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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 271 records · Page 15

Measurements in Flight of the Flying Qualities of a Chance Vought F4U-4 Airplane: TED No. NACA 2388

The results of flight tests to determine flying qualities of a Chance Vought F4U-4 airplane are presented and discussed herein. In addition to comprehensive measurements at low altitude (about 8000 ft), tests of limited scope were made at high altitude (about 25,000 ft). The more important characteristics, based on a comparison of the test results and opinions of the pilots with the Navy requirements, can be summarized as follows: 1. The short-period control-free oscillations of the elevator angle and the normal acceleration were satisfactorily damped. 2. The most rearward center-of-gravity locations for satisfactory static longitudinal stability with power on, as determined by the control-force variations, were approximately 30 and 27 percent M.A.C. with flaps and gear up and down, respectively. 3. In maneuvering flight the conditions for which control-force gradients of satisfactory magnitude were obtained were seriously limited by sizable changes in the gradient with center-of-gravity location, airspeed, altitude, acceleration factor, and direction of turn. 4. The elevator and rudder controls were satisfactory for landings and take-offs. 5. The trim tabs were sufficiently effective for all controls. 6. The directional and lateral dynamic stability was positive, but the rudder oscillation did not damp within one cycle. The airplane oscillation damped sufficiently at low altitude but not at high altitude. 7. Both rudder-fixed and rudder-free static directional stability were positive over a sideslip range of +/-15 deg. However, the rudder force tended to reverse at high angles of right sideslip with flaps and gear up, power on, at low speeds. 8. The stick-fixed static lateral stability (dihedral effect) was positive in all conditions, but the stick-free dihedral effect was neutral at low speeds with flap and gear down, power on. 9. The yaw due to abrupt full aileron deflection at low speed was mot excessive, and the rudder control was adequate to hold trim sideslip. 10. In abrupt rudder-fixed aileron rolls in the clean configuration the maximum pb/2V for full aileron deflection at low and normal speeds was only 0.064. 11. The stalling characteristics were considered unsatisfactory in all configurations in both straight and turning flight due to inadequate stall warning. The motions in the stalls were not unduly severe, and recovery could be effected promptly by normal use of the controls.

Liddell, Charles J., Jr.↗

Thermal Performance of a Conduction-Cooled CCT Dipole ReBCO Magnet: Several Cycles of Cool-Down and Thermal Gradient Measurements

Here, this paper presents experimental results from conduction-cooled thermal testing of a ReBCO canted cosine theta (CCT) magnet (C2), originally designed and fabricated at LBNL using CORC cables. While the performance of the coil under liquid helium and nitrogen environments has been previously established, this study explores its behavior under conduction cooling using a large test cryostat at The Ohio State University. The magnet, measuring 613 mm in length and weighing ∼75 kg, consists of four helical layers wound with ReBCO-based CORC wire and was thermally anchored to a copper cold ring supported by a G-10 strongback. Cooling was provided by two Sumitomo RDK-415D cryocoolers, offering a combined 3 W at 4.2 K and 150 W at 77 K. Multiple thermal cycles were performed, with cooldown durations of up to 45 hours. Final base temperatures of approximately 10.8 K (at the coil edge) and 12.0 K (at the coil center) were achieved, with an axial temperature difference of approximately 1.2 K. The warm-up period extended over approximately 24.6 hours. Voltage measurements from all four layers were recorded during cooldown and warmup. The system demonstrated stable cooldown performance, repeatable gradients, and good thermal anchoring. These results support the feasibility of conduction cooling in large-scale HTS magnets, aligning with broader goals for “green” cryogen-free accelerator technologies and paving the way for more sustainable, scalable, and energy-efficient high-field magnet systems in next-generation particle accelerators.

Canted cosine theta magnets↗

Extending SEER for Extreme Heterogeneity

Heterogeneous and multi-device nodes are increasingly common in high-performance computing and data centers, yet existing programming models often lack simple, transparent, and portable support for these diverse architectures. The main contribution of this work is the development of novel SEER capabilities to address this challenge by providing a descriptive programming model that allows applications to seamlessly leverage heterogeneous nodes across various device types. SEER uses efficient memory management and can select the proper device[s] depending on the computational cost of the applications. This is completely transparent to the programmer, thereby providing a highly productive programming environment. Integrating extreme heterogeneity into the SEER library as shown with the use of NVIDIA and AMD GPUs simultaneously allows it to expand and exploit the performance possibilities. Our analysis based on the well-known Conjugate Gradient algorithm reports accelerations above 1.5 × on computationally demanding steps of such an algorithm by using both architectures simultaneously.

Teranishi, Keita [ORNL] (ORCID:0000000166472690)↗

Megavolt bremsstrahlung measurements from linear induction accelerators demonstrate possible use as a FLASH radiotherapy source to reduce acute toxicity

Abstract Recent studies indicate better efficacy and healthy tissue sparing with high dose-rate FLASH radiotherapy (FLASH-RT) cancer treatment. This technique delivers a prompt high radiation dose rather than fractional doses over time. While some suggest thresholds of > 40 Gy s −1 with a maximal effect at > 100 Gy s −1 , accumulated evidence shows that instantaneous dose-rate and irradiation time are critical. Mechanisms are still debated, but toxicity is minimized while inducing apoptosis in malignant tissue. Delivery technologies to date show that a capability gap exists with clinic scale, broad area, deep penetrating, high dose rate systems. Based on these trends, if FLASH-RT is adopted, it may become a dominant approach except in the least technologically advanced countries. The linear induction accelerator (LIA) developed for high instantaneous and high average dose-rate, species independent charged particle acceleration, has yet to be considered for this application. We review the status of LIA technology, explore the physics of bremsstrahlung-converter-target interactions and our work on stabilizing the electron beam. While the gradient of the LIA is low, we present our preliminary work to improve the gradient by an order of magnitude, presenting a point design for a multibeam FLASH-RT system using a single accelerator for application to conformal FLASH-RT.

42 ENGINEERING↗

Solar flares, the lunar surface, and gas rich meteorites

Investigations on the Fe-group nuclei track density vs depth in lunar rocks and Surveyor 3 TV camera filter glass were critically examined considering more factors than previously. The analysis gives a firmer basis to the observation of the preferential leakage of low energy Fe nuclei from the accelerating region of the sun. The track density gradients in lunar rock 12022 and filter glass are used to determine the lunar erosion rate of 3 angstroms/yr. Track gradients are less steep than predicted from energy spectrum observed in the Surveyor glass, perhaps due to sputtering. High densities of etchable tracks were found at all depths down to 60 cm in fines from Apollo cores and also in thin sections of the Pesjanoe, Pantar, and Fayetteville gas-rich meteorites. It is felt unlikely that suprathermal heavy ions were responsible for the high track densities.

Barber, D. J.↗

Motion of the Heliospheric Termination Shock at High Heliographic Latitude

We expect the mean distance of the heliospheric termination shock to be greater (smaller) at polar latitudes than at equatorial latitudes, depending on whether the mean dynamic pressure of the solar wind is greater or smaller at high latitudes. The heliospheric termination shock is expected to move in response to variation in upstream solar wind conditions, so that at any particular instant the termination shock will resemble a distorted asymmetric balloon with some parts moving inward and others moving outward. If the shock is a gasdynamic or magnetohydrodynamic shock the results of the analysis depend only very weakly on the nature of the upstream disturbance; typical speeds of the disturbed shock are approximately 100 to 200 km/s. In the absence of a significant latitude gradient of the typical magnitude of solar wind disturbances typical motions of the disturbed shock at polar latitudes would be about twice as fast, due to the higher speed of the high-latitude wind. If the dynamics of the termination shock are dominated by acceleration of the anomalous component of the cosmic rays, the motion of the shock in response to a given disturbance is substantially slower than in the gasdynamic case. Conceivably, particle acceleration might be a less important effect at higher latitudes, and we envision the possibility of a termination shock that is dominated by particle acceleration at lower latitudes and is an MHD shock at high latitudes. In this event high latitude solar wind disturbances would produce substantially larger inward and outward motions of the shock in the polar regions.

Barnes, Aaron↗

Understanding particle size effect on fast-charging behavior of graphite anode using ultra-thin-layer electrodes

Extreme fast charging (≤ 15 min) of lithium-ion batteries is highly desirable to accelerate mass-market adoption of electric vehicles. However, significant capacity fading, as well as safety issues due to the lithium plating caused by the fast charging rate, limit its implementation. In this study, we investigated the fast-charging capability of graphite materials with various particle sizes. To eliminate the Li + ion concentration gradient effect across the thickness of the electrode, ultra-thin-layer graphite electrodes were developed to investigate the "real" fast-charging capability of graphite at the particle level. Electrochemical assessments as well as microscopic characterizations revealed that smaller particles exhibited superior fast-charging performance, featuring enhanced capacity reversibility, faster charging rate, and less lithium plating under the same fast-charging conditions. It is shown that small-particle graphite (mean radius of 3.3 μm) could withstand a 4C charge (to 80 % state-of-charge) without plating, with minimal plating occurring at 6C. Thicker particles exhibited plating at lower C-rates. Since the experimental data could not directly explain whether intra-particle diffusion limitations or interfacial reaction limitations dominated the plating mechanism, the pseudo-2-dimensional model was used to evaluate the most likely plating mechanism. The model suggested that particle-level diffusion is the dominant mechanism contributing to plating at high rates. Finally, this work provides comprehensive insights into the particle size effects on fast-charging capability, offering a better understanding of fast-charging behavior and valuable guidance for designing optimal electrode architecture for high-rate lithium-ion batteries.

25 ENERGY STORAGE↗

High-throughput predictions of metal–organic framework electronic properties: theoretical challenges, graph neural networks, and data exploration

Abstract With the goal of accelerating the design and discovery of metal–organic frameworks (MOFs) for electronic, optoelectronic, and energy storage applications, we present a dataset of predicted electronic structure properties for thousands of MOFs carried out using multiple density functional approximations. Compared to more accurate hybrid functionals, we find that the widely used PBE generalized gradient approximation (GGA) functional severely underpredicts MOF band gaps in a largely systematic manner for semi-conductors and insulators without magnetic character. However, an even larger and less predictable disparity in the band gap prediction is present for MOFs with open-shell 3 d transition metal cations. With regards to partial atomic charges, we find that different density functional approximations predict similar charges overall, although hybrid functionals tend to shift electron density away from the metal centers and onto the ligand environments compared to the GGA point of reference. Much more significant differences in partial atomic charges are observed when comparing different charge partitioning schemes. We conclude by using the dataset of computed MOF properties to train machine-learning models that can rapidly predict MOF band gaps for all four density functional approximations considered in this work, paving the way for future high-throughput screening studies. To encourage exploration and reuse of the theoretical calculations presented in this work, the curated data is made publicly available via an interactive and user-friendly web application on the Materials Project.

36 MATERIALS SCIENCE↗

Surface Cracking and Interface Reaction Associated Delamination Failure of Thermal and Environmental Barrier

In this paper, surface cracking and interface reactions of a ZrO2-8wt%Y2O3 and mullite/BSAS/Si thermal and environmental barrier coating system on SiC/SiC ceramic matrix composites were characterized after long-term combined laser thermal gradient and furnace cyclic tests in a water vapor containing environment. The surface cracking was analyzed based on the coating thermal gradient sintering behavior and thermal expansion mismatch stress characteristics under the thermal cyclic conditions. The interface reactions that were largely enhanced by the coating surface cracking in the water vapor environment were investigated in detail, and the reaction phases were identified for the coating system after the long-term exposure. The accelerated coating delamination failure was attributed to the increased delamination driving force under the thermal gradient cyclic loading and the reduced interface adhesion due to the detrimental interface reactions. The coating design issues will also be discussed based on the observed failure mechanisms under the high-heat-flux test conditions.

