Transcript ELEC 3105 Lecture 19 Linear Motor Rail Gunx

Linear motors: Case 1 no load
Case 2 with load: Power consumption
Linear Motor / Generator
Alright class,
tomorrow is your
E&M exam
Next day
You may bring a formula sheet, anything on
the formula sheet may be used on the test.
Linear motors
From this
To these

v
Linear motor
Assume external applied B field
much greater than B field generated
by current in bar.
V
bat


R

B
I
app

B
I
app

v
Metal fixed rail
Magnetic flux density into page
External applied field
Movable metal bar
Linear motor
Moves bar towards the
right increasing the size
of the current loop.
Load force restricts
movement of sliding bar

F
 
I   I  B

F
I 
mag
V
bat


R
Current
limiting
resistor

B

F
load
I

v
I

B
app


v
mag
app
app
Metal fixed rail


v  constant as F
mag

I   F
load
Linear motor
Increasing flux due to
expanding loop
By Lenz’s law induced
magnetic field must be
such as to oppose the
increasing flux.
d  0
 
   B  dA
S
V
bat


R

B
app

B
ind
I

v

This is accomplished by inducing a magnetic field
in the opposite direction to the applied magnetic
field.
Linear motor
The induced current required to produce the
opposing magnetic field has a direction opposite
to the current supplied from the battery.
V
bat


R

B
app

B
I
ind
The induced emf opposing the
battery voltage is known as the
“BACK EMF”
ind
I

emf


v

Linear motor
Work done on positive charge in
moving from bottom to top of bar.


W  F q   
W  qvB 
++++
mag
app
Work per unit charge
W
 vB 
q
V  vB 
emf
app
mag
 
q   qv  B
app
app

q
app
By definition “back emf”given by:

B

F
----

v
Charge moves
along with bar
Linear motor
Equivalent circuit


V
bat
R


V  vB 
emf
Bar
app
Linear
motor
Linear motor
Alternate approach to
obtaining expression for
back emf.
t  t
t
V
bat


R

B
app
I
vt
In time
t
loop increases in area by:


v
Metal fixed rail
A  vt
Linear
motor
Linear motor
Alternate approach to
obtaining expression for
back emf.
A  vt
t  t
t
V
bat


R

B
app

v
I
vt
Change in flux over time interval
t
is:

Metal fixed rail
  B vt
app
Linear
motor
Linear motor
Alternate approach to
obtaining expression for
back emf.
  B vt
app
t  t
t


V
bat

B
R
app
I
vt
From Faraday’s law:

V 
t
emf

v
V  vB 
emf
app

Metal fixed rail
Minus sign reflects Lenz’s law, induced
opposes change in flux.
Linear motors:
Case 1 no load

F 0
Linear motor: Case 1
load
Suppose there is no load force.
Once battery is connected the bar
will accelerate to the right until:
V
bat


R

B
app
I

Fload  0
V V
emf

F
bat
I 

v
mag
Metal fixed rail
Once this speed is reached I = 0 and
there is no force to accelerate the
bar further.
Movable metal bar can slip
without friction, …..

F circuit
0
Equivalent
Linear motor Case 1
V
bat


R
load
I 0


V V
emf
bat

v
terminal
Bar
From general expression of emf
V  vB 
emf
app
Then with no load force.
v
V

B 
bat
terminal
app
Case 2 with load
Linear motor: Case 2
Once battery is connected the bar
will accelerate to the right until:
V
bat


R

B
app
I

F
load
Once this speed is reached the bar
no longer accelerates and I net  0

F is a load
0 force.
Suppose there
load

F

F
load

F
mag
I 
I 

v
mag
Metal fixed rail
Movable metal bar can slip
with friction, …..
Linear motor Case 2


V
bat
Equivalent circuit
I 0
net
R
From balanced forces
F B I 
load
app
app
bat
emf
load
B V  vB  
F 
R
app
load
bat
app
load


V
emf

v
Bar
net
B V  V 
F 
R

F 0
B V  vB 
F 

R
R
2
app
bat
2
app
load
linear relation between
F and v
load
Linear motor Case 2
B V  vB 
F 

R
R
2
Load / speed
characteristic plot
app
V

B 
bat
noload
app
linear relation
load
v
v
bat
2
v0
B V 
F 
R
app
app
load

R
v   
 B 
2
app

V
F  


B



bat
2
load
y  mx  b
app
F
load
bat
Linear motor Case 2
Load / speed
characteristic plot
v
Internal combustion
engine can’t operate at
zero speed. Need
transmission, clutch, …
Motor
Maximum current is drawn at startup
(may need to take action to protect motor
windings from overheating)
A stalled motor burns faster
v0
V
I
R
bat
DC motor does not need a
transmission – major
saving in weight,
assembly, ….
F
load
Maximum force (or torque)
is obtained at zero speed
START Power consumption
Linear motor Power
Mechanical power delivered


