Abstract:
A system for levitating and propelling a vehicle along a stationary guideway includes a linear synchronous motor (LSM) having a component mounted on the vehicle and a component mounted on the guideway. The LSM components interact to generate electromagnetic forces that act to levitate the vehicle and electromagnetic forces that act to propel the vehicle along the guideway. The gap between LSM components is maintained by an electrodynamic system (EDS) having a component mounted on the vehicle and a component mounted on the guideway. The EDS components cooperate to create an electromagnetic force that acts with the levitation forces created by the LSM to maintain the LSM gap within a predetermined range. Maintenance of the LSM gap stabilizes the LSM and allows the LSM to operate efficiently within a pre-selected range of vehicle speeds.

Description:
[0001] “This invention was made with Government support under Agreement No. CA-26-7025 awarded by the Federal Transit Administration. The Government has certain rights in the invention.” 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    The present invention pertains generally to systems for levitating and propelling a magnetically levitated (MAGLEV) vehicle. More particularly, the present invention pertains to levitation and propulsion systems that are energy efficient over a pre-selected range of vehicle speeds. The present invention is particularly, but not exclusively, useful as an efficient levitation and propulsion system consisting of a linear synchronous motor (LSM) and an Electro-Dynamic (levitation) System (EDS) arranged uniquely into an inherently stable system.  
         BACKGROUND OF THE INVENTION  
         [0003]    Magnetic levitation systems, often called MAGLEV systems, use magnetic fields to levitate a vehicle over a stationary guideway. Because the vehicle does not physically contact the guideway during acceleration and normal high-speed operation, energy losses associated with contact friction are greatly reduced. Still, magnetic drag forces, if not taken into consideration, can offset the benefits of reduced contact friction resulting in an inefficient transportation system.  
           [0004]    Heretofore, electromagnetic systems (EMS) and Electro-Dynamic Systems (EDS) have been used to levitate vehicles. The EMS systems use the attraction between electromagnets attached to the vehicle and iron rails on the guideway to produce the required levitation force. Such a system is inherently unstable and active control of the electromagnets is required to maintain the gap between the iron rails and the electromagnets. Specifically, any fluctuation in the gap from irregularities in the track or external forces on the vehicle/guideway must be immediately countered. As one might expect, the required active control system is complicated, expensive and unreliable. With the Electro-Dynamic System (EDS), eddy currents induced in electrically conductive material on the track by a traveling magnetic field from magnets on the vehicle, produce a levitation force by their interaction with the array of magnets in the vehicle. This interaction produces drag forces that must be overcome by the propulsion system.  
           [0005]    A linear synchronous motors (LSM), generates forces that can be used to propel a vehicle and additionally, forces that act in a direction orthogonal to the direction of propulsion. One example of a linear synchronous motor includes an armature having an a.c. poly-phase winding on an armature. This armature can be mounted on the stationary guideway for interaction with permanent magnets mounted on the vehicle. By embedding the armature winding in ferromagnetic material, attractive forces generated between the armature and the magnets can be used to levitate the vehicle. These attractive forces are generated without also generating drag forces.  
           [0006]    Alone, the LSM is unstable and the LSM gap between the armature and magnets cannot be maintained. Specifically, even slight decreases in the LSM gap cause the attractive force between the armature and magnets to increase, and the increased force acts to further close the LSM gap. In addition to stability considerations, the efficiency of the linear synchronous motor must be considered. In this regard, the efficiency of the LSM is highly dependant on the width of the LSM gap. Specifically, the LSM is most efficient when the LSM gap is maintained relatively small.  
           [0007]    In light of the above, it is an object of the present invention to provide systems suitable for the purposes of levitating and propelling a vehicle over a guideway that are stable and energy efficient. It is another object of the present invention to provide MAGLEV levitation and propulsion systems that provide passive levitation control with reduced peak and average magnetic drag forces. It is yet another object of the present invention to provide MAGLEV levitation and propulsion systems that remain stable in spite of unwanted fluctuations in propulsion system currents and/or external forces acting on the vehicle. Still another object of the present invention is to provide MAGLEV levitation and propulsion systems that can be used to provide lateral stability to the MAGLEV vehicle. It is still another object of the present invention to provide MAGLEV levitation and propulsion systems that are efficient during acceleration from low vehicle speeds (i.e. at peak power). It is another object of the present invention to provide MAGLEV levitation and propulsion systems that are efficient at high vehicle speeds (i.e. operating speeds). Yet another object of the present invention is to provide MAGLEV levitation and propulsion systems which are easy to use, relatively simple to implement, and comparatively cost effective.  
