1

Laboratory Prototype of a Launcher Device by Electromagnetic Propulsion using Superconducting

Materials

Ricardo Miguel Ramos Almeida Electrical Engineering Department Instituto Superior Técnico, UTL

Lisbon, Portugal

Abstract— This paper discusses the design and construction of a linear electromagnetic propulsion system that makes use of the property submitted by the diamagnetic superconducting materials. This system consists of two parts: the excitation field system (fixed structure), consisting of several independent magnetic circuits aligned, and the vehicle (mobile system), where it was used a structure with wheels on rails, where a block YBCO (Yttrium barium copper oxide) superconducting material is inserted.

The operation of the implemented propulsion system is based on creating a traveling magnetic wave in the excitation field system, synchronous with the position of the vehicle which the interaction between the magnetic field produced by each vehicle and the superconducting material in, due to the Meissner effect, gives rise to an impulse on the vehicle in synchronism with its displacement.

It was analyzed the magnetic circuit and magnetic field distribution of the excitation field system, was finally given the resulting force, vehicle’s velocity, impulse and the contribution of each magnetic circuit.

In conclusion, it was verified that the magnetic circuits have different contributions depending on the vehicle velocity. The results were compared and analyzed in relation to those provided by the developed model for the propulsion system. Keywords- Linear electromagnetic propulsion system,

superconductor, Railgun, Coilgun.

I. INTRODUCTION

Man has always been compelled to travel, transporting materials and hurl / throw, in order to survive [1]. Currently the four key technologies for propulsion systems are: [2] [3] [6]

− The mechanical propulsion brings together, for instance, gears and mechanisms that leverage renewable energy sources.

− The thermodynamic propulsion combines the steam system and internal combustion engines.

− The chemical propulsion includes rockets propulsion and rocket launchers.

− The electric propulsion covers various electromechanical systems such as electrothermal propulsion, electrostatic propulsion and electromagnetic propulsion.

This paper addresses the development of a linear electric launcher device based on the characteristic of a diamagnetic YBCO superconducting, considering the linear electromagnetic propulsion technology [4] [5] [7] as the most suitable for this application.

A. Main systems of linear electromagnetic propulsion

The railgun and coilgun are the two main linear electromagnetic propulsion systems. The railgun system [8] [9] [10] [12] [15] is based on the principle of the homopolar motor, and characterized by two conducting current rails and also a conducting current material projectile. The flowing current in the system generates in the vehicle a magnetic field with a vertical direction, which combined with the electric current through the vehicle gives rise to a force on the vehicle, pushing it along the rails. This system has two major problems: heavy losses by Joule effect and friction in the contact between the vehicle and rail. The system coilgun [11] [12] [13] as depicted in Fig.1, works by establishing a current in each coil in sequence along the propulsion system, producing an attractive force on the projectile that will move synchronously with the sequential establishment of the magnetic field.

Figure 1 - Diagram of the propulsion system "coilgun"

This system requires a sub-system that controls the current, but can be changed without losing its characteristics. One of the changes can be, for instance, putting the coils perpendicular to the path of the vehicle.

B. Forces in superconducting materials

The superconductor is a perfect diamagnetic material, because it blocks drilling along the magnetic field due to a magnetic flux generated by currents induced in the opposite direction to the external magnetic field. This phenomenon is defined as Meissner effect [14] [15] [16]. When the superconductor is surrounded by a not uniform magnetic field, the Meissner effect originates the removal forces on the

2

surfaces of the superconductor, as illustrated in Fig 2. The combination of all forces generates a resulting force.

Figure 2 - Diagram of forces generated by Meissener effect in the superconductor.

II. MODELLING THE PROPULSION SYSTEM USING

SUPERCONDUCTING MATERIAL

A. Modeling of an ideal solution

The propulsion system consists of two main parts: an excitation field system, responsible for generating a traveling magnetic field wave (B), synchronous with the motion of the vehicle; and the vehicle itself consists of diamagnetic material (superconducting material) inside and where it operates a force (F) of magnetic origin, arising from the Meissner effect, causing on the vehicle a movement of displacement with a certain speed.

B. Concretion of excitation field system

The Fig.3 shows a first substantiation of the excitation field system, which is used two linear stators in parallel, as the superconducting material in the middle of them.

B

F

Figure 3 - Schematic of the propulsion system with

continuous linear stator in excitation and superconductor

Using a continuous linear stator allows a propagation of a continuous magnetic field wave along its length origins a continuous force and consequently a continuous displacement in the superconductor. However, the implementation of this laboratory excitation field system might be complex for a first study of this kind of system, due to generation of continuous magnetic field wave and the need for specific measure materials.

C. Theoretical analysis of electromechanical propulsion system

1) Implementation of the excitation field system by

independent magnetic circuits

Regarding the synchronism required between the vehicle's position and the position of the magnetic field wave generated by the excitation field system, it is achieved in a discreet form by independent magnetic circuits as shown in Fig.4. The propulsion system consists of independent magnetic circuits in sequence and each magnetic circuit is excited in synchronism along the movement of the vehicle, which is caused by the Meissner effect.

B B x

y

z

Figure 4 - Representation of the excitation system implemented

in a discrete form

The Fig.5 illustrates the functioning of an independent magnetic circuit in three dimensions.

B

Supercond.

Figure 5 - Independent magnetic circuit functioning

2) Defining the Magnetic Field

Using the software Comsol Multiphysic 3.2 is feasible to simulate the behavior of the magnetic field in the magnetic circuit by the finite element method.

Fig.6 presents the simulation results. It shows that there is a higher density of magnetic field inside the circuit than air gap, where there is no superconductor. Thus it’s determined the magnetic field B in A and B surfaces, where I is current, N is the number of turns of the winding, f is the thickness of the circuit, δ is the distance between the superconductor and the magnetic circuit, x is the distance already traveled by the vehicle and Rm the magnetic reluctance in A or B surfaces.

Figure 6 - Simulation result of the magnetic fieldindependent magnetic circuit

A BmA mB

N.I N.IB B

R (f .x) R (f . )= =

Besides the theoretical model of the magnetic field of the magnetic circuit, an experimental prototype was constructed (Fig.7) to validate the model.

Figure 7 - Photograph of the prototype

The magnetic field on the surfaces A and B of the superconductor were measured with a probeconsidering x=1cm, x=2cm and x=3cm. graph present on Fig.8

Figure 8 - Graph of the vertical distribution of field Bsurfaces A and B of the superconductor

Enrolamentos Circuito

magnético

Supercondutor Superconductor

Winding MagneticCircuit

B

Ax

d

CD

0 0.02 0.04 0.06 0.08 0.1 0.120

2

4a) x=1cm

B [T]

Ver

tical

dis

tanc

e [c

m]

0 0.02 0.04 0.06 0.08 0.1 0.120

2

4b) x=2cm

B [T]

Ver

tical

dis

tanc

e [c

m]

0 0.02 0.04 0.06 0.08 0.1 0.120

2

4c) x=3cm

B [T]Ver

tical

dis

tanc

e [c

m]

Supercondutor

Windwing Magnetic Circuit

3

of the magnetic field in the

independent magnetic circuit

N.I N.I

R (f .x) R (f . )δ

Besides the theoretical model of the magnetic field of the magnetic circuit, an experimental prototype was constructed

Photograph of the prototype

The magnetic field on the surfaces A and B of the ith a probe of Hall effect,

Resulting on the

Graph of the vertical distribution of field B in the superconductor

Observing Fig.8, it’s conclude that there is greater field density B on the surface A than on the surface B, and there is also the highest density of magnetic the surface A, therefore consider useful area

Figure 9 - Representation of useful area (surface A

Table 1 point out the results of the average magnetic field in useful surface area A measured experimentally obtained by the theoretical model (analytical and simulation).

Table 1 - Results of field B

Analyzing the results presented in Table 1, for N=600 and I=4A, the analytical field position x, because the model createdthroughout all the excitation system. error appears to increase with theof the field B, the experimental measurement errors (bad position of the probe and difficult to control the temperature of the superconductor) and the values of magnetic permeability used in the simulation were defined based on some experimental measurements.

3) Determination of Resulting Force

The resulting force F is a conjunctiongenerated by Meissner effect in superconductingthe deduction of analytical force surfaces A and B of the superconductor, Maxwell Stress Tensor [17]. The equation of forcetangential component B of the magnetic field magnetic permeability of air and surfaces A and B.

sF .S 2

≈

To complete the theoretical forceMaxwell Stress Tensor model calculated the resulting force to a amps and a distance x of 1 cm to 3.5 cm,cm.