P  F  v  F ( I )v
Electrical power consumed
P V I
V
bat


R
mech
elec
V
I
mag
emf


B
app
mech
emf


F
I 

v
mag

Metal fixed rail
For conservation of energy
P P
mech
elec
Linear motor Power
Mechanical power delivered


P  F  v  F ( I )v
Electrical power consumed
P V I
For conservation of energy
P P
mech
elec
mech
mech
mag
emf
elec
Recall
F
mag
I   IB
app

V  vB 
emf
app
Then
 F (I ) 

P  vB  

B



P  vF (I )
elec
mag
mag
elec
app
app
P P
elec
mech
START Linear Motor / Generator
Linear motor / Generator
Suppose direction of
load force is as shown.
We pull on the bar.
V
bat


R

B
app
noload
app
V
emf

F
F I 
load
mag
v

Since magnetic and mechanical forces act in same
direction.
V  vB   V
emf
I

Now
vv

bat
Linear motor / Generator
Load / speed characteristic plot
v
v
V

B 
bat
noload
app
Current
flows in a
direction to
charge the
battery.
Generator
v0
B V 
F 
R
app
load
Motor
F
load
bat
Linear motor / Generator
Decreasing flux
results in reverse
polarity of back emf.
Suppose we reverse the
direction of load force.
We pull on the bar.
V
bat


R

B

V

F
load
app

v

emf
I

Now back emf and battery add giving larger current.
System acts as a generator
v0
V
I
R
Application in electric cars: regenerative braking: motor can be used to recharge battery
during braking.
bat
Linear motor / Generator
Load / speed characteristic plot
v
Back emf and
battery polarities
combine producing
larger current.
Current
flows in a
direction to
charge the
battery.
F
load
Generator
Motor
Generator
Linear motor / Generator
Any mechanical force
on the bar will induce
the bar to move in that
direction.
Suppose now we
remove the battery
altogether
R

B

F
app

v
load
I
I

v

F

load
The load force pulling on the bar will generate a current in the
loop and as such the system acts as a generator for all load forces
applied. The direction of the current is determined by the
direction of the load force.
Linear Generator
Load / speed characteristic plot
No battery in system
v
Current flows in
CCW through
resistor.
Current flows in
CW through
resistor.
F
load
Generator
Generator
The Big Bad Rail Gun
The Big Bad Rail Gun
Welcome to the newly redesigned haven for the rail gun
enthusiast. This page covers some of the latest techniques in
electromagnetic propulsion, but the construction of a rail gun is a
perilous undertaking so use the information contained herein at
your own risk.
NOTE: In the interest of simplicity vector
directions are ignored, it is assumed that the magnitude is as
calculated and in the desired direction.
What is a rail gun?
A rail gun in it's simplest form is a pair of conducting rails separated by a
distance L and with one rail connected to the positive and one the
negative side of a power source supplying voltage V and current I. A
conducting projectile bridges the gap L between the rails, completing the
electrical circuit. As current I flows through the rails, a magnetic field B
is generated with an orientation dictated by the right hand rule and with
a magnitude governed by equation 1.
The Big Bad Rail Gun
(1) B=NuI
• B = Magnetic field strength (Teslas)
• N = Number of turns in solenoid (1 in our case)
• u = 1.26x10^-6 (The magnetic permeability of free space,
Henries/Meter)
• I = Current through rails and projectile (Amperes)
Figure 1:
Simple Rail Gun
The Big Bad Rail Gun
When a current I moves through a conductor of length L in the
presence of a magnetic field B, the conductor experiences a force
F according to equation 2.
(2) F = ILB
• F = Force on conductor (projectile, in Newtons)
• I = Current through rails and projectile (Amperes)
• L = Length of rail separation (Meters)
• B = Magnetic field strength (Teslas)
The direction of the force depends on the direction of the current
through the projectile and the magnetic field since the force is
truly a vector with direction dictated by the cross product of the
vector quantities I and B. In Figure 1, the force is oriented down
the rails, away from the power source. See the section on the
Right Hand Rule below for a detailed description of this.
The Big Bad Rail Gun
How fast does a rail gun projectile go?
Short answer: currently about 4 km/s
The speed of a rail gun slug is determined by several
factors; the applied force, the amount of time that force is
applied, and friction.
Friction will be ignored in this
discussion, as it's effects can only be determined through
testing. If this concerns you, assume a friction force equal
to 25% of driving force.
The projectile, experiencing a
net force as described in the above section, will accelerate
in the direction of that force as in equation 3.
(3) a = F/m
• a = Acceleration (Meters/second^2)
• F = Force on projectile (Newtons)
• m = Mass of projectile (Kilograms)
The Big Bad Rail Gun
Unfortunately, as the projectile moves, the magnetic flux
through the circuit is increasing and thus induces a back
EMF (Electro Magnetic Field) manifested as a decrease in
voltage across the rails. The theoretical terminal velocity
of the projectile is thus the point where the induced EMF
has the same magnitude as the power source voltage,
completely canceling it out.
Equation 4 shows the
equation for the magnetic flux.
(4) H = BA
• H = Magnetic Flux (Teslas x Meter^2)
• B = Magnetic field strength (Teslas) (Assuming uniform
field)
• A = Area (Meter^2)
The Big Bad Rail Gun
Equation 5 shows how the induced voltage V(i) is related to H and the
velocity of the projectile.
(5) V(i) = dH / dt = BdA / dt = BLdx / dt
• V(i) = Induced voltage
• dH / dt = Time rate of change in magnetic flux
• B = Magnetic field strength (Teslas)
• dA / dt = Time rate of change in area
• L = Width of rails (Meters)
• dx / dt = Time rate of change in position (velocity of projectile)
Since the projectile will continue to accelerate until the induced voltage
is equal to the applied, Equation 6 shows the terminal velocity v(max) of
the projectile.
(6) v(max) = V / (BL)
• v(max) = Terminal velocity of projectile (Meters/second)
• V = Power source voltage (Volts)
• B = Magnetic field strength (Teslas)
• L = Width of rails (Meters)
The Big Bad Rail Gun
These calculations give an idea of the theoretical maximum velocity of a
rail gun projectile, but the actual muzzle velocity is dictated by the length
of the rails. The length of the rails governs how long the projectile
experiences the applied force and thus how long it gets to
accelerate. Assuming a constant force and thus a constant acceleration,
the muzzle velocity (assuming the projectile is initially at rest) can be
found using Equation 7.
(7) v(muz) = (2DF / m)^.5 = (2DILB / m)^.5 = I(2DLu / m)^.5
• v(muz) = Muzzle velocity (Meters/Second)
• D = Length of rails (Meters)
• F = Force applied (Newtons)
• m = Mass of projectile (Kilograms)
• I = Current through projectile (Amperes)
• L = Width between rails (Meters)
• B = Magnetic field strength (Teslas)
• u = 1.26x10^-6 (The magnetic permeability of free space, Henries/Meter)
These calculations ignore friction and air drag, which
speeds and forces applied to the rail gun slug. Top rail
launch a 2kg projectile with a muzzle velocity of close to
rails. To reach this kind of velocity, the power source
million Amps. Ouch.
can be formidable at the
gun designs currently can
4km/s on roughly 6 meter
must provide roughly 6.5
The Big Bad Rail Gun
What is the right hand rule?
The right hand rule is a mnemonic for memorizing the orientation
of fields, forces, or other vector quantities after the cross product
of two vector quantities is taken. For example, the direction of
the magnetic field around a conductor due to a current can be
determined by pointing the right thumb in the direction of the
current and curling the other four fingers as if grasping the
conductor. The magnetic field similarly exists as a vector field
circling the conductor in the direction indicated by your fingers.