         SUMMARY OF THE INVENTION  
         [0008]    The present invention is directed to a system for levitating and propelling a vehicle along a stationary guideway. In functional overview, the system is designed for energy efficiency over a predetermined vehicle speed range. In one embodiment, the system is designed for maximum power and efficiency during vehicle acceleration from zero speed. In another embodiment of the present invention, the system is designed for maximum efficiency at operational speeds. In addition to efficiency considerations, the system is designed to be inherently stable (unlike an EMS system or LSM system acting alone) in spite of increases in LSM armature winding current or external forces acting on the vehicle. This inherent stability of the system also allows the system to be used to provide lateral stability to the vehicle.  
           [0009]    In accordance with the present invention, the levitation and propulsion system includes a linear synchronous motor (LSM) having two LSM components. One LSM component is mounted on the vehicle and the other LSM component is mounted on the guideway. When the vehicle is positioned on the guideway, the LSM components of the linear synchronous motor are juxtaposed and define an LSM gap between the LSM components.  
           [0010]    For the present invention, one of the LSM components includes either a switched direct-current winding or a poly-phase winding on an iron core, and the other LSM component includes a plurality of magnetic poles mounted on a rail. Functionally, the linear synchronous motor is provided to produce a first electromagnetic force between the LSM components that acts to levitate the vehicle and a second electromagnetic force between the LSM components that acts to propel the vehicle along the guideway. Importantly, the magnitudes of these electromagnetic forces are dependent on the width of the LSM gap, the LSM armature winding current, the size of the iron core and the total vehicle load. As indicated above, a linear synchronous motor, by itself, is unstable and this instability closes the LSM gap prohibiting movement of the vehicle.  
           [0011]    For the present invention, the levitation and propulsion system includes an electrodynamic system (EDS) to maintain the LSM gap within a desired width range. More specifically, a small LSM gap is maintained by the EDS over a predetermined range of vehicle speeds because the linear synchronous motor is most efficient when the LSM gap is small. Also, by maintaining the LSM gap within a desired width range, the LSM instabilities described above are eliminated.  
           [0012]    Structurally, the electrodynamic system has an EDS component mounted on the vehicle and another EDS component mounted on the stationary guideway. During vehicle movement along the guideway, the EDS components cooperate to create an electromagnetic force that reacts with the levitation forces created by the LSM. Like the LSM, when the vehicle is positioned on the guideway, the EDS components are juxtaposed and define an EDS gap between the EDS components. In the preferred embodiment of the present invention, one of the EDS components is a magnet array and the other EDS component is a plurality of conductive cables, with each cable extending in a direction orthogonal to the direction of vehicle travel and short-circuited at both ends. Importantly, the magnitude of the electromagnetic force generated by the EDS is dependent on the width of the EDS gap and the speed of the vehicle relative to the stationary guideway.  
           [0013]    As indicated above, the linear synchronous motor defines an LSM gap and the electrodynamic system defines an EDS gap. For the present invention, the vehicle is configured relative to the guideway to cause the width of these gaps to vary equally as the amount of vehicle levitation varies. In a first embodiment of the present invention, the widths of both the LSM and EDS gaps decrease with increasing vehicle levitation over the guideway.  
           [0014]    In this embodiment, the LSM establishes an electromagnetic force that tends to levitate the vehicle while the EDS establishes an electromagnetic force that opposes levitation of the vehicle. For a vehicle at constant speed any change in levitation will change both the LSM and EDS gaps equally. Thus any change in levitation force generated by the LSM will be counteracted by a change in the EDS-generated force opposing levitation. By properly sizing the EDS and LSM systems, a substantially constant levitating force at constant speed can be obtained that results in stable vehicle travel.  
           [0015]    For this embodiment, the opposing force generated by the EDS is small at low vehicle speeds. Since the opposing force is small, vehicle levitation is large and the LSM gap is small (See above). During acceleration, which is generally required when the vehicle is at low speeds, the LSM is most efficient with a small gap width. Thus, this embodiment of the present invention which maintains a small LSM gap width at low vehicle speeds, establishes an efficient levitation and propulsion system.  