The previous prototype was developedtheoretical results, adding wheels and rails, and usingsensor to measure the resulting

Circuito

magnético

Vista

Frontal

Vista

Superior Magnetic

Circuit

TopView

FrontView

f

0.14 0.16

0.14 0.16

0.14 0.16

Surface ASurface B

Surface ASurface B

Surface ASurface B

Supercondutor

Ferro

Área considerada

x [cm] Banalytical [mT] Bsimulated [mT]

1,0 151 121

2,0 151 125

3,0 151 124

useful area

Superconductor

Magnétic circuit

Magnetic Circuit

conclude that there is greater field on the surface A than on the surface B, and there is

also the highest density of magnetic field in the central area of therefore consider useful area (2cm2) of Fig.9.

Representation of useful area (2cm2) at the surface A

results of the average magnetic field in useful surface area A measured experimentally obtained by the theoretical model (analytical and simulation).

Results of field B to 3 x positions

Analyzing the results presented in Table 1, it’s check that 4A, the analytical field B is equal to any

the model created is considered uniform ghout all the excitation system. On the other hand, the

with the position x due to edge effects , the experimental measurement errors (bad

position of the probe and difficult to control the temperature of the superconductor) and the values of magnetic permeability used in the simulation were defined based on some

Determination of Resulting Force

a conjunction of vector forces Fs

r effect in superconducting surfaces. For the deduction of analytical force Fs, the useful area of the surfaces A and B of the superconductor, it’s used the method of

The equation of force Fs has the of the magnetic field B, the µ0 is the

magnetic permeability of air and S is the useful area of the

2

0

BF .S

2µ

complete the theoretical force model it’s used the model of Comsol Multiphysics and

force to a direct current I from 2 to 8 1 cm to 3.5 cm, in intervals of 0.5

was developed to confirm the dding wheels and rails, and using a force

force, as shown in Fig.10.

δ

Ferro

Bexperimental [mT] Error [%] ((Bsim.- Bexp.)/Bsim.*100)

127 5,0%

134 7,2%

146 17,7%

Magnétic circuit

a)

b)

Figure 10 - a) Picture of the prototype during a test of strength, b) Picture of the vehicle, c) Picture

superconductor

Fig.11 show the graph with the resulting force F calculations achieved by the theoretical model (analytical and simulated) and tests on experimental prototype.

Figure 11 - Graphs of resulting force from tmethod, simulated and experimental

As the graphs (Fig.11) show above, the varies quadratically with the current. It seems likesituations, the simulated and experimental results have significant error, however, the analytical results show a high error ranging between 21% and 32% This discrepancy results from simplifications and considerations made during the deduction of the analytical model, such as a uniform field the ideality of materials, the contempt of magnetic leakage

Winding Magnetic Circuit

Force Sensor

Vehicle Rail

Copper box containing the superconductor

F x

Wheels

Supercond.

Copper box

Reflector

2 3 4 5 6 7 80

5

10

I [A]

F[N

]

a) x=1cm

2 3 40

5

10

F [N

]

b) x=1,5cm

2 3 4 5 6 7 80

5

10

I [A]

F [N

]

c) x=2cm

2 3 40

5

10

F [N

]

d) x=2,5cm

2 3 4 5 6 7 80

5

10

I [A]

F [N

]

e) x=3cm

2 3 40

5

10

F [N

]

Analytical ForceSimulated ForceExperimental Force

4

c)

of the prototype during a test of Picture of the

graph with the resulting force F by the theoretical model (analytical and

prototype.

from the analytical method, simulated and experimental

the resulting force seems like, for all

, the simulated and experimental results have low the analytical results show a high

This discrepancy results from simplifications and considerations made during the deduction of the analytical model, such as a uniform field B,

agnetic leakage and

consider only the tangential field Maxwell Stress Tensor.

The resulting force F of the three methods to a currentI=7A, along with the position confirm that the analytical method has aother methods show that up to surface B greatly diminishes the force 3] cm the resulting force is maximum and constant. In the last interval, x=[3 3.5] cm, the resultingdue to the no uniformity of the

Figure 12 - Resulting force

III. VEHICLE D

To put the vehicle in motion, prototype shown in Fig.13. Position sensors and the reflectorare fundamental in this propulsion system,synchronized the vehicle and the magnetic field, as explained before in the introduction. It is important to noticemust be an interval between the circuits because of the dimensions of the windings.