See Figure 2 for a visual representation.
Figure 2: Right
hand rule for
magnetic field
from current
through
conductor
The Big Bad Rail Gun
In addition, the right hand rule comes into play when performing cross
products of vector quantities. For example, when figuring out which way
the projectile in a rail gun will go, you look to Equation 2. Equation 2 is
truly a cross product, but presented as a simple multiplication for the sake
of simplicity. The force exerted on the projectile is the cross product of
scalar length L, vector i the path of the current in the projectile, and
vector field B the magnetic field. When determining the direction of this
force we can use the right hand rule. Since all the angles involved are 90
degrees, the resultant force has a magnitude resulting from the simple
multiplication of the magnitude of i and B and the value of L. (|F|=L|i||B|)
To determine the direction, lay your right hand along the path of the
current through the projectile, with your fingers pointing in the direction
the current is traveling. Next, curl your fingers in the direction of the B
field. Your thumb will now be pointing in the direction of the applied force.
See Figure 3 for a visual representation.
Figure 3: Right
hand rule for
cross product
The Big Bad Rail Gun
What should the rails be made of?
The rails can be made of any conductive material.
However, the best rail material will depend on your
specific design. Important characteristics of a good rail
material are high conductivity, high strength, high
machinability, resistance to corrosion, high melting
point, availability, compatibility with slug material, and
finally price.
Clearly, the choice of rail materials will be a
compromise. A good place to start is electrical
conductivity. The amount of heat the rails will need to
withstand will be in large part dependent on their
resistance. Below is a list of several metals and their
conductivities, melting points, and heat capacity.
The Big Bad Rail Gun
Material
Resistivity(Ohm/cm)
Melting Point
CMW® D158F
0.00000174
980
n/a
Silver CP Grade
0.00000177
961.93
0.234
Oxygen Free Copper
0.00000171
1083
0.385
1050-O Aluminum
0.00000281
646
0.9
440-A Stainless Steel
0.000062
1510
0.4
Haynes 25 Super Alloy 0.0000886
1370
0.46
Titanium 6-4 Annealed 0.000178
1660
0.526
Tungsten
3370
0.134
0.0000056
(C)
Heat Capacity (J/g°C)
The Big Bad Rail Gun
Clearly there is a wide range of options. Titanium will absorb 100 times as much
energy from a given current when compared to CP grade (pure) silver. Tungsten
melts at a temperature roughly 5 times higher than aluminum, but aluminum will
take over 6 times more energy per gram to heat. Thus, all other things being
equal, tungsten will melt from a lower input of energy than aluminum. This is a
little misleading, since the heat capacity also is dependent on mass and tungsten is
about 3-4 times as dense as aluminum. Thus the above comparison would involve
a smaller sample of tungsten (3-4 times smaller by volume) than the aluminum
sample.
The ideal rail combines the strengths of several materials, a metal composite with
each metal performing the function it excels at. For example, the contact surfaces
would have high conductivity, low friction, and high melting point; the support
structure would be strong, light, and conduct heat away quickly.
A good rail could be made of 7075 T-6 aluminum supporting a CMW® D158F silver
and graphite low friction contact surface. A pair of rails fabricated in this way could
be combined in a carbon fiber barrel assay for increased stiffness and weight
savings. The strength and stiffness of the rail is of utmost importance, as the
forces generated on the projectile are also felt by the rails.
The Big Bad Rail Gun
How should the rails be shaped?
The primary purpose of the rails in a rail gun is to conduct electricity to the
projectile, build a magnetic field, and guide the projectile out of the device. The
actual shape of the rail is important in two instances. 1) The contact patch
between rail and projectile. 2) The structural rigidity of the rail in the horizontal
plane (in plane with but perpendicular to projectile motion).
Obviously, the rail surface in contact with the projectile should have the same
contour as the projectile itself. The best shape for this interface is flat. This shape
is optimal because it is cheaper to make, simplifies the production of highprecision surfaces, facilitates rail compositing as mentioned above, and minimizes
match-up errors between projectile and rail. Use of a grooved rail and projectile
could be performed, with the benefit of increased contact area and thus a
reduction in current density, but in practice, producing these parts would be too
costly. Considering the lifespan of rails (around 100 shots, give or take 100), the
simplicity of the rail is imperative.
The shape of the rail not in contact with the projectile must be designed for the
utmost in structural rigidity. Fortunately the vast bulk of force experienced by the
rails is in one direction, a result of the same equation that dictates the forward
motion of the projectile. Thus the rail must be designed to withstand an outward
force equal to that exerted on the projectile. As you can imagine this force is huge,
as it tends to send the projectile out of the gun at a few km/s.
The Big Bad Rail Gun
So, borrowing a few lessons from structural engineering, an ideal rail
support (structural backing for contact/conducting surface) would
resemble a beam or truss designed for maximum resistance to bending.
The cross section of this beam can take on many shapes based on the
resources at hand, I or H beam, U channeled, closed rectangular, closed
triangular, and so forth. If you don't already have a bunch of steel
girders laying around, I'd get our the old mechanics textbook and
calculate the bending moments for some different cross sections and
determine which you'll use. The complexity, the strength to weight of the
cross-section, availability, and ultimately cost will determine your choice
of rail.
How stiff do the rails need to be?
The rails need to be stiff enough that at maximum force, they do not
deflect enough to break the circuit of rails and projectile. The tolerances
