Post on 17-Oct-2019
DEMO 2010/1
ΑΡΙΘΜΗΤΙΚΗ ΜΕΛΕΤΗ ΕΝΟΣ ΗΛ/ΜΑΓΝΗΤΙΚΟΥ ΕΚΤΟΞΕΥΤΗΡΑ
Θ. Ε. ΡΑΠΤΗΣ
NNNNumerical umerical umerical umerical Study of anStudy of anStudy of anStudy of an E/M E/M E/M E/M LauncherLauncherLauncherLauncher. . . .
T. E. RAPTIS
ΕΚΕΦΕ «∆ΗΜΟΚΡΙΤΟΣ»
153 10, T.Θ. 60228, ΑΓ. ΠΑΡΑΣΚΕΥΗ ΑΤΤΙΚΗΣ, ΕΛΛΑΣ
“DEMOKRITOS”
National Centre for Scientific Research
153 10, PO Box 60228, AG. PARASKEVI, ATTIKI, GREECE
AΡΙΘΜΗΤΙΚΗ ΜΕΛΕΤΗ ΕΝΟΣ H/M ΕΚΤΟΞΕΥΤΗΡΑ
Θ. Ε. Ράπτης
ΕΚΕΦΕ «∆ΗΜΟΚΡΙΤΟΣ»
∆ιεύθυνση Τεχνολογικών Εφαρµογών (rtheo@dat.demokritos.gr)
NUMERICAL STUDY OF AN E/M LAUNCHER
T. E. Raptis
NCSR “DEMOKRITOS” Division of Applied Technology
(rtheo@dat.demokritos.gr)
Aθήνα, 22, Ιανουαρίου, 2010
Athens, 22, January, 2010
DEMO 2010/1
Numerical Study of an E/M Launcher.
T. E. Raptis
National Centre for Scientific Research “Demokritos”
Division of Applied Technologies
rtheo@dat.demokritos.gr
Abstract: We report on a new design for an Electromagnetic Launcher (EML)
which combines both magnetic levitation and propulsion characteristics based on an
asymmetric combination of dipoles superposed on a simple magnetic rail. We
provide both a pole method and a Finite Element analysis of a planar section of the
overall configuration of a single accelerating stage and derive the force
characteristics. We also describe the limitations of this system with respect to actual
applications
1. Introduction
The subject of Electromagnetic Launchers (EML) has recently been introduced
as an alternative method for propulsion as well as for defense applications due to its
simplicity and its capability to abolish chemical propellants.
While a lot of work has been done which can be found in a number of
conference proceedings on the subject [4 - 6] the main point of view is towards the
rail-gun and coil-gun concepts. These are more or less directly based on the current
interaction in order to produce a subsequent Lorentz force as the main propulsion
mechanism. A review of the various types of configuration of coilguns can be found
in [10] with a direct comparison of their properties.
Lately, NASA developed an alternative technology (ELAM) [11] based on the
combination of a Maglift rail similar to the one used in the magnetic train
(MAGLEV) for levitation purposes associated with a linear induction motor for
acceleration with promising results. In this report we examine a slightly different
mechanism which provides for both simplicity of construction and for simultaneous
levitation and propulsion forces.
Although this technology is not yet mature enough for a full scale Mass Driver
capable of directly setting a vehicle into Earth’s orbit it has other potential
applications. Its main advantage would be that of reducing the cost by cutting the
propellant weight in a two-stage assisted launch system. Other applications include
replacement of old steam based aircraft boosters used in carrier ships at sea
operations.
In section 2 the main idea is presented with the aid of a simplified model based
on permanent magnets forming a magnetic catapult. It is shown through numerical
simulation that it is in principle possible to form the shape of the resulting potential
obtained with the method of poles through the introduction of an idealized
asymmetry in the rail magnet poles. In section 3 a realistic model based on
electromagnets is presented with a magnetic driving head with two separate
electromagnets carrying strongly asymmetric currents. A full FEM study of a planar
configuration based on the model of previous section is performed and the force
curve is derived by sliding the driving head across the magnetic rail. An approximate
equation of motion for a vehicle is also deduced and the limitations of the device
functioning in open air are explored.
2. A simple magnetic catapult
A basic model can be introduced using permanent magnets that form a two-
part system composed of a 1) driving head with a two pole bar magnet shaped so that
the two poles both face downward and 2) a magnetic rail with a number of dipole
moments equally distributed and directed towards the normal to the ground plane.
