autonomous Triggering of In-Situ Sensors; Wireless Fluid-Level Sensors for Harsh Environments; Interference-Detection Module in a Digital Radar Receiver; Modal Vibration Analysis of Large Castings; Structural/Radiation-Shielding Epoxies; Integrated Multilayer Insulation; Apparatus for Screening Multiple Oxygen-Reduction Catalysts; Determining Aliasing in Isolated Signal Conditioning Modules; Composite Bipolar Plate for Unitized Fuel Cell/Electrolyzer Systems; Spectrum Analyzers Incorporating Tunable WGM Resonators; Quantum-Well Thermophotovoltaic Cells; Bounded-Angle Iterative Decoding of LDPC Codes; Conversion from Tree to Graph Representation of Requirements; Parallel Hybrid Vehicle Optimal Storage System; and Anaerobic Digestion in a Flooded Densified Leachbed.

Source record↗
NASA NTRS1978

Radiative transfer in spherical shell atmospheres. I - Rayleigh scattering

The plane-parallel approximation and the more realistic spherical shell approximation for the radiance reflected from a planetary atmosphere are compared and are applied to the study of a planet the size of the earth with a homogeneous conservative Rayleigh scattering atmosphere extending to a height of 100 km. Inadequacies of the approximations are considered. Radiance versus height distributions for both single and multiple scattering are presented, as are results for the fractional radiance from altitudes in the atmosphere which contribute to the total unidirectional reflected radiance at the top of the atmosphere. The data can be used for remote sensing applications and planetary spectroscopy.

Adams, C. N.↗
NASA NTRS1992

Efficiencies of Rotational Raman, and Rayleigh Techniques for Laser Remote Sensing of the Atmospheric Temperature

Various lidar methods have been developed for measuring the atmospheric temperature, making use of the temperature dependant characteristics of rotational Raman scattering (RRS) from nitrogen and oxygen, and Rayleigh or Rayleigh-Brillowin scattering (RS or RBS). These methods have various advantages and disadvantages as compared to each other but their potential accuracies are principal characteristics of their efficiency. No systematic attempt has been undertaken so far to compare the efficiences, in the above meaning, of different temperature lidar methods. Two RRS techniques have been compared. Here, we do such a comparison using two methods based on the detection and analysis of RS (RBS) spectra. Four methods are considered here for measuring the atmospheric temperature. One of them (Schwiesow and Lading, 1981) is based on an analysis of the RS linewidth with two Michelson interferometers (MI) in parallel. The second method (Shimisu et al., 1986) employs a high-resolution analysis of the RBS line shape. The third method (Cooney, 1972) employs the temperature dependance of the RRS spectrum envelope. The fourth method (Armstrong, 1974) makes use of a scanning Fabry-Perot interferometer (FPI) as a comb filter for processing the periodic RRS spectrum of the nitrogen. Let us denote the corresponding errors in measuring the temperature by sigma(sub MI), sigma(sub HR), sigma(sub ENV), and sigma(sub FPI). Let us also define the ratios chi(sub 1) = sigma(sub MI)/sigma(sub ENV), chi(sub 2) = sigma(sub HR)/sigma(sub ENV), and chi(sub 3) = sigma(sub FPI)/sigma(sub ENV) interpreted as relative errors with respect to sigma(sub ENV).

Ivanova, I. D.↗
NASA NTRS2006

Electro-Active Transducer Using Radial Electric Field To Produce/Motion Sense Out-Of-Plane Transducer

An electro-active transducer includes a ferroelectric material sandwiched by first and second electrode patterns. When the device is used as an actuator, the first and second electrode patterns are configured to introduce an electric field into the ferroelectric material when voltage is applied to the electrode patterns. When the device is used as a sensor. the first and second electrode patterns are configured to introduce an electric field into the ferroelectric material when the ferroelectric material experiences deflection in a direction substantially perpendicular thereto. In each case, the electrode patterns are designed to cause the electric field to: i) originate at a region of the ferroelectric material between the first and second electrode patterns. and ii) extend radially outward from the region of the ferroelectric material (at which the electric field originates) and substantially parallel to the ferroelectric material s plane.