of your design, sabot geometry, and even pulse shape will determine the
structural requirements. You may want to design in some interference to
account for the spreading of the rails, build in some toe-in, design a
suspension system to maintain solid contact, or design the sabot to ride
on top of the rails rather than between them. This will allow you to
account for rail movement at the expense of increased projectile mass,
difficulty in maintaining optimal current density, and so forth. As you
may have noticed, rail guns are a pile of compromises. It is definitely no
easy task to trick the forces of nature into throwing a 2 kg piece of
tungsten around at 4 km/s.
The Big Bad Rail Gun
Working from the example given earlier (2 kg projectile, 4 km/s muzzle velocity, 6
m rail length) the forces present are as follows.
Assuming constant acceleration, the time the projectile spends in the rails is:
(1) T = d / va
• t = time spent in contact with rails, (seconds)
• d = distance traveled, length of rails, .006 km (kilometers)
• va = average velocity, (vm-vo)/2, muzzle velocity minus initial, 2 km/s
(kilometers/second)
Thus t = 0.003 seconds, a very short time. The acceleration needed to produce the
4 km/s muzzle velocity is:
(2) a = dv / dt
• a = projectile acceleration (kilometers/second^2)
• dv = change in velocity, 4 km/s (kilometers.sec)
• dt = time spent under acceleration, 0.003 s (seconds)
Thus the acceleration is 1333 km/s^2. Talk about whiplash. The force on the
projectile and thus on the rails as well is determined by the acceleration and mass
of projectile:
The Big Bad Rail Gun
(3) F = ma
• F = force on projectile and rails (Newtons)
• m = mass of projectile, 2 kg (kilograms)
• a = projectile acceleration, 1333000 m/s^2 (meters/second^2)
Drum roll please...the force is 2666000 N, or 599316 lbf. To get
an idea of how much force this is, lets assume we wanted to keep
the stress in the rail beam under 50 ksi (345 MPa):
(4) A = F / tau
• A = area of beam in tension (square inches)
• F = force on projectile and rails, 599316 lbf (pound force)
• tau = stress on beam in tension, 50 ksi (thousand pound force
per square inch)
The cross-sectional area of beam required to meet this spec
would be 11 in^2. That is a lot of metal. The above was for a
purely tensile load, but the geometry of the actual situation is
more complicated. The portion of the rail beam nearest the
projectile will be in compression, with the farthest portion of the
beam cross section in tension. The ratio of these stresses will
depend on the cross sectional geometry of the rail and thus the
position of the neutral axis. The neutral axis is the line parallel to
the rail and the direction of projectile motion where there is no
stress, compression and tension are in balance.
The Big Bad Rail Gun
What kind of slugs (projectiles) can a rail gun fire?
A rail gun can fire virtually any type of projectile, provided that a least some
portion of it conducts electricity and makes contact with the rails. Home built
systems often use quarters, washers, or ball bearings as projectiles. Mostly, these
do not work, and just end up welding to the rails. Welding is the most common
problem in home rail gun design, and is difficult to overcome using traditional
methods. Some guns have used graphite projectiles in an effort to eliminate
welding, provide lubrication, and increase rail life time. While solving the welding
issues of more conventional types, these projectiles have several disadvantages:
they are low density, and provide increased electrical resistance.
How do I keep the projectile from welding to the rails?
Welding is strictly a problem of current density and heat. Current density refers to
the amount of current flowing through a particular portion of the circuit, and
generally reaches its highest levels at the interface between the slug and the
rails. The contact area between the slug and the rails must be as large as possible
to keep the current density from welding the two together before the projectile
can begin moving. In an advanced high power design, the projectile will ionize
(can you say plasma?) due to the heat generated by the extremely high currents
involved. The major difficulty in getting optimum rail to slug contact is the
balancing act of projectile to rail surface are contact, aerodynamic stability of
projectile, heat dissipation, and friction with rails. One solution to these issues,
which results in exceptional projectile performance is the sabot round.
The Big Bad Rail Gun
How does the sabot rail gun slug work?
The main interest in creating a weapon that fires a projectile is
transferring muzzle energy to the target through momentum (velocity
and mass). At the same time aerodynamic stability and drag and thus
weapon accuracy and range are of concern. The sabot round uses a
disposable case (sabot) to carry the projectile clear of the weapon
barrel. In the rail gun case, the sabot allows the best of both worlds,
allowing the sabot to be designed for optimum current carrying capacity
and heat dissipation while the projectile itself may be designed for
stability and drag. Recent efforts use an aluminum sabot cradle that
carries a tungsten, fin-stabilized round down the rails and off into and
through the target. The cradle must carry all or most of the current
provided by the power supply and thus contact area is very
important. In these designs, the power is provided by a compulsator
and often results in the ionization and vaporization of portions of the
sabot cradle. Tungsten makes an ideal metal for the projectile due: it's
high density (19.3 g/cc) , hardness (31 Rockwell C), and extremely high
melting point (3370 C). See figure 1 for a sample rail gun sabot design.
The Big Bad Rail Gun
Figure 1 Sample
Rail Gun Sabot
**Note, I have been informed that the use of multiple fins in the sabot casing has been found
to result in non-optimal current distribution and eddying. Current designs utilize a single
contact sabot cradle. (Thanks Ben!) --- (Who is Ben????)
The Big Bad Rail Gun
How do you fire a rail gun?
Firing a compulsator-powered rail gun is a delicate undertaking. The basic idea is to tap the