Zhu, Dongming↗

Conventional and Bimodal Nuclear Thermal Rocket (NTR) Artificial Gravity Mars Transfer Vehicle Concepts

A variety of countermeasures have been developed to address the debilitating physiological effects of zero-gravity (0-g) experienced by cosmonauts and astronauts during their approximately 0.5 to 1.2 year long stays in low Earth orbit (LEO). Longer interplanetary flights, combined with possible prolonged stays in Mars orbit, could subject crewmembers to up to approximately 2.5 years of weightlessness. In view of known and recently diagnosed problems associated with 0-g, an artificial gravity (AG) spacecraft offers many advantages and may indeed be an enabling technology for human flights to Mars. A number of important human factors must be taken into account in selecting the rotation radius, rotation rate, and orientation of the habitation module or modules. These factors include the gravity gradient effect, radial and tangential Coriolis forces, along with cross-coupled acceleration effects. Artificial gravity Mars transfer vehicle (MTV) concepts are presented that utilize both conventional NTR, as well as, enhanced bimodal nuclear thermal rocket (BNTR) propulsion. The NTR is a proven technology that generates high thrust and has a specific impulse (Isp) capability of approximately 900 s-twice that of today's best chemical rockets. The AG/MTV concepts using conventional Nuclear Thermal Propulsion (NTP) carry twin cylindrical International Space Station (ISS)- type habitation modules with their long axes oriented either perpendicular or parallel to the longitudinal spin axis of the MTV and utilize photovoltaic arrays (PVAs) for spacecraft power. The twin habitat modules are connected to a central operations hub located at the front of the MTV via two pressurized tunnels that provide the rotation radius for the habitat modules. For the BNTR AG/MTV option, each engine has its own closed secondary helium(He)-xenon (Xe) gas loop and Brayton Rotating Unit (BRU) that can generate 10s of kilowatts (kWe) of spacecraft electrical power during the mission coast phase eliminating the need for large PVAs. A single inflatable TransHab-type habitation module is also used with multiple vertical floors oriented radial to the MTV spin axis. The BNTR MTV's geometry-long and linear-is naturally compatible with AG operation. By rotating the vehicle about its center-of-mass (CM) and perpendicular to its flight vector at approximately 3.0 to 5.2 rpm, a centrifugal force and AG environment corresponding to approximately 0.38 to 1.0 g can be established to help maintain crew fitness out to Mars and back. Vehicles using NTP/ Bimodal Nuclear Thermal Propulsion (BNTP) can more readily accommodate the heavier payload mass and increased RCS propellant loading associated with AG operation, and can travel faster to and from Mars thereby reducing the crew's exposure to galactic cosmic radiation and solar flares. Mission scenario descriptions, key vehicle features and operational characteristics for each propulsion option are presented using the lift capability and payload volumes estimated for the Space Launch System (SLS)-1B and followon Heavy Lift Vehicle (HLV).

Nuclear Propulsion↗

Advancements in HF-free bipolar pulsed electropolishing for next-generation superconducting cavities

Hydrofluoric acid (HF)-free bipolar pulsed electropolishing (BPEP) offers an environmentally sustainable alternative to conventional Buffered Chemical Polishing (BCP) and Electropolishing (EP) techniques for superconducting radiofrequency (SRF) cavities. Recent studies at Jefferson Lab have demonstrated that a single-cell 1.3 GHz niobium cavity processed using HF-free BPEP achieved an accelerating gradient Eacc of 35 MV/m with a quality factor Q0 of 1E10 at 2 K, following extensive research and optimization. This talk will highlight the challenges encountered in developing this technique, key insights gained from experimental studies, and ongoing efforts to enhance its capabilities. In particular, we will explore its potential for refining Nb3Sn-coated niobium cavities via vapor diffusion techniques and for electroplating Nb3Sn films onto various cavity substrates, contributing to the advancement of high-performance SRF systems.

