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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mechanical Toughening of Two-Dimensional Covalent Organic Frameworks Enabled by Graphene-Based Sandwich-Structured Nanocomposites

Low resistance to fracture in two-dimensional covalent organic frameworks (2D COFs) limits their practical applications, especially in mechanically demanding fields, such as flexible electronics and sensing devices. We address this critical limitation by fabricating a sandwich-structured nanocomposite consisting of graphene layers sandwiched between 2D COF layers (2D COFs/graphene/2D COFs) via chemical vapor deposition. Here, our sandwich-structured nanocomposites exhibit a remarkable improvement in modulus E, fracture toughness K IC , and critical energy release rate G C compared to pure 2D COFs. This enhancement is likely due to the graphene layers as the backbone of the sandwich structure effectively carrying and redistributing mechanical stress within the nanocomposite. Our findings demonstrate that a sandwich structure can improve the mechanical robustness of a 2D COF so that it can preserve the functionality and mechanical integrity for applications in stretchable electronics.

36 MATERIALS SCIENCE↗
NASA NTRS2013

Robotic Ankle for Omnidirectional Rock Anchors

Future robotic exploration of near-Earth asteroids and the vertical and inverted rock walls of lava caves and cliff faces on Mars and other planetary bodies would require a method of gripping their rocky surfaces to allow mobility without gravitational assistance. In order to successfully navigate this terrain and drill for samples, the grippers must be able to produce anchoring forces in excess of 100 N. Additionally, the grippers must be able to support the inertial forces of a moving robot, as well gravitational forces for demonstrations on Earth. One possible solution would be to use microspine arrays to anchor to rock surfaces and provide the necessary load-bearing abilities for robotic exploration of asteroids. Microspine arrays comprise dozens of small steel hooks supported on individual suspensions. When these arrays are dragged along a rock surface, the steel hooks engage with asperities and holes on the surface. The suspensions allow for individual hooks to engage with asperities while the remaining hooks continue to drag along the surface. This ensures that the maximum possible number of hooks engage with the surface, thereby increasing the load-bearing abilities of the gripper. Using the microspine array grippers described above as the end-effectors of a robot would allow it to traverse terrain previously unreachable by traditional wheeled robots. Furthermore, microspine-gripping robots that can perch on cliffs or rocky walls could enable a new class of persistent surveillance devices for military applications. In order to interface these microspine grippers with a legged robot, an ankle is needed that can robotically actuate the gripper, as well as allow it to conform to the large-scale irregularities in the rock. The anchor serves three main purposes: deploy and release the anchor, conform to roughness or misalignment with the surface, and cancel out any moments about the anchor that could cause unintentional detachment. The ankle design contains a rotary DC motor that can drag the microspine arrays across the surface to engage them with asperities, as well as a linear actuator to disengage the hooks from the surface. Additionally, the ankle allows the gripper to rotate freely about all three axes so that when the robot takes a step, the gripper may optimally orient itself with respect to the wall or ground. Finally, the ankle contains some minimal elasticity, so that between steps, the gripper returns to a default position that is roughly parallel to the wall.

Parness, Aaron↗
DOE OSTI2023

Self‐Propelling Macroscale Sheets Powered by Enzyme Pumps

Abstract Nanoscale enzymes anchored to surfaces act as chemical pumps by converting chemical energy released from enzymatic reactions into spontaneous fluid flow that propels entrained nano‐ and microparticles. Enzymatic pumps are biocompatible, highly selective, and display unique substrate specificity. Utilizing these pumps to trigger self‐propelled motion on the macroscale has, however, constituted a significant challenge and thus prevented their adaptation in macroscopic fluidic devices and soft robotics. Using experiments and simulations, we herein show that enzymatic pumps can drive centimeter‐scale polymer sheets along directed linear paths and rotational trajectories. In these studies, the sheets are confined to the air/water interface. With the addition of appropriate substrate, the asymmetric enzymatic coating on the sheets induces chemically driven, buoyancy flows that controllably propel the sheet's motion on the air/water interface. The directionality and speed of the motion can be tailored by changing the pattern of the enzymatic coating, type of enzyme, and nature and concentration of the substrate. This work highlights the utility of biocompatible enzymes for generating motion in macroscale fluidic devices and robotics and indicates their potential utility for in vivo applications.