           [0016]    In an alternate embodiment of the present invention, the vehicle is configured wherein the width of the LSM gap decreases with increasing vehicle levitation over the guideway, while the width of the EDS gap increases with increasing vehicle levitation over the guideway. For this embodiment, both the LSM and the EDS establish electromagnetic forces that act to levitate the vehicle (i.e. no opposing force is created). For a vehicle at low speed and low vehicle levitation, the LSM gap is relatively large and the EDS gap is relatively small. Accordingly, both the LSM and EDS levitating forces are relatively weak. On the other hand, at higher vehicle speeds and levitations, the LSM gap is relatively small and the EDS gap is relatively large. Accordingly, at higher vehicle levitations the LSM levitating force is relatively strong and the EDS levitating force is relatively weak.  
           [0017]    Like the first embodiment described above, in this embodiment, the EDS force acts with the LSM force to establish a substantially constant force over a range of LSM gap widths. This embodiment differs from the above described embodiment, however, because in this embodiment, maximum LSM efficiency is obtained at high vehicle speeds (i.e. operating speed) rather than during acceleration from low speed. In greater detail, at operating speed, the EDS force is relatively strong, the LSM levitating force is relatively weak, and the LSM gap is small. Thus, since the LSM is efficient at small LSM gap widths, in this embodiment, the system is efficient at operating speed. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0018]    The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which:  
         [0019]    [0019]FIG. 1 is a perspective view of a MAGLEV vehicle traveling along a guideway;  
         [0020]    [0020]FIG. 2 is a sectional view as seen along line  2 - 2  in FIG. 1 showing a levitation and propulsion system in accordance with the present invention;  
         [0021]    [0021]FIG. 3 is a sectional view as seen along line  3 - 3  in FIG. 2 showing a portion of an LSM armature and corresponding LSM magnet array;  
         [0022]    [0022]FIG. 4 is a sectional view as in FIG. 3 showing an alternate embodiment of an LSM magnet array and corresponding portion of an LSM armature;  
         [0023]    [0023]FIG. 5 is a sectional view as seen along line  5 - 5  in FIG. 2 showing a portion of an EDS having a conductive track and a magnet array;  
         [0024]    [0024]FIG. 6 is a sectional view as in FIG. 5 showing an alternate embodiment of an EDS magnet array and the corresponding EDS conductive track;  
         [0025]    [0025]FIG. 7 is a sectional view as in FIG. 2 showing an alternate embodiment of a levitation and propulsion system in accordance with the present invention;  
         [0026]    [0026]FIG. 8 is a sectional view as in FIG. 2 showing another alternate embodiment of a levitation and propulsion system in accordance with the present invention; and  
         [0027]    [0027]FIG. 9 shows the variation of the EDS and LSM forces as a function of EDS and LSM gap. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0028]    Referring to FIG. 1, a MAGLEV system in accordance with the present invention is shown and generally designated  10 . As shown in FIG. 1, the system  10  includes a vehicle  12  having an optional passenger compartment  14 . It is to be appreciated that the vehicle  12  is provided for levitation over and travel along a guideway  16 . Although a vehicle  12  is shown for the system  10 , it is to be appreciated that the system  10  can levitate and propel other objects and is not limited to the levitation and propulsion of manned vehicles. Referring now to FIG. 2, it can be seen that a levitation and propulsion system is provided having a linear synchronous motor (LSM) and an electrodynamic system (EDS). More specifically, the LSM includes a plurality of LSM armatures  18  and corresponding LSM magnet arrays  20 ,  22 . As further shown, the electrodynamic system includes EDS conductive tracks  24 ,  26  and corresponding EDS magnet arrays  28 ,  30 .  
         [0029]    With cross reference now to FIGS. 2 and 3, it can be seen that each LSM armature  18  is mounted on the guideway  16  and includes a winding  32 . For the present invention, the winding  32  is connected to an electrical power source (not shown) and can be a switched direct-current winding or a set of a.c. poly-phase distributed windings. Also shown, each LSM armature  18  further includes an armature core that preferably includes a pair of ferromagnetic bars  34 ,  36  that are separated from each other by an air gap. The winding  32  is placed into grooves in the ferromagnetic bars  34 ,  36  to establish the LSM armature  18 .  
         [0030]    With continued cross reference to FIGS. 2 and 3, it can be seen that each LSM magnet array  20 ,  22  is mounted on the vehicle  12  and substantially centered opposite a corresponding ferromagnetic bar  34 ,  36  of the LSM armature  18 . Although the LSM magnet arrays  20 ,  22  are shown mounted on a shelf of the vehicle  12 , it is to be appreciated that the LSM magnet arrays could also be mounted on the top of the vehicle  12  for interaction with a guideway  16  that extends above the vehicle  12 . Further, the LSM magnet arrays  20 ,  22  are spaced from the corresponding ferromagnetic bar  34 ,  36  by an LSM gap having an LSM gap width  38 . It is to be appreciated from cross referencing FIGS. 1 and 2 that the LSM gap width  38  varies with the variation in levitation of the vehicle  12  over the guideway  16 .  