Tian, Hui [Thomas Jefferson National Accelerator F↗

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗

Field, frequency, and temperature dependencies of the surface resistance of nitrogen diffused niobium superconducting radio frequency cavities

We investigate the rf performance of several single-cell superconducting radio-frequency cavities subjected to low temperature heat treatment in nitrogen environment. The cavities were treated at temperature 120 – 165 ° C for an extended period of time (24–48 h) either in high vacuum or in a low partial pressure of ultrapure nitrogen. The improvement in Q 0 with a Q rise was observed when nitrogen gas was injected at ∼ 300 ° C during the cavity cooldown from 800 ° C and held at 165 ° C , without any degradation in accelerating gradient over the baseline performance. The treatment was applied to several elliptical cavities with frequency ranging from 0.75 to 3.0 GHz, showing an improved quality factor as a result of low temperature nitrogen treatments. The Q rise feature is similar to that achieved by nitrogen alloying Nb cavities at higher temperature, followed by material removal by electropolishing. The surface modification was confirmed by the change in electronic mean free path and tuned with the temperature and duration of heat treatment. The decrease of the temperature-dependent surface resistance with increasing rf field, resulting in a Q rise, becomes stronger with increasing frequency and decreasing temperature. The data suggest a crossover frequency of ∼ 0.95 GHz above that the Q rise phenomenon occurs at 2 K. Some of these results can be explained qualitatively with an existing model of intrinsic field-dependence of the surface resistance with both equilibrium and nonequilibrium quasiparticle distribution functions. The change in the Q slope below 0.95 GHz may result from masking contribution of trapped magnetic flux to the residual surface resistance. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Conventional and Bimodal Nuclear Thermal Rocket (NTR) Artificial Gravity Mars Transfer Vehicle Concepts

A variety of countermeasures have been developed to address the debilitating physiological effects of "zero-gravity" (0-g) experienced by cosmonauts and astronauts during their approximately 0.5-1.2 year long stays in LEO (Low Earth Orbit). Longer interplanetary flights, combined with possible prolonged stays in Mars orbit, could subject crewmembers to up to approximately 2.5 years of weightlessness. In view of known and recently diagnosed problems associated with 0-g, an artificial gravity spacecraft offers many advantages and may indeed be an enabling technology for human flights to Mars. A number of important human factors must be taken into account in selecting the rotation radius, rotation rate, and orientation of the habitation module or modules. These factors include the gravity gradient effect, radial and tangential Coriolis forces, along with cross-coupled acceleration effects. Artificial gravity (AG) Mars transfer vehicle (MTV) concepts are presented that utilize both conventional NTR, as well as, enhanced "bimodal" nuclear thermal rocket (BNTR) propulsion. The NTR is a proven technology that generates high thrust and has a specific impulse (I (sub sp)) capability of approximately 900 s - twice that of today's best chemical rockets. The AG/MTV concepts using conventional NTP carry twin cylindrical "ISS-type" habitation modules with their long axes oriented either perpendicular or parallel to the longitudinal spin axis of the MTV and utilize photovoltaic arrays (PVAs) for spacecraft power. The twin habitat modules are connected to a central operations hub located at the front of the MTV via two pressurized tunnels that provide the rotation radius for the habitat modules. For the BNTR AG/MTV option, each engine has its own "closed" secondary helium-xenon gas loop and Brayton rotating unit that can generate tens of kilowatts (kW (sub e)) of spacecraft electrical power during the mission coast phase eliminating the need for large PVAs. A single inflatable "TransHab-type" habitation module is also used with multiple vertical floors oriented radial to the MTV spin axis. The BNTR MTV's geometry - long and linear - is naturally compatible with AG operation. By rotating the vehicle about its center-of-mass and perpendicular to its flight vector at approximately 3.0 - 5.2 rpm, a centrifugal force and AG environment corresponding to approximately 0.38 - 1.0 g can be established to help maintain crew fitness out to Mars and back. Vehicles using NTP/BNTP can more readily accommodate the heavier payload mass and increased RCS propellant loading associated with AG operation, and can travel faster to and from Mars thereby reducing the crew's exposure to galactic cosmic radiation and solar flares. Mission scenario descriptions, key vehicle features and operational characteristics for each propulsion options are presented using the lift capability and payload volumes estimated for the SLS-1A and HLV.