Song, Jiaqi↗
DOE OSTI2023

Self‐Propelling Macroscale Sheets Powered by Enzyme Pumps

Nanoscale enzymes anchored to surfaces act as chemical pumps by converting chemical energy released from enzymatic reactions into spontaneous fluid flow that propels entrained nano‐ and microparticles. Enzymatic pumps are biocompatible, highly selective, and display unique substrate specificity. Utilizing these pumps to trigger self‐propelled motion on the macroscale has, however, constituted a significant challenge and thus prevented their adaptation in macroscopic fluidic devices and soft robotics. Using experiments and simulations, we herein show that enzymatic pumps can drive centimeter‐scale polymer sheets along directed linear paths and rotational trajectories. In these studies, the sheets are confined to the air/water interface. With the addition of appropriate substrate, the asymmetric enzymatic coating on the sheets induces chemically driven, buoyancy flows that controllably propel the sheet's motion on the air/water interface. The directionality and speed of the motion can be tailored by changing the pattern of the enzymatic coating, type of enzyme, and nature and concentration of the substrate. This work highlights the utility of biocompatible enzymes for generating motion in macroscale fluidic devices and robotics and indicates their potential utility for in vivo applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2014

Aeroflex Technology as Class-Y Demonstrator

Modern space field programmable gate array (FPGA) devices with increased functional density and operational frequency, such as Xilinx Virtex 4 (V4) and S (V5), are packaged in non-hermetic ceramic flip chip forms. These next generation space parts were not qualified to the MIL-PRF-38535 Qualified Manufacturer Listing (QML) class-V when they were released because class-V was only intended for hermetic parts. In order to bring Xilinx V5 type packages into the QML system, it was suggested that class-Y be set up as a new category. From 2010 through 2014, a JEDEC G12 task group developed screening and qualification requirements for Class-Y products. The Document Standardization Division of the Defense Logistics Agency (DLA) has completed an engineering practice study. In parallel with the class-Y efforts, the NASA Electronic Parts and Packaging (NEPP) program has funded JPL to study potential reliability issues of the class-Y products. The major hurdle of this task was the absence of adequate research samples. Figure 1-1 shows schematic diagrams of typical structures of class-Y type products. Typically, class-Y products are either in ceramic flip chip column grid array (CGA) or land grid array (LGA) form. In class-Y packages, underfill and heat spread adhesive materials are directly exposed to the spacecraft environment due to their non-hermeticity. One of the concerns originally raised was that the underfill material could degrade due to the spacecraft environment and negatively impact the reliability of the package. In order to study such issues, it was necessary to use ceramic daisy chain flip chip package samples so that continuity of flip chip solder bumps could be monitored during the reliability tests. However, none of the commercially available class-Y daisy chain parts had electrical connections through flip chip solder bumps; only solder columns were daisy chained, which made it impossible to test continuity of flip chip solder bumps without using extremely costly functional parts. Among space parts manufacturers who were interested in producing class-Y products, Aeroflex Microelectronic Solutions-HiRel had been developing assembly processes using their internal R&D classy type samples. In early 2012, JPL and Aeroflex initiated a collaboration to study reliability of the Aeroflex technology as a class-Y demonstrator.