         [0031]    With cross reference to FIGS. 2 and 3, it can be seen that each LSM magnet array  20 ,  22  includes a plurality of magnet poles that alternate in polarity (i.e. N, S, N, S . . . ) along the magnet array  20 ,  22 . In an alternate embodiment as shown in FIG. 4, each LSM magnet array such as LSM magnet array  22 ′ is configured as a Halbach array, with each magnet being polarized in the direction as indicated by the corresponding arrow. Although the LSM armature  18  is shown mounted on the guideway  16  and the corresponding LSM magnet arrays  20 ,  22  are shown mounted on the vehicle  12  in FIG. 2, it is to be appreciated by those skilled in the pertinent art that the same effect could be achieved by mounting the LSM armature  18  on the vehicle  12  and mounting the corresponding LSM magnet arrays  20 ,  22  on the guideway  16 .  
         [0032]    Functionally, the linear synchronous motor is provided to produce an attractive electromagnetic force between the LSM armature  18  and LSM magnet arrays  20 ,  22  that acts to levitate the vehicle  12  and an electromagnetic force between the LSM armature  18  and LSM magnet arrays  20 ,  22  that acts to propel the vehicle  12  along the guideway  16 . Importantly, the magnitudes of these electromagnetic forces are dependent on the LSM gap width  38 , the magnitude of the current in the winding  32  of the LSM armature  18  and the size of the ferromagnetic bars  34 ,  36 . As indicated above, a linear synchronous motor, by itself, is unstable and these instabilities close the LSM gap prohibiting the movement of the vehicle.  
         [0033]    Referring now with cross reference to FIGS. 2 and 5, it can be seen that the electrodynamic system includes EDS conductive tracks  24 ,  26  that are mounted on the guideway  16  and EDS magnet arrays  28 ,  30  that are mounted on the vehicle  12 . As further shown, each conductive track  24 ,  26  preferably includes a plurality of parallel, conductive cables  40  that run orthogonal to the direction in which the corresponding EDS magnet array  28 ,  30  moves during travel of the vehicle  12 . Each conductive cable  40  is short circuited between a pair of conductive bus bars  41  to allow induced currents to be formed in each conductive cable  40  as the corresponding magnet array  28 ,  30  moves relative to the conductive track  24 ,  26 . Although the conductive tracks  24 ,  26  are shown having conductive cables  40 , it is to be appreciated by those skilled in the pertinent art that other types of conductive tracks can be used in the electrodynamic system of the present invention. Examples of conductive tracks  24 ,  26  that can be used in the present invention include laminated sheets of conductive material (not shown).  
         [0034]    Preferably, as shown, each cable  40  includes a plurality of conductive strands  42  that are individually insulated in an insulation jacket  44 , as shown in FIG. 5. Although seven strands  42  have been shown for each cable  40 , it is to be appreciated that seven strands  42  is merely exemplary and that any number of strands  42 , such as several dozen, may be used in each cable  40 . Further, in the preferred embodiment of the present invention, each conductive strand  42  is twisted around the other conductive strands  42  in the cable  40  to fully transpose each conductive strand  42  and thereby allow at least a portion of each strand  42  to reside near the surface of the cable  40 . This cooperation of structure reduces the skin effect that would otherwise limit the formation of current in conductive cables  40  to a small cross-sectional area. Each cable  40  further includes a casing  46  made of a low magnetic permeability material.  
         [0035]    With continued cross-reference to FIGS. 2 and 5, it can be seen that each EDS magnet array  28 ,  30  is mounted on the vehicle  12  and substantially centered opposite a corresponding EDS conductive track  24 ,  26 . Further, the EDS magnet arrays  28 ,  30  are spaced from the corresponding EDS conductive tracks  24 ,  26  by an EDS gap having an EDS gap width  48 . It is to be appreciated from cross referencing FIGS. 1 and 2 that the EDS gap width  48  varies with the variation in levitation of the vehicle  12  over the guideway  16 .  
         [0036]    It can be further seen by cross referencing FIGS. 2 and 5 that each EDS magnet array  28 ,  30  includes a plurality of magnet poles that alternate in polarity (i.e. N, S, N, S . . . ) along the EDS magnet array  28 ,  30 . In an alternate embodiment as shown in FIG. 6, each EDS magnet array  28 ,  30  such as EDS magnet array  28 ′ is configured as a Halbach array, with each magnet being polarized in the direction as indicated by the corresponding arrow. Although the EDS conductive tracks  24 ,  26  are shown mounted on the guideway  16  and the corresponding EDS magnet arrays  28 ,  30  are shown mounted on the vehicle  12  in FIG. 2, it is to be appreciated by those skilled in the pertinent art that the same effect could be achieved by mounting the EDS conductive tracks  24 ,  26  on the vehicle  12  and mounting the corresponding EDS magnet array  28 ,  30  on the guideway  16 .  
