Railguns
Paul Bosscher
ENGR 302
Prof. Ribeiro
5/16/01
Abstract
This paper presents the basics of what railguns are, why they were developed, and how
they work. It then proceeds to explain some of the more detailed physics and
electromagnetics that govern this device and its operation. Some of the specific
implementation issues are explored, and finally the future of railguns is discussed.
Outline
I.
Introduction and Overview
A.
B.
II.
What is a railgun?
History/Development
Railgun Physics
Equations – Including Biot-Savart Law, Ampere’s Law, Lorentz Force
III.
Railgun Implementation and Engineering Issues
A.
B.
C.
D.
IV.
Power – Compulsators
Rails – Materials and geometry
Slugs – Materials and geometry
Firing – Timing, slug injection
The Future of Railguns
A.
B.
Railgun uses/applications
Conclusion
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Introduction and Overview
Over the past few decades railguns have grown in popularity. After having been brought
into the public’s eye by the movie Eraser, many people are wondering how railguns work
and what the possibilities are for using them to develop futuristic high velocity weapons.
First developed in the 1970’s, railguns are a relatively new concept. A railgun is a
relatively simple device conceptually, using the flow of current through a loop to
generate a Lorentz force on a projectile, thereby accelerating it to high velocities. This
electromagnetic phenomenon is the same one used to power a linear DC motor. The
railgun is unique from other guns or cannons in that no chemical combustion is necessary
to fire the projectile. Railguns are, however, very inefficient. Rarely do railguns operate
with a total efficiency of over 2%.
The first railguns were tested in the early 1970’s at the Australian National University. In
the 1980’s, research into railguns increased drastically due to the United States’ initiation
of the Strategic Defense Initiative, nicknamed “Star Wars.” The goal of the initiative was
to place advanced weaponry in orbit to knock out enemy missiles from space. Although
originally conceived as a land based missile defense system, railguns were suddenly a
topic of heavy research and heavier funding from the “Star Wars” program. Many
different defense contractors worked on developing different versions of railguns, but the
degrees of success varied greatly.
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The basic components of a railgun include two rails, a projectile, an armature, an
insulating dielectric, the gun barrel, a power supply and a firing mechanism, as
diagrammed in Figure 1.
Figure 1) Schematic of a railgun barrel
The power supply and a firing mechanism are not shown in Figure 1, and would be
included at the base of the gun connecting the two rails together. The rails are spaced
apart by the width of the projectile, which slides between them as it is accelerated out of
the barrel. The plasma shown in Figure 1 is behaving as the armature. The armature is
an optional part of the design and will be discussed in more detail in the Implementation
and Engineering Issues section of this paper. As Figure 1 illustrates, the insulating
dielectric surrounds the rails and projectile and is itself surrounded by the gun barrel.
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Railgun Physics
The physics of a railgun are not conceptually difficult. The basic principles are
essentially the same as those for a linear DC motor. The current flowing through the rails
and armature forms a closed loop, which in turn creates a magnetic field as shown in
Figure 2.
Figure 2) Current and magnetic field within railgun
This magnetic field generates a Lorentz force on every part of the closed loop in an
outward direction. The railgun takes advantage of this phenomenon and uses the Lorentz
force to accelerate the armature and fire it out of the gun barrel. Although the process is
qualitatively simple, the physics get somewhat more complex due to the time varying
dynamics of the current, electric field, magnetic field, and position of the armature. Most
of the upcoming equations and their derivations can be found at http://www.railgun.org.
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First, the instantaneous induced magnetic field must be determined at any point as a
function of the loop geometry and loop current. This is given by the Biot-Savart law as:
(1)
where the integration is done around the path of the current in the direction of the current
flow and r is a vector from dl to the point at which the field is being evaluated.
At this point Ampere’s Law should also be considered:
(2)
Because the electric field can be expected to change with time, there will be some
contribution to the B field by the displacement current, but it is likely to be small. For
example, if a railgun used a 10 kV power source (very high), a loop perimeter of 0.1m
(very small) and a switch that switches in 1 ms, the resulting displacement current would
be roughly 1 A. This is dwarfed by the thousands and millions of amps that are used to
power these guns and can therefore be ignored.
To get a value for B(t), the Biot-Savart integral can be broken into four parts: the two
rails, the slug and the connection between the rails caused by the switch. It is assumed
that the connection at the switch, which in reality consists of a power source, the firing
relay and the connecting bus bar, can be modeled as a simple connection between the
rails.
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Given a rectangular conducting loop of dimension L x W, a current I, and the geometry
diagrammed as:
It can be shown that:
(3)
Thus the contribution to B of the first leg is:
(4)
The contribution to B of the second leg is:
(5)
The contribution to B of the armature is:
(6)
And the contribution to B of the switch or ‘back connection’ is:
(7)
Derivations of each of these are given in Griffiths’ Introduction to Electrodynamics.
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The total B field is a summation of the separate contributions:
(8)
Thus with some algebraic manipulation, the B field can be expressed as:
(9)
The loop of current flowing in this magnetic field generates a Lorentz force outwards on
each segment of the loop. Also included in in Griffiths’ Introduction to Electrodynamics
is an analytical expression for the Lorentz force:
(10)
where Barm refers to the field at the armature. Because the armature does not produce any
contribution to the B field passing through itself, this component of the expression for B
can be ignored. Thus, by eliminating this term and evaluating at the armature (x = L):
(11)
Combining this with (10) yields the final expression for the force on the armature:
(12)
Accordingly, the acceleration on any particular projectile would then be determined by F
= ma. The expression of the Lorentz force on the armature can be simplified by
introducing the term L1, the inductance gradient of the loop, reducing the expression to:
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Fmag
L1  I (t ) 2

2
(13)
This demonstrates the significance of the current to the effectiveness of the railgun and
why the addition of any resistance to the loop would decrease current and significantly
impair the acceleration of the projectile. Based on these equations, some experts
postulate that projectile exit velocities of 150 km/s are possible, but current technology
limits the maximum attainable velocities to roughly 10 km/s. In comparison, the
maximum velocity that a light gas gun has fired a projectile is less than 8 km/s.
Railgun Implementation and Engineering Issues
While the physics of railguns is fairly simple, applying those physics to a working design
is very difficult. The engineering design of railguns can be divided into four basic
categories: power, rails, slugs and firing.
One of the most difficult design aspects of railguns is providing them with sufficient
power. As shown in (13), the force with which a railgun propels the projectile is
proportional to the square of the current, thus it is imperative that the power source be
able to provide a tremendous amount of current. In order to provide the most
acceleration at the lowest power consumption, this high amount of current must be
provided at a relatively low voltage level. Early railgun projects used very large
generators, sometimes two stories high, to create up to 1.6 million amps of current. For
some projects, large generators were used to charge up a bank of discharge capacitors
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which were then discharged through the railgun. One railgun project, housed in the Air
Force Armament Laboratory at Eglin Air Force Base in Florida, chose a somewhat
different method of providing current. Rather than using a large and rather expensive
generator, the power was provided by 14,000 12 V car batteries. Stacked 20 feet high
and covering over 6,000 square feet, they were able to provide a 5 second burst of up to
2.5 million amps of current.
Unfortunately, designing an effective power supply for a railgun is not as simple as using
large capacitors or truckloads of batteries. If it were, it would be fairly simple for just
about every third world country to be lobbing shells at their enemies. The problem with
these solutions is one of rise time. The pulse that needs to be delivered to the railgun
must provide millions of amps very quickly; otherwise the projectile will be launched out
of the gun barrel before the gun has a chance to accelerate it to a sufficiently high
velocity. The solution to this problem is using a compulsator.
A compulsator is a compensated pulsed alternator. It is very similar to an alternator
found in most automobiles, but it is much larger and is equipped with impedance
compensation windings that decrease the rise time of the output pulses. The compulsator
consists of a mechanical rotational input, a stator with field coils, a rotor with armature
coils, a shield with compensating coils and a switching system. The compulsator
converts mechanical rotational energy into electrical energy by producing an alternating
voltage signal across the rotor coil terminals in response to being rotated through a
magnetic field set up by the stator. The switching system allows the AC voltage
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generated at the rotor to be tapped and directed into the rails and projectile. Building an
effective compulsator is one of the most difficult aspects of railgun design and requires a
great deal of expertise.
The next engineering challenge of railguns is the design of the rails. Because the Lorentz
force that accelerates the projectile is exerted on all four sides of the current loop,
extreme forces are applied to the rails and because of this the rails tend to wear out
quickly. In fact, average railguns require the complete replacement of the rails after only
100 shots. Not only do these excessive forces wear out the rails, they also tend to cause
large deflection of the rails. Because contact with the projectile or armature must be
maintained over the length of the barrel to guarantee conduction of current, the rails must
be very stiff so as to avoid significant deflection. Very often a rail support which
resembles a truss structure is added to provide additional mechanical strength to the rails.
Because the rails are typically replaced very frequently, they need to be affordable and
easy to produce. Very often the cross sections of the rails will be very simple, allowing
for ease of manufacturing as well as providing plenty of contact surface for conduction of
the current. In addition to being strong and affordable, the rails must be excellent
conductors. Approximately 50% of the energy delivered to the railgun by the power
supply is lost in resistive heating of the rails. Other important characteristics of good rail
material are resistance to corrosion, high machinability, high melting point and
compatibility with the slug material.
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The third major area of railgun engineering is design of the projectile. A railgun can fire
just about any type of projectile, as long as at least some portion of it conducts electricity
and makes contact with the rails. There are three main methods of launching the
projectile, or slug, from the railgun. The first method simply involves using a projectile
that is a conductor. Because the projectile itself conducts electricity and rides along the
rails, it closes the current loop and can be launched from the gun as is, with no additional
components. The major drawback of this method is that the high heat and current density
involved in launching the projectile from the gun can cause the projectile to weld to the
rails. If a projectile welds itself to the rails the current loop remains closed and in
addition to ruining the rails and the projectile, serious damage may occur in the power
supply. Obviously, this situation should be avoided.
The second method of launching the projectile involves a nonconductive projectile and a
plasma armature (shown in Figure 2). In this method a small filament is placed behind a
nonconductive projectile. When power is applied to the rails, the filament vaporizes and
an arc of conducting plasma is formed between the two rails. This arc is then accelerated
down the barrel by the Lorentz force, pushing the projectile as it goes. This method
solves the problem of projectile welding, but in practice it is somewhat difficult to
implement.
The third method of launching projectiles involves a conductive casing, called a sabot. A
sabot is a conductive casing that holds the projectile while conducting current between
the rails (see Figure 3). When the gun is fired the sabot and projectile are accelerated and
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fired out of the barrel. Once they have cleared the barrel, the sabot splits and falls away
from the projectile.
Figure 3) Simple railgun sabot
There are several advantages to using sabots to launch projectiles. First, the projectile
can be designed to be as aerodynamic as any other projectile. If the projectile must make
contact with the rails, much of the aerodynamics of the projectile must be sacrificed in
order to provide sufficient surface area for current conduction. Second, it allows the
projectile to be nonconductive without the difficulty caused by plasma armatures. Third,
the sabot can be designed out of low resistance material that might otherwise not be
practical to make a projectile out of. If only a projectile is used, it must not only conduct
current well, it must also be hard enough to withstand the flight and impact after it is
launched. Using a sabot, the projectile can be made very hard while the sabot itself can
be made of a softer material that is a better conductor, thus improving the efficiency of
the gun. It should be noted that current sabot designs utilize a single contact, rather than
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the three contacts shown in Figure 3. The multiple contacts have been found to produce
eddy currents and non-optimal current distribution.
The last major area of railgun engineering is design of the firing mechanism. When using
a compulsator to power the gun, timing of the firing is crucial. The goal for the firing
mechanism is to tap the power signal at the desired voltage. The simplest way to perform
this is by using a shaft encoder on the compulsator to sense the position of the rotor and
stator and extrapolate this to a voltage. Ideally the signal would be tapped at or near the
peak voltage, but it is possible to vary the output by tapping the signal at various points in
the waveform to provide variable projectile velocities. One of the main concerns with the
firing mechanism is that the switch must withstand all of the current that is passing
through the rails without welding shut. As with projectile welding, switch welding can
wreak havoc on the power supply and the rails, causing serious damage. Switch design is
very important, but also very difficult.
As mentioned previously, one of the major problems in railguns is the welding of
projectiles to the rails. In order to avoid this, the firing of the railgun can include
mechanical injection of the projectile. Injection of the projectile into the barrel gives the
projectile forward momentum before it comes in contact with the rails and currents, thus
decreasing friction and decreasing the occurrence of projectile welding. When an
injection system is used, it is important to time the switching very well. This can be
accomplished fairly easily using an optical gate that senses the presence of the projectile
and signals the switch to close.
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The Future of Railguns
With all of the technology and research that has been put into the development of
railguns, how will they be used in the future? As the movie Eraser demonstrates in
Figure 4, some people envision small, lightweight railguns as futuristic firearms.
Figure 4) Arnold Schwarzenegger in Eraser, touting two fictional railgun rifles
Unfortunately for Arnold, there is no way such handheld firearms will ever exist. By the
law of conservation of momentum, firing a 100 gram bullet at 99% the speed of light (as
claimed in the movie) would send a 245 lb. Arnold flying backwards at a ludicrous
267,000 m/s. If railguns are used as weapons, they will have to be land, ship or tank
based and will be limited to much more reasonable muzzle velocities.
In addition to the original concept of ballistic missile interception, railguns have been
considered for launching cargo into space. Because of the excessive acceleration,
however, railguns could not be used to launch humans or any other acceleration sensitive
cargo into space. In order to be practical for launching cargo into space, railguns would
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need to be able to attain muzzle velocities of 11 km/s with cargo much heavier than small
projectiles. In comparison, effective ballistic missile interception requires muzzle
velocities of approximately 12 km/s.
One last possibility for railgun use is in the area of nuclear fusion. Research is currently
underway at the Fusion Technology Research Laboratory at the University of Illinois in
Urbana-Champaign to investigate the possibilities of accelerating particles into a fusion
reactor using a railgun. The high velocity of the particles would cause instantaneous
fusion with target particles upon collision. In addition to beginning the fusion process,
these particle injectors could be used to refuel the reactors continuously as they operate.
Realization of this railgun application is still a long ways off, unfortunately, as muzzle
velocities of 150 km/s must be produced.
In conclusion, railguns are a very intriguing technology and have several exciting
potential applications. While the physics of the electromagnetic phenomena are fairly
simple, implementation of the technology has proven to be very difficult. The future of
railgun development depends not only on continued development of technology, but also
on continued financial support of railgun research.
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Works Cited
Griffiths, David J. Introduction to Electrodynamics – 2nd ed. 1989. Prentice-Hall,
Inc. Englewood Cliffs, NJ.
http://horehound.infostry.com/rail/rail-power.html
http://www.cmn.net/~molly/railguns.html
http://www.railgun.org
http://www.scienceweb.org/movies/eraser.html
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