Suh, Jong-ook↗
NASA NTRS2000

A Light-Weight Inflatable Hypersonic Drag Device for Planetary Entry

The author has analyzed the use of a light-weight inflatable hypersonic drag device, called a ballute, for flight in planetary atmospheres, for entry, aerocapture, and aerobraking. Studies to date include Mars, Venus, Earth, Saturn, Titan, Neptune and Pluto, and data on a Pluto lander and a Mars orbiter will be presented to illustrate the concept. The main advantage of using a ballute is that aero, deceleration and heating in atmospheric entry occurs at much smaller atmospheric density with a ballute than without it. For example, if a ballute has a diameter 10 times as large as the spacecraft, for unchanged total mass, entry speed and entry angle,the atmospheric density at peak convective heating is reduced by a factor of 100, reducing the heating by a factor of 10 for the spacecraft and a factor of 30 for the ballute. Consequently the entry payload (lander, orbiter, etc) is subject to much less heating, requires a much reduced thermal. protection system (possibly only an MLI blanket), and the spacecraft design is therefore relatively unchanged from its vacuum counterpart. The heat flux on the ballute is small enough to be radiated at temperatures below 800 K or so. Also, the heating may be reduced further because the ballute enters at a more shallow angle, even allowing for the increased delivery angle error. Added advantages are less mass ratio of entry system to total entry mass, and freedom from the low-density and transonic instability problems that conventional rigid entry bodies suffer, since the vehicle attitude is determined by the ballute, usually released at continuum conditions (hypersonic for an orbiter, and subsonic for a lander). Also, for a lander the range from entry to touchdown is less, offering a smaller footprint. The ballute derives an entry corridor for aerocapture by entering on a path that would lead to landing, and releasing the ballute adaptively, responding to measured deceleration, at a speed computed to achieve the desired orbiter exit conditions. For a lander an accurate landing point could be achieved by providing the lander with a small gliding capacity, using the large potential energy available from being subsonic at high altitude. Alternatively the ballute can be retained to act as a parachute or soft-landing device, or to float the payload as a buoyant aerobot. As expected, the ballute has smaller size for relatively small entry speeds, such as for Mars and Titan, or for the extensive atmosphere of a low-gravity planet such as Pluto. Details of a ballute to place a small Mars orbiter and a small Pluto lander will be given to illustrate the concept. The author will discuss presently available ballute materials and a development program of aerodynamic tests and materials that would be required for ballutes to achieve their full potential.

McRonald, Angus D.↗
NASA NTRS1995

A Light-Weight Inflatable Hypersonic Drag Device for Planetary Entry

The author has analyzed the use of a light-weight inflatable hypersonic drag device, called a ballute, (balloon + parachute) for flight in planetary atmospheres, for entry, aerocapture, and aerobraking. Studies to date include missions to Mars, Venus, Earth, Saturn, Titan, Neptune and Pluto. Data on a Pluto lander and a Mars orbiter will be presented to illustrate the concept. The main advantage of using a ballute is that aero deceleration and heating in atmospheric entry occurs at much smaller atmospheric density with a ballute than without it. For example, if a ballute has a diameter 10 times as large as the spacecraft, for unchanged total mass, entry speed and entry angle,the atmospheric density at peak convective heating is reduced by a factor of 100, reducing the peak heating by a factor of 10 for the spacecraft, and a factor of about 30 for the ballute. Consequently the entry payload (lander, orbiter, etc) is subject to much less heating, requires a much reduced thermal protection system (possibly only an MLI blanket), and the spacecraft design is therefore relatively unchanged from its vacuum counterpart. The heat flux on the ballute is small enough to be radiated at temperatures below 800 K or so. Also, the heating may be reduced further because the ballute enters at a more shallow angle, even allowing for the increased delivery angle error. Added advantages are a smaller mass ratio of entry system to total entry mass, and freedom from the low-density and transonic instability problems that conventional rigid entry bodies suffer, since the vehicle attitude is determined by the ballute, usually released at continuum conditions (hypersonic for an orbiter, and subsonic for a lander). Also, for a lander the range from entry to touchdown is less, offering a smaller footprint. The ballute derives an entry corridor for aerocapture by entering on a path that would lead to landing, and releasing the ballute adaptively, responding to measured deceleration, at a speed computed to achieve the desired orbiter exit conditions. For a lander an accurate landing point could be achieved by providing the lander with a small gliding capacity, using the large potential energy available from being subsonic at high altitude. Alternatively the ballute can be retained to act as a parachute or soft-landing device, or to float the payload as a buoyant aerobot. As expected, the ballute has smaller size for relatively small entry speeds, such as for Mars, or for the extensive atmosphere of a low-gravity planet such as Pluto. The author will discuss presently available ballute materials and a development program of aerodynamic tests and materials that would be required for ballutes to achieve their full potential.