This configuration is shown in Fig. 1
A first analysis of a “slingshot” effect in a linear arrangement of permanent
magnets has been given by D. Roper [3]. To this aim the method of poles has been
employed in order to obtain an approximate potential describing the forces between
the poles. Assuming an equally distributed amount of magnetic charge across the
surface of each pole in the form wm / where w is the length of the pole surface one
can write the potential energy of the interaction between two separate magnetic poles
as
( )[ ]∫ =+−′
=L
a
w
mm
yxx
dxV
0
2/122
,β
αβ µµ (1)
With recourse to Fig. 1, where g is the gap between the rail magnets, w and h is the
length and height respectively of each identical rail magnet, l is the length of the
driving head while the length of each head pole is also w, one gets the total potential
function which upon integration yields
1
{ }M
NN NS SN SS
n
V V V V V=
= − − +∑ (2a)
2 2
2 2ln
np np ij
ij n
nm nm ij
x x yV
x x yµ
+ + =
+ + (2b)
where
( 1) /2, , ( , )nm np nm ijx n g nw x l x x w y y h y= − + − = + = −m
A calculation with w = 2, h = 0.5, g = 1, l = 5.2, y = 1.5 and M = 50 results in
the potential of Fig. 2. We take initially µn = µ0 = 1 in arbitrary units (the log term
does not contribute to the dimensions). There it is shown that the system has an
average slope towards the positive direction of the z-axis.
We next try to improve this characteristic by introducing a modulation of the
rail dipole moments in the form of a “frozen” stationary wave. To this aim we
introduce the modulated terms
+=
)(
2sin0
gwM
knn
πµµ
(3a)
+
+=)(
2sin10
gwM
knn
πµµ
(3b)
where M is the number of rail dipoles and k is an effective magnetization wavelength
for the frozen wave across the rail length. The new configuration and the associated
potentials for the two cases above are shown in Fig. 3-5 respectively for the values w
= 8, h = 0.4, g = 2, l = 10.4, y = 2, M = 6, L = 60, k = L/3 = 20, µ0 = 1.
Further testing with the above model showed that it is possible to shape the
potential in an almost linear smooth form by taking simply a linear variation of the
rail dipoles and an asymmetric distribution of magnetization on the head poles. An
important conclusion of this toy model is that such a catapult must be activated only
when the magnetically assisted launch vehicle is inside a certain useful range
between the barriers of the potential. This shows that a proper application requires
the use of electromagnets and an appropriate automatic control system (ACS). The
rail must then be constructed by a number of independent accelerating stages
activated with the aid of a mechanism similar to a photocell with the emitter located
on the vehicle and a receiver at each end of a separate such stage in order to activate
and deactivate the currents locally.
3. FEM modeling of the EML system
We propose here a simple and effective design of a full EML system
composed of a special driving head and a linear rail of electromagnets. In the
analysis that follows we used the finite element software FEMM4.2 by David
Meeker (www.femm.info) that is capable of handling a 2-dimensional planar
configurations.
In order to achieve an enhanced performance we design the driving head in a
special way. The head is now composed of two separate iron core gamma-shaped
electromagnets in order to introduce an asymmetry in the magnetic flux during the
interaction with the rail. A planar section of this configuration with the resulting
fields is shown in Fig. 6. The rail is composed of a series of iron core electromagnets
of which the current values fall linearly from a maximum to a minimum values like
InII ∆−= max .
Two simulations were performed under the condition that the rail current
limits are lesser or equal to those of the driving head. Under this condition both the
horizontal and vertical forces were found to be positive resulting into a simultaneous
levitation and propulsion effect. The forces were computed from the Maxwell stress
tensor as
[ ]nBHnHBnBH )()()(2
1•−•+•= ∫dCf (3)
using a square contour surrounding the driving head where n stands for the unit
vector normal to the contour while the driving head was moving from left to right
along the rail.
In both simulations 15 electromagnets were used for the rail elements with the
same indicative values for the currents of the driving head. These were 100 A for the
left part and 1000 A for the right one. The total head length and height were 160mm
and 80mm respectively with a 20mm inner diameter. The head coils had a winding
radius of 20mm and length of 80mm.
In the first simulation we used Imax = 500 A and Imin = 173.3 A with a step of
23.3A for the rail elements. The gap between the rail elements was 15mm and the
vertical distance from the head was 10mm. The coil length and height was chosen to
be 6mm and 50mm while the iron core length and height were 10mm and 60mm. In
Fig. 7 we show both the vertical and horizontal force components which were
sampled at steps of 5mm. The continuous line represents the horizontal propulsion
component while the discontinuous curve is the vertical repulsive component. In the
second simulation only the rail geometry and currents are changed. We chose Imax =
1000 A and Imin = 253.3 A with a step of 53.3A. The gap is also taken to be 5mm and
the vertical head distance to be 20mm. The rail coils length and height are 10mm and
50mm and the iron core length and height are 30mm and 60mm respectively. In Fig.