         [0037]    It is to be further appreciated by those skilled in the pertinent art that during movement of the vehicle  12  along the guideway  16 , a repulsive electromagnetic force between the EDS conductive tracks  24 ,  26  and the EDS magnet arrays  28 ,  30  is created. This repulsive electromagnetic force created by the EDS reacts with the levitation forces created by the LSM. Importantly, the magnitude of the electromagnetic force generated by the EDS is dependent on the EDS gap width  48  and the speed of the vehicle  12  relative to the stationary guideway  16 .  
         [0038]    From FIG. 2 it is to be appreciated that the linear synchronous motor produces an upward directed force that acts to levitate the vehicle  12  while the EDS produces a downward directed force that opposes levitation of the vehicle  12 . An alternate embodiment of the present invention is shown in FIG.  7  which operates in a similar manner as the embodiment shown in FIG. 2. Specifically, in both embodiments (i.e. the embodiments shown in FIG. 2 and FIG. 7), the LSM acts to levitate the vehicle  12  while the EDS opposes levitation of the vehicle  12 . In the embodiment shown in FIG. 7, the vehicle  112  is formed with two shelves  50 ,  52 . As further shown in FIG. 7, a single EDS magnet array  128  is mounted on shelf  52  for interaction with EDS conductive track  124  that extends horizontally from guideway  116 . Thus, an EDS gap width  148  is established between the EDS magnet array  128  and the EDS conductive track  124 . Additionally, as shown, LSM magnet arrays  120 ,  122  are mounted on shelf  50  for interaction with a plurality of LSM armatures  118  that are mounted on guideway  116 , establishing LSM gap width  138 .  
         [0039]    With reference now to FIG. 7, the operation of the FIG. 7 embodiment will now be described. It is to be appreciated that this description of operation is equally applicable to the embodiment shown in FIG. 2, unless otherwise indicated herein. For the present invention, the electrodynamic system is provided to maintain the LSM gap width  138  within a desired width range. More specifically, a small LSM gap width  138  is maintained by the EDS while the vehicle  112  is at low speeds. At these low speeds where acceleration is required, the linear synchronous motor is most efficient when the LSM gap width  138  is small. Also, by maintaining the LSM gap width  138  within a desired width range at all vehicle  112  speeds, the LSM instabilities described above are eliminated.  
         [0040]    With the vehicle  112  configured relative to the guideway  116  as shown in FIG. 7, both the LSM gap width  138  and the EDS gap width  148  decrease with increasing levitation of the vehicle  112  over the guideway  116 . Further, the LSM establishes an electromagnetic force that tends to levitate the vehicle  112  while the EDS establishes an electromagnetic force that opposes levitation of the vehicle  112 .  
         [0041]    With the vehicle  112  stationary and no current flowing through the LSM armature  118 , a levitating force is provided by the attraction between the LSM magnet arrays  120 ,  122  and the ferromagnetic bars  134 ,  136  of the LSM armature  118 . Preferably, the ferromagnetic bars  134 ,  136  and LSM magnet arrays  120 ,  122  are sized large enough to levitate the vehicle  112  while the vehicle  112  is stationary and no current is flowing through the LSM armature  118 . Levitation stops  54  are provided to limit the amount of levitation while the vehicle  112  is stationary and thereby establish a minimum LSM gap width  138  and EDS gap width  148 . For the present invention, these stops  54  may consist of rollers, wheels or a low friction sliding surface (not shown).  
         [0042]    When current is passed through the windings  132  of the LSM armature  118 , the vehicle  112  accelerates from a stationary position, and the LSM levitation force increases due to the current in the winding  132 . At the same time, movement of the vehicle  112  causes the EDS magnet array  128  to move relative to the EDS conductive track  124  and this movement creates a force that opposes levitation of the vehicle  112 . Preferably, the EDS and LSM are sized so that the opposing force created by the EDS at a predetermined vehicle speed is slightly stronger than the levitating force created by the LSM. Accordingly, as the vehicle  112  accelerates from a stationary position, the EDS force pushes the vehicle  112  down and disengages the levitation stops  54  until an equilibrium between the LSM levitating force and the EDS opposing force is established. More specifically, the LSM and EDS are configured to maintain a minimum LSM gap width  138  above the predetermined vehicle  112  speed.  
         [0043]    During constant vehicle  112  speed and low vehicle  112  levitation, both the LSM levitating force and the EDS opposing force are weak since both the LSM gap width  138  and EDS gap width  148  are large. On the other hand, at higher vehicle levitation, when both the LSM gap width  138  and EDS gap width  148  are small, both the LSM levitating force and the EDS opposing force are strong. Thus, the levitating and opposing forces combine to establish a fairly constant force over a range of LSM gap widths  138 . By properly sizing the EDS and LSM systems, a substantially constant levitating force can be obtained that results in a stable travel for the vehicle  112 . More specifically, external forces acting on the vehicle  112  from wind, aerodynamic drag, etc. that tend to reduce or increase the LSM gap width  138  will not significantly alter the levitating force, and thus, these external forces will not result in the closure of the LSM gap. It is to be appreciated from FIG. 1 that a levitation and propulsion system having an EDS and LSM can be provided on both sides of the vehicle  112  to provide lateral stability to the vehicle  112  (in addition to providing propulsion and levitation). In addition, lateral stability is provided due to the attraction between ferromagnetic bar  34  and LSM magnet array  20  and ferromagnetic bar  36  and LSM magnet array  22 .  