Bryant, Robert G.↗
NASA NTRS1998

Incompressible Turbulent Wing-Body Junction Flow

The overall objective of this study is to contribute to the optimized design of fan bypass systems in advanced turbofan engines. Increasing the engine bypass ratios have provided a major boost in engine performance improvement over the last fifty years. An engine with high bypass ratio (11-16:1) such as the Advanced Ducted Propulsion (ADP) is being developed and is expected to provide an additional 25% improvement in overall efficiency over the early turbofans. Such significant improvements in overall efficiency would reduce the cost per seat mile, which is a major government and Industry challenge for the 21th century. The research is part of the Advanced Subsonic Technology (AST) program that involves a NASA, U.S. Industry and FAA partnership with the goal of a safe and highly productive global air transportation system. The immediate objective of the study is to perform numerical simulation of duct-strut interactions to elucidate the loss mechanisms associated with this configuration that is typical of advanced turbofan engines such as ADP. However, at present experimental data for a duct-strut configuration are not available. Thus, as a first step a wing-body junction flow would be studied and is the specific objective of the present study. At the outset it is to be recognized that while duct-strut interaction flow is similar to that of wing-body junction flows, there are some differences owing to the presence of a wall at both ends of the strut. Likewise, some differences are due to the sheared inflow (as opposed to a uniform inflow) velocity profile. It is however expected that some features of a wing-body junction flow would persist. Next, some of the salient aspects of the complex flow near a wing-body junction, as revealed by various studies reported in the literature will be reviewed. One of the principle characteristics of the juncture flow, is the presence of the mean flow components in a plane perpendicular to the direction of the oncoming free-stream flow. The lateral curvature of the wing/strat causes the oncoming turbulent layer to skew about am axis (x-axis) parallel to the plane (xz-plane) of the mean shear. This is the principle mechanism for the generation of secondary flow. Such skew-induced secondary flows are slow to be attenuated by Reynolds stresses. Additional contribution to the generation of secondary flow comes from anisotropies in Reynolds stresses. Upstream of the strut, the mean-vorticity is directed span wise (along the y-direction). The presence of secondary flow in the vicinity of the strut causes the vorticity to stretch around the obstacle in a horse-shoe shape, with each leg having a vorticity of the opposite sense. The blockage effect of the strut imposes a severe adverse pressure gradient on the oncoming turbulent shear layer, causing boundary layer separation ahead of the leading edge, resulting in a vortex that rolls up and flows downstream into the juncture region. The separation vortices trailing in the wake of the wing can alter the lift or drag characteristics of the surfaces downstream of the wing-body juncture. Likewise, on submarines, the wake flow behind the appendage can degrade the performance of the propeller located downstream. The complex nature of this flow is caused by the presence of all six components of Reynolds stresses. Devenport and Simpson report that in the vicinity of the horse-shoe vortex there is intense recirculation with turbulent stresses being much larger than those normally observed in turbulent flows. These features contribute to making this flow a challenge to predict numerically. Some of the past studies provide useful insights into this flow that would guide our numerical efforts. In measurements reported by Shabaka and Bradshaw, the eddy viscosity tensor is seen to be non-isotropic and has negative components in certain regions. In an effort to evaluate the closure assumptions of various turbulence models, Devenport and Simpson used their own extensive measurements in juncture flows around the nose of a wing-body junction. Measured values of mean-velocity and/or turbulence kinetic energy was used to predict the magnitude of the shear stress vector. Algebraic stress models performed the best followed by Cebeci-Smith eddy viscosity model. The flow is reported to be dominated by a pressure field produced by the wing and the velocity field generated by the horseshoe vortex that is wrapped around the junction between the wing and wall. Kubendran et al. conclude from an experimental study that the shape of leading edge of the wing as characterized by its slenderness ratio is a major factor in determining the flow fields in the juncture region. The more thinner the leading edge of the juncture, the weaker the horseshoe vortex is. Also, with a slender leading edge, the secondary flow in the juncture would be due mainly to the cross-stream gradients of Reynolds stresses rather than due to a lateral skewing of the shear layer.

Krishnamurthy, R.↗
NASA NTRS1999

Hyperspectral Thermal Fabry-Perot Modeling

Fabry-Perot interferometer are simple elegant, tunable filters that can be used to make compact hyperspectral thermal imaging system. To foster the development of these sensors, software tools for the design and simulation of tunable Fabry-Perot infrared imagers have been developed. The tools are provided at three levels: basic, design, and system. Basic tools describe a nearly ideal Fabry-Perot filter with perfectly flat and parallel mirrors in collimated space. Design tools that take into account non-ideal behavior such as mirror and collimation defects calculate free spectral range, finesse, and spectral width of the interferometer. System tools help analyze an integration of the Fabry-Perot filter into a camera system. They include spectral convolution, first-order optical layout, and an estimation of signal-to-noise ratio. The complete set of tools allows for simulations of system operation and performance with various illumination sources. Spectral images generated in such simulations were used to examine applicability of Fabry-Perot system in remote sensing of atmospheric gases including detection of environmental pollutants and hazardous gases. Different operating conditions and system configurations are presented.

Ryan, Robert↗
NASA NTRS2012

Ultra-Compact Motor Controller

This invention is an electronically commutated brushless motor controller that incorporates Hall-array sensing in a small, 42-gram package that provides 4096 absolute counts per motor revolution position sensing. The unit is the size of a miniature hockey puck, and is a 44-pin male connector that provides many I/O channels, including CANbus, RS-232 communications, general-purpose analog and digital I/O (GPIO), analog and digital Hall inputs, DC power input (18-90 VDC, 0-l0 A), three-phase motor outputs, and a strain gauge amplifier. This controller replaces air cooling with conduction cooling via a high-thermal-conductivity epoxy casting. A secondary advantage of the relatively good heat conductivity that comes with ultra-small size is that temperature differences within the controller become smaller, so that it is easier to measure the hottest temperature in the controller with fewer temperature sensors, or even one temperature sensor. Another size-sensitive design feature is in the approach to electrical noise immunity. At a very small size, where conduction paths are much shorter than in conventional designs, the ground becomes essentially isopotential, and so certain (space-consuming) electrical noise control components become unnecessary, which helps make small size possible. One winding-current sensor, applied to all of the windings in fast sequence, is smaller and wastes less power than the two or more sensors conventionally used to sense and control winding currents. An unexpected benefit of using only one current sensor is that it actually improves the precision of current control by using the "same" sensors to read each of the three phases. Folding the encoder directly into the controller electronics eliminates a great deal of redundant electronics, packaging, connectors, and hook-up wiring. The reduction of wires and connectors subtracts substantial bulk and eliminates their role in behaving as EMI (electro-magnetic interference) antennas. A shared knowledge by each motor controller of the state of all the motors in the system at 500 Hz also allows parallel processing of higher-level kinematic matrix calculations.

Townsend, William T.↗
NASA NTRS1973

The remote sensing of Saturn's rings. 1: The magnetic alinement of the ring particles

Because of the potential implications for the optical properties of Saturn's rings, the orientation of nonspherical ring particles at equilibrium is investigated with respect to four stochastic influences: interactions with the interplanetary medium, interactions with the expected magnetic field of Saturn, thermal fluctuations due to the internal temperature of the ring particles; collisions between ring particles. The solution of the homogeneous Fokker-Planck equation for nearly spherical spheroids is presented and investigated in general. Values of the pertinent physical parameters in the vicinity of Saturn are estimated, and the implications for the alignment of the ring particles are investigated. It is concluded that for some alignment mechanisms, small ring particles can be expected to be almost completely aligned. This alignment results in each particle spinning around its shortest body axis with this axis parallel to the magnetic field direction (perpendicular to the ring plane).

Evans, L. C.↗
NASA NTRS1999

On the Fast Evaluation Method of Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Planetary Atmospheres in Thermal IR and Microwave

Evaluation of weighting functions in the atmospheric remote sensing is usually the most computer-intensive part of the inversion algorithms. We present an analytic approach to computations of temperature and mixing ratio weighting functions that is based on our previous results but the resulting expressions use the intermediate variables that are generated in computations of observable radiances themselves. Upwelling radiances at the given level in the atmosphere and atmospheric transmittances from space to the given level are combined with local values of the total absorption coefficient and its components due to absorption of atmospheric constituents under study. This makes it possible to evaluate the temperature and mixing ratio weighting functions in parallel with evaluation of radiances. This substantially decreases the computer time required for evaluation of weighting functions. Implications for the nadir and limb viewing geometries are discussed.

Ustinov, E. A.↗