McRonald, Angus D.↗
NASA NTRS2005

Control of Combustion-Instabilities Through Various Passive Devices

It is well known that under some operating conditions, rocket engines (using solid or liquid fuels) exhibit unstable modes of operation that can lead to engine malfunction and shutdown. The sources of these instabilities are diverse and are dependent on fuel, chamber geometry and various upstream sources such as pumps, valves and injection mechanism. It is believed that combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system [1, 2]. Giammar and Putnam [3] performed a comprehensive study of noise generated by gasfired industrial burners and made several key observations; flow noise was sometimes more intense than combustion roar, which tended to have a characteristic frequency spectrum. Turbulence was amplified by the flame. The noise power varied directly with combustion intensity and also with the product of pressure drop and heat release rate. Karchmer [4] correlated the noise emitted from a turbofan jet engine with that in the combustion chamber. This is important, since it quantified how much of the noise from an engine originates in the combustor. A physical interpretation of the interchange of energy between sound waves and unsteady heat release rates was given by Rayleigh [5] for inviscid, linear perturbations. Bloxidge et al [6] extended Rayleigh s criterion to describe the interaction of unsteady combustion with one-dimensional acoustic waves in a duct. Solutions to the mass, momentum and energy conservation equations in the pre- and post-flame zones were matched by making several assumptions about the combustion process. They concluded that changes in boundary conditions affect the energy balance of acoustic waves in the combustor. Abouseif et al [7] also solved the one-dimensional flow equations, but they used a onestep reaction to evaluate the unsteady heat release rate by relating it to temperature and velocity perturbations. Their analysis showed that oscillations arise from coupling between entropy waves produced at the flame and pressure waves originating from the nozzle. Yang and Culick [8] assumed a thin flame sheet, which is distorted by velocity and pressure oscillations. Conservation equations were expressed in integral form and solutions for the acoustic wave equations and complex frequencies were obtained. The imaginary part of the frequency indicated stability regions of the flame. Activation energy asymptotics together with a one-step reaction were used by McIntosh [9] to study the effects of acoustic forcing and feedback on unsteady, one-dimensional flames. He found that the flame stability was altered by the upstream acoustic feedback. Shyy et al [10] used a high-accuracy TVD scheme to simulate unsteady, one-dimensional longitudinal, combustion instabilities. However, numerical diffusion was not completely eliminated. Recently, Prasad [11] investigated numerically the interactions of pressure perturbations with premixed flames. He used complex chemistry to study responses of pressure perturbations in one-dimensional combustors. His results indicated that reflected and transmitted waves differed significantly from incident waves.

Frendi, Kader↗
DOE OSTI2025

Increasing Radon Daughter Plate-out onto Superconducting Qubits

Radon daughter plate-out may pose a fundamental limitation to realizing large-scale superconducting quantum computers. Radon daughters plated-out onto a superconducting qubit chip can decay, releasing energy into the substrate, producing phonons. Phonon induced quasiparticles generate bit flip errors and reduce coherence times. We seek to increase plate-out on chips to enable future study of the impact of Radon on coherence times. In this project, we utilize COMSOL Multiphysics simulations to finalize design for a device to increase radon plate-out.

Kay, Dax [Northwestern U.]↗
NASA NTRS1993

Versatile Lightweight Ladder

Proposed multipurpose escape-and-rescue device primarily ladder but also used as escape chute, stretcher, or float. Ladder fabricated as single composite piece, with staggered openings for feet and an integral handrail. Foot openings designed less likely to cause injuries by jamming one's hands, arms, and legs between ladder and structure on which mounted. Quick-release fasteners used for mounting.

Breen, Clarence F.↗
DOE OSTI2022

Parametric Study of Panel PCM–Air Heat Exchanger Designs

Heat exchangers, devices for the transfer of heat between two or more working fluids, are extensively used in cooling applications and heating applications. Heat exchangers in buildings are typically components of space-conditioning systems, as well as of water-heating applications. Heat exchangers are also sometimes used in applications that require storage and release of energy at specific times. Phase change materials (PCMs) enhance these heat-exchange processes, given their ability to melt and solidify at a fixed range of temperatures, absorbing or releasing significant amounts of latent heat. Five different configurations of PCM–air heat exchangers for thermal control in buildings are analyzed in this work. The heat exchangers were fitted with PCM encapsulated in plastic and composite pouches of various shapes, and packaged in stackable panel layers. Three-dimensional computational fluid dynamics (CFD) modeling of coupled incompressible fluid and conjugate heat transfer were performed on the designs. The phase change process was numerically modelled using the apparent heat capacity method. Steady-state CFD simulations provided quantification of pressure drop as a function of air flow velocity. Transient simulation results describe the thermal evolution of PCM in the pouches, helping to determine the best performing configuration with respect to total thermal charging time.