         [0044]    For these embodiments (i.e. FIG. 2 and FIG. 7), the opposing force generated by the EDS is weakest at low vehicle  112  speeds. Since the opposing force is weak, vehicle levitation is large and the LSM gap width  138  is small. During acceleration at low speeds, the LSM is most efficient with a small LSM gap width  138 . Thus, the embodiments of the present invention shown in FIGS. 2 and 7 maintain a small LSM gap width  138  at low vehicle  112  speeds and thus provide a levitation and propulsion system that is efficient during acceleration from low vehicle  112  speeds.  
         [0045]    [0045]FIG. 8 shows another embodiment of a levitation and propulsion system in accordance with the present invention. Unlike the embodiments described above (i.e. FIGS. 2 and 7), in this embodiment the force generated by the EDS acts to levitate the vehicle  212 . In the embodiment shown in FIG. 8 the vehicle  212  is formed with shelf  56 . As further shown in FIG. 8, a single EDS magnet array  228  is mounted on a first side of shelf  56  for interaction with EDS conductive track  224  that extends horizontally from guideway  216 . Thus, an EDS gap width  248  is established between the EDS magnet array  228  and the EDS conductive track  224 . Additionally, as shown, LSM magnet arrays  220 ,  222  are mounted on a second side of shelf  56  for interaction with a plurality of LSM armatures  218  that are mounted on guideway  216 , establishing LSM gap width  238 .  
         [0046]    With this cooperation of structure, LSM gap width  238  decreases with increasing vehicle  212  levitation over the guideway  216 , while the EDS gap width  248  increases with increasing vehicle  212  levitation over the guideway  216 . For the FIG. 8 embodiment, both the LSM and the EDS establish electromagnetic forces that act to levitate the vehicle  212  (i.e. no opposing force is created). Preferably, the ferromagnetic bars  234 ,  236  and magnet arrays  220 ,  222  of the LSM are sized wherein the levitation force generated by the LSM alone, is insufficient to levitate the vehicle  212 . Also, the EDS is sized wherein the levitation force generated by the EDS alone, is insufficient to levitate the vehicle  212 . Rather, only the combination of the levitating forces generated by the EDS and LSM are sufficient to levitate the vehicle  212 . Since the EDS only generates a levitating force when the vehicle  212  is in motion, a support system  58 , which may consist of wheels or rollers, is provided to support the vehicle until it has been accelerated by the LSM to lift-off speed. As shown, support system  58 , which may consist of wheels or rollers, is provided to support the vehicle  212  until the minimum speed is obtained and levitation is achieved At this minimum speed, the EDS produces a levitation force that can combine with the levitation force of the LSM to levitate the vehicle  212  and allow the vehicle  212  to be propelled by the LSM.  
         [0047]    Once the vehicle  212  is levitated by the EDS and LSM (i.e. at vehicle  212  speeds greater than the minimum speed described above), the EDS and LSM combine to maintain a substantially constant levitating force over a wide range of LSM gap widths  238 . More specifically, consider a vehicle  212  at constant speed and relatively low levitation, the LSM gap width  238  is relatively large and the EDS gap width  248  is relatively small. Accordingly, the LSM levitating force is relatively weak and the EDS levitating force is relatively strong. On the other hand, at higher vehicle  212  levitations, the LSM gap width  238  is relatively small, the EDS gap width  248  is relatively large, and accordingly, the LSM levitating force is relatively strong and the EDS levitating force is relatively weak.  
         [0048]    In the embodiment shown in FIG. 8, maximum LSM efficiency is obtained at high vehicle speeds (i.e. operating speeds). In greater detail, the EDS force is strongest at high vehicle  212  speeds. Since this force is repulsive between the EDS magnet array  228  and EDS conductive track  224 , a relatively large EDS gap width  248  occurs at high vehicle speeds. Accordingly, a relatively small LSM gap width  238  occurs at high vehicle  212  speeds. As indicated above, the LSM is most efficient at small LSM gap widths  238 . Thus, for the FIG. 8 embodiment, the LSM is most efficient at operating speed.  
         [0049]    Mathematically, the stability of the system can be shown by calculating the LSM levitation force as a function of LSM gap and comparing it to the EDS levitation force. Starting with the LSM system, the magnetomotive levitation force, θ can be calculated as:  
         θ=Rφ  Eq. 1  
         [0050]    where R is reluctance,  
         1     Ω                 sec       ,                         
 