Figure 13 - Prototype propulsion system

A. Verification of friction between wheels and rail

To develop a theoretical model necessary to estimate the value of friction between the wheels and rails. Using the method of the inclined planachieves a system which intervene and the frictional force Fa. Ngravitational acceleration and αand the horizontal plane. Using an ultrasonic

Force Sensor

4 5 6 7 8I [A]

b) x=1,5cm

4 5 6 7 8I [A]

d) x=2,5cm

4 5 6 7 8I [A]

f) x=3,5cm

1 1.5 24.5

5

5.5

6

6.5

7

7.5

8

F [N

]

Force - x (I=7A)

Analytical Force

Simulated Force

Experimental Force

Superconductor

Vehicle

Copper box

Reflector

consider only the tangential field B in the calculation of the

of the three methods to a current position x, as illustrated in Fig.12,

the analytical method has a significant error. The other methods show that up to x=2cm the force Fs of the

greatly diminishes the force F. On the interval x=[2 force is maximum and constant. In the last

resulting force returns to decrease magnetic field.

force F along x diagram, for I=7A

DYNAMIC MODEL

To put the vehicle in motion, it was developed the Position sensors and the reflector

this propulsion system, because they the vehicle and the magnetic field, as explained

It is important to notice that there must be an interval between the circuits because of the

rototype propulsion system scheme

Verification of friction between wheels and rail

To develop a theoretical model as experimental model is ssary to estimate the value of friction between the wheels

Using the method of the inclined plane (Fig.14), it intervene only the gravity force Fg

N is the normal force, g is the α is the angle between the rails

Using an ultrasonic sensor is possible

2.5 3 3.5x [cm]

Force - x (I=7A)

Magnetic Circuit

Position Sensors

rails

Winding

5

to evaluate the vehicle's acceleration during descent way and thus determine the friction.

Figure 14 - Inclined plane scheme

The following equation enables to calculate the coefficient

of friction of the system (βc).

c

dvg.sen( ) dtg.cos( )

α −β =

α

Considering that M is the mass of the vehicle and v its velocity, it has as a theoretical dynamics model of the propulsion system:

2

c0

Bdv.S .g.cos( )

dt 2M

dxv

dt

= − β α µ

=

B. Experimental tests of position and velocity

The theoretical dynamic model can be validated by

comparing the calculated velocity from the model with experimental velocities achieved from the prototype. With a provided current of 4 amps on the windings, it was considered four values for vehicle mass M: 300gr, 800gr, 1100gr and 1200gr.

Using a positioning-time ultrasonic sensor on prototype it can be determined the experimental velocity. Thus, it is pointed out on the graphs from Fig.15 to Fig.18, the representation of theoretical velocity (o) and experimental velocity (blue). Furthermore, the location of magnetic circuits is represented on the abscissa axis.

The data experimentally obtained by the ultrasonic sensor had to be developed, due to the sampling frequency. Therefore the data were filtered, then derived (in order to achieve the velocity) and finally filtered again.

Figure 15 - Graph of experimental and theoretical velocity for

a vehicle with a mass=300gr

Figure 16 - Experimental and theoretical velocity graph for a

vehicle with a mass=800gr

Figure 17 - Experimental and theoretical velocity graph for a

vehicle with a mass=1100gr

Figure 18 - Experimental and theoretical velocity graph for a

vehicle with a mass=1200gr

The four previous figures show that the vehicle increases its velocity when it is in the magnetic circuit air gap and decreases velocity when is in the interval between magnetic circuits. Each magnetic circuit provides a different increase of velocity, because the resulting force value is constant in all circuits. When the velocity is increased the vehicle is less time in the air gap, and the force is applied for less time, so we have less acceleration and less increase in velocity. There are two possible solutions to this problem, one is build circuits with increasing magnetic sizes along the path, the other is creating an increasing intensity of magnetic field along the path, which may be obtained by changing the current or the number of turns of the windings.

Vehicle

α

Fg

Fg.sen(α)

Fa

Rails Fg.cos(α)

N

α

π/2-α

0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3

0

0.5

1

1.5Graphic x-v (vehicle mass: 300gr)

x [m]

v [m

/s]

Experimental velocityTheoretical velocity

0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Graphic x-v (vehicle mass: 800gr)

x [m]

v [m

/s]

Experimental velocityTheoretical velocity

0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Graphic x-v (vehicle mass: 1100gr)

x [m]

v [m

/s]

Experimental velocityTheoretical velocity

0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Graphic x-v (vehicle mass: 1200gr)

x [m]

v [m

/s]

Experimental velocityTheoretical velocity

6

Considering experimental data, it seems that all graphs demonstrate theoretical and experimental velocities similar to x=0.07m. On the remaining path, the difference between theoretical and experimental velocity will depend on the speed of vehicle. Suggesting that there is a reduction of the resulting force caused by currents induced in the superconductor, when it crosses the air gap, creates a magnetic field on opposite direction to the magnetic air gap, and turns lower the magnetic field B as well as the resulting force.

However, the theoretical model shows acceptable results, especially for lower velocities.

C. Impulse of the vehicle determination

The impulse is defined by the movement quantity variation of the vehicle.

If ∆v is the variation on velocity, the impulse I is given by:

I M. v= ∆

As illustrated on Fig.15 to Fig.18 is possible to determine the value of the impulse given to vehicle by the propulsion system, as illustrated in Fig.19.

Figure 19 – Vehicle impulse graph

The graph shows that the impulse is higher for a larger

mass of the vehicle. The error is higher for a smaller mass vehicle and it fades when comparing to the vehicle with larger mass.

This is the evidence that the error evolution increases when we increase as well the vehicle velocity.

1) Force exerted by the magnetic circuit on the vehicle

It is considered the force exerted on the superconducting magnetic circuit as the unit force Fu that can be defined by:

u

IF

t=

∆

The determination of I in each impulse on the excitation field circuit and the determination of the duration of the vehicle in the air gap ∆t enables to calculate the unit force exerted by each magnetic circuit on the vehicle.

Table 2 – Theoretical Unit Force

Table 3 – Experimental Unit Force

Theoretical and experimental values of unit force, present on tables 2 and 3, represent four magnetic circuits of the propulsion system and the four vehicle mass values. It seems that the theoretical unit force is constant in the four magnetic circuits for a given mass, but on contrary on the experimental unit force it is not.

Table 4 – Percentage error between the theoretical and

experimental unit force

Table 4 shows the percentage error between experimental and theoretical unit force, and is evidence that for any mass, in the first circuit the error value lower than 10% and can be considered a small error, especially for the masses of 300gr, 800gr and 1100gr. In the second and third magnetic circuits the error gets higher, however, on the fourth circuit it has the highest value. In sum, these results indicate that the circuits where the vehicle goes with higher velocity the error between the experimental and theoretical unit force is superior.

The cause of this effect has already been mentioned earlier, with the increase of vehicle velocity by current induced in the superconductor, which generates an induced magnetic field and decreases the intensity of the magnetic field inside the air gap, reduces the unit force on the conductor.

300 400 500 600 700 800 900 1000 1100 12000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Vehicle mass [gr]

I [N

.s]

Theoretical ImpulseExperimental ImpulseError

Force [N]

1st circuit

Force [N]

2nd circuit

Force [N]

3rd circuit

Force [N]

4th circuit

300gr 1,86 1,86 1,86 1,86

800gr 1,47 1,47 1,47 1,47

1100gr 1,24 1,24 1,24 1,24

1200gr 1,16 1,16 1,16 1,16

Force [N]

1st circuit

Force [N]

2nd circuit

Force [N]

3rd circuit

Force [N]

4th circuit

300gr 1,92 0,97 1,13 1,23

800gr 1,49 1,29 1,38 1,11

1100gr 1,28 1,27 1,06 0,98

1200gr 1,25 1,23 1,25 0,89

Error [%]

1st circuito

Error [%]

2nd circuito

Error [%]

3rd circuito

Error [%]

4th circuito

300gr 3,1 48,0 39,4 33,9

800gr 1,0 12,0 6,4 24,3

1100gr 2,9 2,6 14,7 21,0

1200gr 9,1 5,6 7,9 23,5

7

Figure 20 – Unit Force for a vehicle with a mass=1100gr

As an example, Fig.20 illustrates the evolution of both unit forces to the mass of 1100gr, disclosing that for lower velocities, the experimental unit force is similar to the theoretical unit force. However, with increasing velocity on the third and fourth magnetic circuits, the experimental force decreases in comparison with the theoretical force.

IV. CONCLUSION

Regarding the several types of existing propulsion systems, in this particularly case, it was designed and built an electromagnetic propulsion system with the excitation system by independent magnetic circuits, that were set aligned in a path, including a vehicle with perfect diamagnetic properties, using a superconducting material. This propulsion system applies a synchronous magnetic field to the circuit, which with the motion of the vehicle, due to the Meissner effect, provides a repulsive force.

The magnetic field was analyzed with superconductor in the air gap existing on the magnetic circuit, as well as the force that causes the magnetic field by the Meissner effect. It was found as a result that the magnetic field has more intensity in surface A and B of the superconductor and also on the surface area of 2cm2. Besides this, the force was not constant, it depended on the intensity on the magnetic field and on the superconductor position within the air gap.