power signal at the desired voltage. This can be performed in several ways, with the
simplest being using a shaft encoder to sense the position of the rotor in the stator and
extrapolate this to a voltage. In a properly designed compulsator/rail gun design, you would
fire at or near peak signal voltage at all times. However, if mission parameters call for
projectiles of various mass, g sensitivity, or melting points the ability to vary the output
voltage by tapping the signal at various points in the waveform will be desirable.
As with a simple generator, the output across the compulsator terminals will be a voltage
signal that varies in frequency according to the number of stator poles and shaft RPM. The
more poles the compulsator has, the slower the shaft must spin for the output signal to reach
a certain frequency. The rail gun is fired when a switching system closes the circuit between
the compulsator output, the rails, and the projectile. The rail gun will continue to fire as long
as the switch remains closed, the compulsator is spinning and powered, and the projectile is
completing the circuit between the rails.
In practice, the compulsator output signal frequency will have a much longer period than the
time the projectile is in between the rails. With a 4km/s muzzle velocity and 10m rails, the
projectile is in contact with the rails for 0.005 seconds. If your compulsator has 8 poles and is
spinning at 900 RPM, the output signal frequency will be 60 Hz and a period of 0.017
seconds. In general a compulsator with a greater number of poles is desired in order to
reduce the required rotational speed of the rotor assy. This is advantageous because of the
size and mass required of the compulsator to withstand the forces and energy dissipation
required of such a high power device. Thus the higher the required rotational speed the more
critical rotor balancing and bearing forces become.
The Big Bad Rail Gun
How can I switch the Rail Gun current?
Closing the circuit between the compulsator and the rail gun itself is a design
challenge unto itself. The "switch" must withstand all of the current that goes
through the rails and projectile, which as we saw earlier can be very substantial.
Basically, the switching mechanism MUST NOT weld itself closed. If it does, the
pulses of current will continue to be sent through the circuit, possibly overheating
your rails, thus warping, delaminating, melting, or destroying them. If the
projectile has cleared the rails, this is of course of no consequence. However, as
you will discover, working the bugs out of any system, especially a mega-joule rail
gun, is a difficult task and you don't want your entire project to turn to melted slag
if your projectile gets stuck in the rails.
This said, you should design each separate component of your rail gun to be selfresetting or self-arresting. This means that the switching mechanism should not
rely on the projectile to clear the rails to turn off the gun, the compulsator should
not continue to spin or discharge unchecked, etc.
The switching system must also introduce the minimum of electrical resistance to
the completed circuit. Since the compulsator is a relatively low-voltage device
(<1kV), all effort must be spent on keeping the resistance of the total circuit as
close to zero as possible. In addition, the higher the resistance of the switch, the
more heat it will generate and thus the faster it will destroy itself. As you may
imagine this is a tenuous balancing act.
The Big Bad Rail Gun
The best solution is good old solid state electronics. The SCR (silicon controlled
rectifiers) is basically a diode that can be turned on and off. Designed for power
systems, SCRs are available in ratings that will handle rail gun sized current pulses
for short durations. By using a properly sized SCR or array of SCRs the compulsator
power signal may be tapped using a a fixed or adjustable voltage sensing circuit that
actuates the SCR at the desired point in the output wave. Proper heat sinking of the
SCRs will determine their service life and rate of fire. As you may imagine, the SCR
will introduce a voltage drop like any semi-conductor device.
Another consideration of the SCR, is the turn off time. Once an SCR is triggered "on"
it does not stop conducting until the voltage signal across it drops below a threshold
level. In an AC situation like our compulsator, this is where the voltage signal crosses
zero. So the longest pulse an SCR can pass is one half waveform, roughly from zero
to peak and back to zero. Therefore, if the projectile has not cleared the rails, you
must wait a half cycle to pulse again, or use two SCRs in a triac type formation to
pass the last half of the wave, zero to negative peak to zero. This will result in a
current through the rails of opposite direction as the previous pulse, and you will have
to "destroy" the field established by the previous pulse before building the new
opposite sign field. This will introduce phase lag, increased inductive impedance, and
other effects that may be less than optimal.
So, the point I am trying to make is, your compulsator and switching system should
produce a pulse of sufficient duration and power to eject the projectile just as or just
after the SCR shuts off. This balancing can be performed by rail length, peak voltage,
pulse shaping, output frequency, etc.
The Big Bad Rail Gun
How can I inject or load the projectile?
As mentioned in other areas of the site, projectile/rail welding is a
common problem in rail guns. In order to avoid this, many designs
call for a mechanical injection system to give the projectile forward
motion before it comes in contact with the rails and currents. As you
know, kinetic friction is less than static friction. (think about four
wheel drifting in your favorite automobile...)
One important consideration when designing an injection system is of
course timing. Making sure that the projectile has entered the rails
while the compulsator is tapped at the desired voltage and so forth is
very important, considering that the compulsator may be tapped for a
duration of less than 10 msec. It is for this reason that highest power
rail guns do not use an injection system, but rather a simple breech
loading procedure.
The Big Bad Rail Gun
If an injection system is desired, there are a number of ways
to "squirt" the projectile into the rail assy. You can use springloaded, centrifugal, compressed air, or any other method you
can think of. The best method is most likely compressed air,
which can provide a large force and thus higher injection
speeds. With a projectile cross section of 2 square inches and
50 PSI air, you could use PVC as your material and generate
100 pounds of force on the projectile. With a 1 pound
projectile, this would generate an acceleration of roughly 3
g's.
For timing, you could use an optical gate to switch you SCRs
as the projectile crosses the breech of the rails themselves.
This would allow fairly precise timing, as most SCRs have a
fairly rapid response time (on the order of a dozen or so
msec). By the time the compulsator is tapped the projectile
would have traveled only a few inches.
Another Big Bad Rail Gun
The Big Bad Rail Gun
Fatro and Jengel's Rail Gun
Your one stop, step by step guide to home rail gun technology
Updated 9/17/99
Here lies the musings and possible truths of several engineering students on the subject of
rail gun design. As of yet, all information is theoretical, which means we think it would
work but are too lazy and poor to do anything about it. This page is provided for
entertainment and informative purposes only and any connection to reality is sketchy at
best.
First off, for a rail gun to work you need a roughly uniform parallel magnetic field
encompassing the rails and it needs to be perpendicular to the desired plane of motion.
For example, if you want the projectile to go parallel to the plane of the earth's surface
then you want your field to be oriented either pointing straight up or straight down. (See
diagram)
The Big Bad Rail Gun
So now we know what we need, but how do you generate a roughly uniform parallel magnetic field?
The answer is using a solenoid. A solenoid is a coil of wire with N turns per inch and L inches long.
The magnetic field created when a current is run through the coil is roughly parallel in the center of the
coil (L/2). The strength of the field in an ideal solenoid is given by: B=Nui (1) Where B is the magnetic
field, N is the turns per unit length, u is the permeability constant (u=1.26x10^-6 H/m), and i is the
current through the wire. This equation suggests that the strength of the field in an ideal solenoid does
not depend on the diameter. This equation holds for a real solenoid of finite length best at the center of
the solenoid, at L/2, half the length.
So we have a field, but what do we do with it? Since we need the rails to be perpendicular to the field,
we'll have to run them in the coil, along its diameter. Thus, we'll need an aperture for the projectile to
escape from. The rails should be as close to parallel as possible, and the projectile needs to be an
electrically conductive object which spans the two rails, making solid electrical contact with each. The
force applied to the projectile depends on three things, the strength of the magnetic field, the current
through the rails and projectile, and the width between the rails. F=iLxB (eq 2) Equation 2 shows that
the force is given by the cross product of the current times length with the B field. Thus, we see that we
get maximum force when the current, and thus the L is perpendicular to the B (magnetic) field. See
Diagram.
The Big Bad Rail Gun
What now? We know that with a field and a current we can apply a force to an object, thus accelerating
it, but how do we use this to build an actual rail gun? Our idea for a design was to use a ball bearing as
a projectile, thus allowing less friction with the rails, a fairly aerodynamic shape and most of all ball
bearings are cheap and abundant. For rails, we decided that angled steel would be best. The right angles
can be used to confine the ball to one dimension of freedom and offer enhanced rigidity to resist the
forces between the rails. This turned out to be a good idea in theory, but the area of contact between the
ball and rails is insufficient, resulting in high current density and immediate welding. A traditional flat
washer would serve better, as the area of contact limits the current that can pass through the projectile
before welding occurs. Picking a gauge of wire for the solenoid is also important. You need to find the
right balance between current capacity and turns per inch. Recall that the strength of the field generated
relies both on number of turns per unit length and the current through each turn. Stacking layers of
turns can be used to make up for a lower current, but each layer has a decreasing effect on the internal
B field. Look for enameled winding wire, it has a thin painted on coating so that you won't get a short
but it's thin so it won't limit the amount of turns too much. Wire like this (24 AWG) costs around 4
bucks a pound with about 1000 feet per pound.
The Big Bad Rail Gun
Another problem with our design is that unlike other rail gun designs where the only circuitry is a bank
of capacitors that discharge into the rails, our design builds a magnetic field in the coil before sending a
current into the rails. In this way we can increase our field B, achieving a greater force without a
greater current. However, it takes a discrete amount of time for the field to build in the coil, which is
really an inductor. Thus as the field builds, the voltage across the coil (inductor) drops to zero as the
derivative of the current through the coil drops to zero. Once the steady state value, or max current is
reached, the voltage across the inductor is zero and current flows freely through the inductor. The result
is that if our current in is a sinusoid cos(x) then the voltage signal would be cos(x-pi/2) = -sin(x) or
lagging by a phase of pi/2. Our current in will most likely be provided by a car battery which is a 12V
high amperage current source. As a result our input signal will be a unit step input with a finite rise
time the voltage will lag here as well, being highest initially and then falling off as the current
stabilizes.
When properly designed, our rail gun will have a maximum allowable current right at the maximum