         [0051]    and  
         [0052]    φ is the Flux, V·sec x 10 −8  (Maxwell) the reluctance can be calculated as:  
             R   =     ∑     l       μ   0        μ                 A                 Eq   .              2                               
 
         [0053]    where  
         [0054]    l is the length of magnetic circuit (general) cm,  
         [0055]    μ 0  is the permeability of vacuum, (1.256×10 −6  Ω·sec/cm),  
         [0056]    μ is the permeability constant (≅1 for air), and  
         [0057]    A is the cross-sectional area of circuit path segment, cm 2 . Summing over the magnetic circuit path, the magnetomotive force is:  
             θ   =     φ        (         l   0         μ   0        μ                 A       +       l   g         μ   0                   A         )               Eq   .              3                               
 
         [0058]    where l 0  is the length of permanent magnet bridge in cm and l g  equals the total length of all air gaps. The flux can be calculated as:  
         φ=BA   Eq. 4  
         [0059]    where B is the magnetic field in gauss.  
         [0060]    Combining Eq. 3 and Eq. 4:  
             θ   =     BA        (         l   0         μ   0        μ                 A       +       l   g         μ   0                   A         )               Eq   .              5                               
 
         [0061]    which can be simplified to:  
             θ   =       B     μ   0            (         l   0     μ     +     l   g       )               Eq   .              6                               
 