The velocity of the vehicle was also examined and it was concluded that each circuit of excitation contribute differently for the vehicle’s velocity. Thus, on the first circuit there is a superior increased of velocity, when comparing with the fourth circuit, that shows a less velocity increase.

The theoretical and experimental velocities reveal a small difference between slower velocities, but with the increase of velocities the differential is higher.

Analyzing the impulse and the unit force it can be concluded that the theoretical and the experimental model, have an error that occurred depending on the increasing of velocity.

In conclusion, the theoretical model sets reasonably well the experimental model, especially for low speeds.

V. REFERENCES

[1] Elior de Oliveira Faria, “Histórias dos Transportes Terrestres no Mundo”, Universidade Federal do Rio de Janeiro, http://www.transitocomvida.ufrj.br/download /Hist%F3ria%20dos%20transportes%20terrestres.pdf

[2] Lino Guzzella ; Antonio Sciarretta, “Vehicle Propulsion Systems : introduction to modeling and optimization”, Springer, segunda edição, 2007.

[3] Paul A. Czysz e Claudio Bruno “Future Spacecraft Propulsion Systems”, Springer, 2009, pp. 11-13.

[4] Rodolfo A. D. Oliveira, A. Leão Rodrigues, “Desenho e Construção de um Motor Linear de Indução de Baixa Velocidade”, DEE-FCT, Univ. Nova de Lisboa.

[5] Davide Sérgio Baptista da Fonseca, “Accionamento Linear de Relutância Variável Comutado para Tracção Eléctrica Ligeira” Tese de Doutoramento da Univ. da Beira Interior, 2008

[6] Robert G. Jahn , Edgar Y. Choueiri “Electric Propulsion: Encyclopedia of Physical Science and Technology” Third Edition, Volume 5

[7] Kurt J. Kloesel, Jonathan B. Pickrel e Emily L. Sayles,“First Stage of a Highly Reliable Reusable Launch System” AIAA SPACE 2009 Conference & Exposition, Pasadena - California.

[8] Victor Sung,“Lumped Parameter Modeling of the Ideal Railgun: Examining Maximum Electromechanical Energy Conversion Efficiency” Rose-Hulman Institute of Technology,

[9] S. Barker, Ben Roberts e outros. “A Power Supply Oriented Small-Caliber EML Design Methodology”, Final Report to the U.S. Army Research Laboratory, Maryland, 2005

[10] Matthew Assey, “General Railgun Function” http://www.matthewmassey.com/ RailgunTheory.pdf

[11] T. J. Burgess, E. C. Cnare, W. L. Oberkampf, S. G. Beard, and M. Cowan, "The Electromagnetic Theta Gun and Tubular Projectiles", IEEE Transactions on Magnetics, VOL. MAG-18, NO. 1, January 1982

[12] Henry Kolm, Kevin Fine, Fred Williams and Peter Mongeau, “ELECTROMAGNETIC GUNS, LAUNCHERS and REACTION ENGINES” Massachusetts Institute of Technology, Francis Bitter National Magnet Laboratory, Cambridge, Massachusetts, 1980.

[13] Wikipédia, a enciclopédia livre. Railgun e Coilgun. [Online] [Citação: 27 de Setembro de 2010.] http://en.wikipedia.org/wiki/Railgun e http://en.wikipedia.org/wiki/Coilgun

[14] Bruno Miguel Carones Painho, “Protótipo Laboratorial de um Veículo de Levitação Magnética (MAGLEV) com Utilização de Supercondutores”, Tese de Mestrado Integrado em Eng. Electrotécnica e de Computadores de Outubro de 2009, DEEC-IST, UTL.

[15] Ricardo Nuno de Brito Barros André, “Protótipo Laboratorial de um Veículo de Levitação Magnética (MAGLEV) com Utilização de Supercondutores” Tese de

0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x [m]

F[N

]Unitary Force (vehicle mass=1100gr)

Unitary Theoretical Force Unitary Experimental Force

8

Mestrado Integrado em Eng. Electrotécnica e de Computadores de Setembro de 2007, DEEC-IST, UTL.

[16] F. M. Araújo-Moreira, A. J. C. Lanfredi, C. A. Cardoso, W. Maluf, e outros ”O fascinante mundo dos materiais Supercondutores” Revista Univerciência, Brasil, Dezembro 2002.

[17] Herbert H. Woodson e James R. Melcher, “Electromechanical Dynamics – Part II: Fields, Forces and Motion”, Robert E. Krieger Publishing Company.