10 SYNTHETIC FUELS↗
NASA NTRS2016

Reconstructed Parachute System Performance During the Second LDSD Supersonic Flight Dynamics Test

NASA’s Low-Density Supersonic Decelerators project (LDSD) has developed and tested four new aerodynamic decelerator technologies for future Mars missions: two attached toroidal inflatable decelerators, a ballute, and a large supersonic parachute. On June 8, 2015, the project conducted a high-altitude, supersonic flight test of a 30.5-meter supersonic Ringsail (SSRS) canopy at the US Navy’s Pacific Missile Range Facility (PMRF) on Kauai, HI. This test, the second in a series of Supersonic Flight Dynamics Tests (SFDT-2), allowed the LDSD project to test the deployment and performance of its parachute decelerator system in the wake of a representative test vehicle (a 4.7-meter aeroshell and 6-meter toroidal inflatable aerodynamic decelerator) at conditions relevant to Mars entry for the second time. The parachute decelerator system consisted of the SSRS main parachute and a 4.4-meter ballute (called the parachute deployment device, or PDD) for its extraction. The ballute was mortar-deployed at a Mach number of 2.78 and a dynamic pressure of 493 Pa, and inflated with the aid of a water-methanol based gas generator. After flying in the wake of the test vehicle for ten seconds, the PDD was released and allowed to extract the main parachute pack. The SSRS reached line-stretch at a Mach number of 2.37 and dynamic pressure of 602 Pa. Following full inflation, the propagation of a tear in the canopy led to the failure of the parachute skirt band and to the subsequent failure of the vent band. The test vehicle was instrumented with load sensors, inertial sensors, and high-speed and high resolution cameras that provided data on the performance of the PDD and SSRS through deployment, inflation, and flight. This paper describes the resulting reconstructed behavior of the PDD and SSRS during deployment and inflation, their aerodynamic performance on SFDT-2, the failure of the SSRS shortly after full inflation, and the LDSD project’s investigation into its underlying causes.

O'Farrell, Clara↗
DOE OSTI2020

Heat generation due to the Anderson catastrophe in mesoscopic devices

Anderson's orthogonality catastrophe (AOC) theorem establishes that the ground state of the many-body fermion system is asymptotically orthogonal to the ground state of the same system perturbed by a scattering potential so that the overlap between the original and new ground states decays to zero with the system size. We adopt the AOC for a description of heat production in a complementary metal-oxide-semiconductor transistor. We find that the heat released in the transistor comprises two distinct components, contribution from the dissipation accompanying electron transmission under the applied voltage and purely quantum-mechanical AOC part due to the change in scattering matrix for electrons upon switching between high and low conductance regimes. We calculate the AOC-induced heat production, which we call switching heat.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Disruption prediction with artificial intelligence techniques in tokamak plasmas

In nuclear fusion reactors, plasmas are heated to very high temperatures of more than 100 million kelvin and, in so-called tokamaks, they are confined by magnetic fields in the shape of a torus. Light nuclei, such as deuterium and tritium, undergo a fusion reaction that releases energy, making fusion a promising option for a sustainable and clean energy source. Tokamak plasmas, however, are prone to disruptions as a result of a sudden collapse of the system terminating the fusion reactions. As disruptions lead to an abrupt loss of confinement, they can cause irreversible damage to present-day fusion devices and are expected to have a more devastating effect in future devices. Disruptions expected in the next-generation tokamak, ITER, for example, could cause electromagnetic forces larger than the weight of an Airbus A380. Furthermore, the thermal loads in such an event could exceed the melting threshold of the most resistant state-of-the-art materials by more than an order of magnitude. In this work, to prevent disruptions or at least mitigate their detrimental effects, empirical models obtained with artificial intelligence methods, of which an overview is given here, are commonly employed to predict their occurrence—and ideally give enough time to introduce counteracting measures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Thiol-based defect healing of WSe 2 and WS 2