         [0062]    Eq. 6 can be solved to obtain the magnetic field:  
             B   =         μ   0        θ       (         l   0     μ     +     l   g       )               Eq   .              7                               
 
         [0063]    For an initial air gap l g1 , the magnetic field is:  
               B   1     =         μ   0        θ       (         l   0     μ     +     l     g                 1         )               Eq   .              8                               
 
         [0064]    and for an air gap l g2 , the field is:  
               B   2     =         μ   0        θ       (         l   0     μ     +     l     g                 2         )               Eq   .              9                               
 
         [0065]    Equations 9 and 10 can be combined to obtain an expression relating the field B 2  with the air gap l g2 , and the field B 1  with initial air gap l g1 :  
               B   2     =         B   1                l   0     μ     +     l     g                 1               l   0     μ     +     l     g                 2             ≅       B   1            l     g                 1         l     g                 2                     Eq   .              10                               
 
         [0066]    The levitation force can be calculated as:  
               F   =         B   2        A       2                   μ   0                
          thus   :             Eq   .              11                   F   1       F   2       =       B   1   2       B   2   2               Eq   .              12                               
 
         [0067]    and solving Eq. 12 for F 2 :  
               F   2     =       F   1            B   2   2       B   1   2                 Eq   .              13                               
 
         [0068]    combining Eq. 10 and Eq. 13:  
               F   2     =       F   1              (       B   1            l     g                 1         l     g                 2           )     2       B   1   2                 Eq   .              14                               
 
         [0069]    which can be simplified to obtain the LSM force as a function of LSM gap:  
               F   2     =         (       l     g                 1         l     g                 2         )     2          F   1               Eq   .              15                               
 
         [0070]    A similar analysis can be conducted for the EDS system. The peak magnetic field at the surface of Halbach array, B 0 , is:  
               B   0     =         B   r          (     1   -     e     -   kd         )              sin        π   m         π   m                 Eq   .              16                               
 
         [0071]    where: B r  is the residual permanent magnet flux density,  
         [0072]    m is the number of magnets in array  
       k   =       2      π     λ                           
 
         [0073]    with λ=wavelength of the Halbach array, and  
         [0074]    d is the permanent magnet thickness.  
         [0075]    The lift pressure can be calculated as:  
               p   y     =         B   0   2     μ          (     1     1   +     α   2         )          e       -   2        ky                 Eq   .              17                               
 
         [0076]    where μ is the permeability constant (≅1 for air) and  
       α   =     1       ω                 L     R                             
 
         [0077]    where: L is the inductance of guideway Henry&#39;s, H,  
         [0078]    R is the resistance of guideway, Ω, and  
       ω   =       2      π                 v     λ                           
 
         [0079]    with v being the vehicle velocity in m/sec.  
         [0080]    The lift force can be calculated as:  
         K y =p y A  
         [0081]    where A is the footprint. For an initial EDS gap y 1 ,  
                 p     y   1       =         B   0   2     μ          (     1     1   +     α   2         )          e       -   2          ky   1                  
          Thus   ,             Eq   .              18                 K     y   1       =         AB   0   2     μ          (     1     1   +     α   2         )          e       -   2          ky   1                   Eq   .              19                               
 
         [0082]    and for an EDS air gap y 2   
               K     y   2       =         AB   0   2     μ          (     1     1   +     α   2         )          e       -   2          ky   2                   Eq   .              20                               
 
         [0083]    combining Eq. 19 and Eq. 20:  
               K     y   2       =       K     y   1                     -   2          ky   2                  -   2          ky   1                     Eq   .              21                               
 
         [0084]    which can be simplified to obtain the EDS force at any gap y 2  based on the EDS force at the initial EDS gap y 1 .  
           K   y2   =K   y1   e   2k(y     1     -y     2     )    Eq. 22  
         [0085]    Typical values for the above equations are:  
           B   0   =B   1 =1  T  ( T =Tesla=10 4  Gauss)  
         [0086]    l 0 =12 cm  
         [0087]    μ=1600  
         [0088]    v=22 m/sec  
         [0089]    λ=0.4 m, and  
         [0090]    k=15.7 m −1    
         [0091]    The variation in EDS and LSM force as a function of EDS and LSM gap can be tabulated (see below) and graphed (see FIG. 9) to show the stability of the system. The tabulation below assumes an initial LSM gap of 1 cm, initial LSM force of 100, initial EDS gap of 1 cm and initial EDS force of 100.  
                                                       l g     F                       0.25   1600           0.5    400           0.75   178           1.00   100           1.25   64           1.50   44.4           1.75   32.7           2.00   25                       y   K                       0.25   126.6           0.5    117           0.75   108           1.00   100           1.25   92           1.50   85           1.75   79           2.00   73                      
 
         [0092]    While the particular Magnetic Levitation and Propulsion System as herein shown and disclosed in detail is fully capable of obtaining the objects and providing the advantages herein before stated, it is to be understood that it is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.