output of our battery(ies), at this current the wire in the coils would melt, but we will design a cutoff
circuit that will turn off the current to the inductor right before this point. This can be accomplished
using a transistor cutoff circuit that senses the voltage across the rails and triggers a high current relay
to turn off the voltage to the coil as this reaches a predetermined level.
Another consideration is the fact that as the projectile moves down the rails, the magnetic flux will be
increasing. As a result an induced voltage will oppose the voltage applied to the rails until the voltage
across the rails is zero. This limits our rail length and thus the time that a force is applied to the
projectile, limited by the strength of the magnetic field and the voltage applied across the rails.
The Big Bad Rail Gun
Magnetic flux ø = BA for a uniform field over an area A
Voltage induced= V(ind) = dø/dt = BdA/dt in our case since the field B is constant while the area is
increasing.
dA/dt = Ldx/dt where L is the width of the rails and thus the width of the projectile and dx/dt is the
linear velocity of the projectile. As a result we have a terminal velocity for our rail gun.
Max Velocity=v(max)= V(applied)/BL
Finding an acceptable balance of cost and velocity is the hardest part of home rail gun design. Using
two car batteries in series you can double the applied voltage and theoretically double the terminal
velocity. In practice (mathematically) you will not reach the maximum velocity unless your rails are
very long. Thus using 24V would increase the force on the projectile by increasing current, but be
careful that you are not extending the draw beyond the capabilities of your battery. Most lead acid car
batteries can put out 100 amps without breaking a sweat, so don't worry too much. Measure the DC
resistance of your completed circuit before powering up to get a rough estimate of the current draw.
Some other ideas when designing and building a rail gun are to limit welding, focus on increasing the
magnetic field along the rails, and to increase the rail length to take full advantage of the forces you
are generating. Several ideas that I have for this are as follows.
The Big Bad Rail Gun
First, when a ferromagnetic material is placed in a magnetic field, the field permeates the
material and locally aligns the magnetic orientation of the normally randomly oriented
magnetic zones (due to grain structure in metals) along the direction of the applied field.
Internally, this results in huge increases in magnetic field strength. This phenomenon is
taken advantage of in electric motors and transformers. In addition, the internal alignment
tends to focus the magnetic field lines in the vicinity of the ferromagnetic object, entering in
the top (North) pole and exiting the bottom (South) pole. See diagram.
The Big Bad Rail Gun
By using this effect to our advantage, we can concentrate the field generated by
our solenoid into the area where the rails are, thus increasing the magnetic flux in
the area of the rails. In this way the field strength is increased and thus the force
generated on the projectiles. Proper geometry of the pole pieces placed within the
coil can possibly concentrate virtually the entire field into the area of the rails,
much like a primitive AC motor. This is of course only an idea. See below for
more details.
The Big Bad Rail Gun
In order to lengthen the rails, and thus the time the force is applied to the projectile and
ultimately increasing muzzle velocity, we can squish the solenoid or even make it
rectangular. By making the solenoid long and rectangular, we allow ease of finding pole
pieces to capitalize on the effect mentioned above as well as limiting the space our rail gun
will occupy and the wire needed. The drawbacks to changing the geometry is making
calculation of the field within the solenoid very difficult. It may be adequate to assume
uniform dispersion, but due to geometric effects, the field will vary along the length of the
solenoid, with areas of unknown or hard to predict strength at each end. This is problematic
in that a strong field is needed when the projectile is beginning to be accelerated in order to
limit welding tendencies. One way to overcome this, and most likely a good idea in all rail
guns is to have a mechanical injection system.
A mechanical injection system imparts the projectile with an initial velocity as it enters the
coil and makes contact with the rails. Problems with building a system such as this are the
mechanical complexity, timing the electrical circuits to synch with the injection, and
ensuring good electrical contact of the projectile with the rails. One idea that I had for
bypassing most of these caveats is to use a surplus pinball launcher, the thing that you pull
back to shoot the ball. Using this, and a simple switch or two, you could jump start the
projectile and start the current flowing as the plunger pushes the projectile into the rails.
Another alternative is to use a smaller solenoid actuator with a iron rod that moves in and
out according to voltage applied to smack the projectile. Use of a swinging arm like a clay
pigeon launcher could also be used but would be more complicated. Use your imagination.
The Big Bad Rail Gun
Further design enhancements that would help rail gun operation are
using conductive greases to initially maintain forward motion since
kinetic friction is less than static friction (once something starts to
slip, it tends to continue slipping due to this effect). However, once
the grease has heated up enough it will no doubt break down and
possibly necessitate cleaning before firing again. The use of a plastic
rail follower to maintain constant pressure on the projectile could help
keep current densities below the welding point by maintaining good
surface area contact. Conductive powder based lubricants like
graphite could also be used, but due to the decreased conductivity
could limit current. Ramping the current through the rails up after
projectile injection and rail contact has been made could also help
alleviate welding by allowing the projectile to build speed before
applying the full current.