Recent research on two-dimensional (2D) transition metal dichalcogenides (TMDCs) has led to remarkable discoveries of fundamental phenomena and to device applications with technological potential. Large-scale TMDCs grown by chemical vapor deposition (CVD) are now available at continuously improving quality, but native defects and natural degradation in these materials still present significant challenges. Spectral hysteresis in gate-biased photoluminescence (PL) measurements of WSe 2 further revealed long-term trapping issues of charge carriers in intrinsic defect states. To address these issues, we apply here a two-step treatment with organic molecules, demonstrating the “healing” of native defects in CVD-grown WSe 2 and WS 2 by substituting atomic sulfur into chalcogen vacancies. We uncover that the adsorption of thiols provides only partial defect passivation, even for high adsorption quality, and that thiol adsorption is fundamentally limited in eliminating charge traps. However, as soon as the molecular backbone is trimmed and atomic sulfur is released to the crystal, both bonds of the sulfur are recruited to passivate the divalent defect and the semiconductor quality improves drastically. Time-dependent X-ray photoelectron spectroscopy (XPS) is applied here together with other methods for the characterization of defects, their healing, leading energies and occupation. First-principles calculations support a unified picture of the electronic passivation of sulfur-healed WSe 2 and WS 2 . This work provides a simple and efficient method for improving the quality of 2D semiconductors and has the potential to impact device performance even after natural degradation.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Attention Network Forecasts Time-to-Failure in Laboratory Shear Experiments

Rocks under stress deform by creep mechanisms that include formation and slip on small-scale internal cracks. Intragranular cracks and slip along grain contacts release energy as elastic waves termed acoustic emissions (AE). AEs are thought to contain predictive information that can be used for fault failure forecasting. Here, we present a method using unsupervised classification and an attention network to forecast labquakes using AE waveform features. Our data were generated in a laboratory setting using a biaxial shearing device with granular fault gouge intended to mimic the conditions of tectonic faults. Here, we analyzed the temporal evolution of AEs generated throughout several hundred laboratory earthquake cycles. We used a Conscience Self-Organizing Map (CSOM) to perform topologically ordered vector quantization based on waveform properties. The resulting map was used to interactively cluster AEs. We examined the clusters over time to identify those with predictive ability. Finally, we used a variety of LSTM and attention-based networks to test the predictive power of the AE clusters. By tracking cumulative waveform features over the seismic cycle, the network is able to forecast the time-to-failure (TTF) of lab earthquakes. Our results show that analyzing the data to isolate predictive signals and using a more sophisticated network architecture are key to robustly forecasting labquakes. In the future, this method could be applied on tectonic faults to monitor earthquakes and augment early warning systems.

58 GEOSCIENCES↗
NASA NTRS1980

Silent Sentry

NASA developed personal security system, commercialized by Sentry Products, Inc. enables resident to summon instant help in case of medical emergency or threatened violence. Its principal elements are a pen-shaped signaling device, "silent" because its ultrasonic alert signal is inaudible to the human ear, and a system of receivers interconnected with a constantly-monitored aster console. SCAN pen weighs only two ounces and is worn on necklace or attached by a clip to the user's clothing. The person in trouble simply presses a clasp, releasing a hammer inside the pen which strikes an aluminum bar. The impact causes the bar to resonate like a tuning fork and emit the ultrasonic signal, which is detected by the nearest receiver.

Source record↗
NASA NTRS1977

Mass drivers. 1: Electrical design

A mass driver is an electrical device used to accelerate payloads of any material to a high velocity. Small vehicles (called buckets) containing superconducting coils carry the payloads. These buckets are accelerated by pulsed magnetic fields, timed by information on their position, and are guided by induced magnetic fields set up in a surrounding guideway. Upon reaching the correct velocity, the buckets release their payloads, then they are slowed for recirculation to be reused. A rationale is presented that leads to a relatively simple and near-optimum design, as well as basic programs for calculating acceleration. The transverse oscillation frequencies are found to be invariant to guideway transverse dimensions.

William H. Arnold↗