Nuclear Propulsion↗

Shaped Beams from Diamond Field-Emitter Array Cathodes

Diamond field-emitter arrays (DFEAs) are arrays of diamond pyramids with exquisitely sharp tips and micrometer-scale bases that produce high current densities. These arrays can be fabricated in arbitrary shapes, ranging from single tips to many millions of tips, so that they produce an inherently shaped electron beam. Each tip emits a modest current, but the large dense array can produce many Amps. We are investigating these cathodes for use in dielectric wakefield accelerators; however, they may also be applicable to vacuum microwave tubes. Recently, shaped beam production and transport have been demonstrated in the 1.3-GHz RF gun at the Argonne Cathode Test Stand at the Argonne National Laboratory. The charge was measured on a Faraday cup and the beam imaged on a YAG screen with peak electric field gradients on the cathode ranging from 12 to 35 MV/m. Three cathode geometries were tested: one 1-mm equilateral triangle with 7-mu m base pyramids and 10-mu m pitch, one 1-mm equilateral triangle with 10-mu m base and 25-mu m pitch, and one sparse 5 x 5 square array with 20-mu m base and 400-mu m pitch. The two triangular arrays emitted 35 nC in an RF macropulse at 35 MV/m and 13-nC charge at 27 MV/m, respectively, while the sparse array emitted 0.060-nC charge at 15 MV/m. This article presents the results of the triangular array experiments, including damage due to breakdown in the RF gun and initial models of tip-to-tip shielding.

Cathodes↗

Collisionless relativistic magnetic reconnection driven by electron vortices in laser-plasma interaction

Magnetic reconnection (MR) is a fundamental process in space and laboratory plasmas. The appearance of high power lasers opens a new way to investigate MR under the relativistic condition. In this paper, relativistic collisionless MR driven by two ultra-intense lasers and a pair of asymmetric targets is studied numerically via the kinetic simulations. The static magnetic fields produced by the electron vortex structures with opposite magnetic polarities approach each other driven by the magnetic pressure and the density gradient. The antiparallel magnetic fields annihilate accompanied with the topological variation and the corresponding magnetic field energy is being dissipated to the kinetic energy of the nonthermal charged particles. Besides the outflows along the current sheet, a fast particle bunch is accelerated perpendicularly contributed by the displacement current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reducing field emission in superconducting cavities with ozone

Contaminations on the active surface of high-power microwave resonators, such as radio-frequency accelerator cavities, can greatly enlarge electron field emission and reduce their performance. In this work, we demonstrate the use of ozone to clean the surface of niobium superconducting radio-frequency cavities resulting in reduced field emission and enhanced accelerating gradient before onset of field emission. We report results from processing four cavities.

43 PARTICLE ACCELERATORS↗

STS-40 orbital acceleration research experiment flight results during a typical sleep period

The Orbital Acceleration Research Experiment (OARE), an electrostatic accelerometer package with complete on-orbit calibration capabilities, was flown for the first time aboard the Space Shuttle on STS-40. This is also the first time an accelerometer package with nano-g sensitivity and a calibration facility has flown aboard the Space Shuttle. The instrument is designed to measure and record the Space Shuttle aerodynamic acceleration environment from the free molecule flow regime through the rarified flow transition into the hypersonic continuum regime. Because of its sensitivity, the OARE instrument defects aerodynamic behavior of the Space Shuttle while in low-earth orbit. A 2-hour orbital time period on day seven of the mission, when the crew was asleep and other spacecraft activities were at a minimum, was examined. During the flight, a 'trimmed-mean' filter was used to produce high quality, low frequency data which was successfully stored aboard the Space Shuttle in the OARE data storage system. Initial review of the data indicated that, although the expected precision was achieved, some equipment problems occurred resulting in uncertain accuracy. An acceleration model which includes aerodynamic, gravity-gradient, and rotational effects was constructed and compared with flight data. Examination of the model with the flight data shows the instrument to be sensitive to all major expected low frequency acceleration phenomena; however, some erratic instrument bias behavior persists in two axes. In these axes, the OARE data can be made to match a comprehensive atmospheric-aerodynamic model by making bias adjustments and slight linear corrections for drift. The other axis does not exhibit these difficulties and gives good agreement with the acceleration model.

Blanchard, R. C.↗