8 we again show the resulting force components.
It is observed that while the propulsive term has an almost smooth piecewise
linear behavior the repulsive levitation component has a strongly oscillating
characteristic which can be a source of instability. This can be compensated by the
addition of a separate magnetic levitation line which does not add to the propulsion
effect but acts in combination with the ACS to regularize the behavior of the total
repulsive term. A compensator can be part of the ACS in order to fill in the
oscillating terms of the accelerating line by a complementary force so that their total
would remain almost constant.
The propulsion term can be simulated relatively well by a piecewise parabolic
potential like the one of Fig 9 which is obtained by interpolating the force
components with two straight lines and integrating. The slope is the same on both
intervals but with opposite sign and equal to 240 for the data of Fig. 7. For a real
launcher it would be necessary to incorporate several accelerating stages which
correspond to a periodic repetition of the potential of Fig 9.
Assuming that the model can be scaled up to a realistic vehicle with an
accelerating stage of 300m one can estimate the efficiency of a multi-stage system by
studying the motion in open air. Including air resistance and a small lifting angle for
the launcher ramp and taking into account a small gap between accelerating stages as
an arbitrary parameter we may write an equation of motion in the form
φρ sin2
1 2 Mgdz
dVvSK
dt
dvM d −−−= (4)
where ρ is the air density ~1.2kg/m3
at 25o C, S is the cross section area of the
vehicle towards the air, Kd the drag coefficient ~0.05 – 0.1 for aerodynamically
shaped objects, V(z) is a scaled up periodic version of the potential of Fig 9
including a gap parameter and φ is the ramp angle.
The above was solved numerically for a mass of 1Kg, S = 0.1 m2, φ = 30
o and
a gap of 10 meters between subsequent accelerating stages. It is also assumed an
arrow shaped object with a minimum drag coefficient 0.05 which gives a total of
0.006 in open air for the velocity coefficient in (4). The result is shown in Fig. 10
where the solid line represents position and the dotted one the velocity. It is shown
that the system has a maximum limiting velocity of ~2km/sec which can be reached
in less than 0.3 sec. At this point the arrow has reached almost 600 m which proves
that it is inefficient to use more than two accelerating stages in open air.
It might be possible to reduce the air resistance using additional aerodynamic
effects like the well known “groung effect” first used in the Russian ekranoplane and
do the installation inside a tunnel. Study of the overall behavior in such a system is
more complicated than our simplified model used here and lies beyond the scope of
the present report.
4. Conclusions
In this report we show that it is possible to construct electromagnet based
systems that can be used for propulsion with purely magnetic forces. We designed a
system more complicated than existing coilguns that can work on open air in a way
similar to magnetic trains. It was shown that such a system can comprise an amount
of upward levitating forces and horizontal propulsion forces. Based on this we gave a
simplified model of motion which shows that the system can achieve strong
accelerations for a limited length after which it becomes inefficient due to increased
air resistance. Possible improvements are proposed that require a more detailed 3-
dimensional simulation in a tunnel.
References
[1] J. D. Jackson, “Classical Electrodynamics” (1975) Wiley
[2] P. Hammond, J. K. Sykulski, “Engineeering Electromagnetism” (1994)
Oxford Univ. Press
[3] D. Roper, http://www.roperld.com/Science/LinearMotor.pdf
[4] IEEE Trans. Magnetics Special Issue 27 1991
[5] IEEE Trans. Magnetics Special Issue 29 (1) 1993
[6] IEEE Trans. Magnetics Special Issue 39 (1) 2003
[7] A R Hoyle et al 2000 J. Phys. D: Appl. Phys. 33 120-126
[8] Ian R. McNab, IEEE Transactions on Magnetics, Vol. 39, No. 1, January
2003.
[9] D. Wetz et al., Acta Phys. Pol. A, 115 (6) 2009.
[10] T. G. Engel et al., Power Modulator Symposium, 2006. Issue , 14-18 May
2006 405 – 410
[11] AIAA, SAE, ASME, and ASEE, Joint Propulsion Conference, 26th,
Orlando, FL, July 16-18, 1990, NASA Tech. Report Server (NTRS)
FIGURES
Fig. 1
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Fig. 9
Fig. 10