Earnshaw’s theorem states that a collection of point charges cannot be maintained in a stable Earnshaw’s theorem forbids magnetic levitation in many common situations. If the materials are not hard, Braunbeck’s extension shows that. The electromagnets on the underside of the train pull it up to the ferromagnetic stators on the track and levitate the train. The magnets on the side keep the train . Safety of High Speed Magnetic Levitation Transportation Systems: German Published Date: Language: English. Filetype [PDF MB].

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Bureau of Transportation Statistics. This report presents the results of a systematic review of the safety requirements selected for the German Transrapid electromagnetic EMS type maglev system to determine filetypee applicability and completeness with respect to the construction and operation of maglev systems in levitatuon United States. A stable equilibrium of the particle cannot exist and there must be an instability in some levittaion. Findings are presented regarding proposed safety requirements for the construction and operation of high-speed maglev systems in the United States.

These questions eventually pointed the way to quantum mechanical explanations of the structure of the atom, where the existence of stationary non-radiative states in which the electron has a nonzero momentum and therefore is not actually static resolves the above conundrum at a fundamental level. In paramagnetic and diamagnetic materials the dipoles are aligned parallel and antiparallel to the field lines, respectively. Lastly, I think it would be most valuable to conduct experiments on my own, testing the relationships filehype by physicists in fuletype past, and searching to develop a model to describe the exact relationship between the speed of the train or some scale model and the levitation force, magnetic drag force, and aerodynamic drag force that result.

The levitahion objective of this program is to develop magnetic levitation technology that is a cost levitztion, reliable,: Unique aspects of the U. This page was last edited on 22 Augustat Recommendations are also included for FRA consideration. Also, the drag peak might vary, thus causing a change in the train speed at which the lifting force surpasses the drag force. Here is a link to the Mathematica code used to produce the various graphs and plots in my project:.

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As the top coil is pulled downwards by gravity, the two fields will interact much more, increasing the repulsion force, and thus levitating the train containing the superconducting coils. I may also look into magnetic pressure, and how this variable might explain how and why the object levitates.

Earnshaw’s theorem

Earnshaw’s theorem applies to classical inverse-square law forces electric and gravitational and also to the magnetic forces of permanent magnetsif the magnets are hard the magnets do not vary in strength with external fields. Though most of the force created by the images is repulsive, there is still the electromagnetic drag force created by the remaining currents in the passed loops, which can be thought of as coming from the previous images.

So, after having done extensive research into the various types of maglev technologies, I have found that the methods of electromagnetic suspension EMS and electrodynamic suspension EDS are the most developed and practiced types of magnetic levitation. This document cannot be previewed automatically as it exceeds 5 MB.

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To extend upon this project, I would like to do several things: For this reason, some items on this page will be unavailable. From now on, I will focus on finding the relationships between the speed of the train or, rather, the superconducting coils inside of itthe distance between the train and the tracks, and the magnetic lifting force and drag force that allow the EDS system to function.

There are three main methods that allow Maglev technologies to operate. Here are the various filetjpe that I consulted while researching the methods of magnetic levitation:. Retrieved from ” https: The dipole will only be stably levitated at points where the energy has a minimum. The second method, called electrodynamic suspension EDS levitatoon, requires that both the levitating object and the track exert a magnetic field, so that the object is levitated by the repulsive force between the two fields.

These can thus seem to be exceptions, though in fact they exploit the constraints of the theorem. I am expecting my plots to show a strong relationship between force and distance from the track, such that the distance steadies out to a constant height over a length of time.


These findings are intended to assist FRA in establishing safety requirements for U. With this I will model the force of repulsion between the train and the tracks, which should display how the force varies as the distance between the train and the track changes.

Additionally, for this magnetic dipole approximation, the ratio of lifting force to drag force remains fairly linear and very steep. However, this equation would still only apply under the assumption that the superconducting coils on board the train act as a perfect dipole.

As a result, due to the loss in current during bthere is a net negative current the shaded region flowing in the lower loop after the upper loop passes. The induction process of the EDS system is depicted in the diagram below: Of course, both materials can have saddle points. This works because the theorem shows only that there is some direction in which there will be an instability. Additional effects that allow maglev trains to remain at a steady height above the track include the Meissner effect, and magnetic flux trapping.

The induced Fietype in the lower loop, and the lagging induced current, are graphed with respect to time below. Diamagnetic materials are excepted because they exhibit only repulsion against the magnetic field, whereas the theorem requires materials that have both repulsion and attraction.

Advanced Search Small Search Button. The frequency of the AC current is coordinated such that the field always repels the magnets in the object, sending it forward. The safety of various magnetically levitated maglev trains underdevelopment for possible implementation in the United States is ofdirect concern to the Federal Railroad Administration FRA.

Javascript is disabled or is not supported by your browser. Here is a link to the Mathematica code used to produce the various graphs and plots in my project: