Classroom Rail Gun

posted on 25 Jan 2013 by guy
last changed 23 Oct 2013

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ages: 9 to 99 yrs
budget: $2.00 to $20.00
prep time: 15 to 120 min
class time: 20 to 60 min

This lesson introduces two homemade versions of the "electric rail gun", a device that uses the principles of electromagnetic propulsion to drive a rod or axle along a pair of conducting rails. Both versions are suitable for in-class demonstration or hands-on activities. They offer very basic lessons for how an electric current interacts with a magnetic field, and help develop a basis for understanding how electric motors work.

Some lead time may be necessary to order the appropriate magnets. Files with all the diagrams are attached.

 

 

 

required equipment: aluminum rod, aluminum bar (2), ceramic block magnet (many), 9 volt battery, wire, washers (nylon)
optional equipment: knife switch, board (for mounting), poster tape
subjects: Engineering, Physics
keywords: rail gun, electric train, homopolar, motor

file attachment(s): 



The electric rail gun demonstrated.

 

Our two designs are based on the principle of the "rail gun", in which a conducting rod or axle straddles a pair of conducting rails and is propelled along the rails by a magnetic force.

design 1 - materials

The first and simplest version of the rail gun is demonstrated in the video above. For this device we used:

  • a 30" board for mounting
  • two 1/8" by 3/4" by 36" aluminum bars for the rails
  • 1/4"D by 3"L aluminum rod
  • two 1/4" I.D. nylon washers
  • 19  2" by 1" ceramic block magnets (15 for the track and 4 more to hold the rails in place)
  • double-sided poster tape and duct tape to hold the magnets down
  • a 9 V battery
  • connecting leads (alligator clips preferred)
  • a knife switch (optional)

The video shows the basic construction. I'll assume it is self-explanatory.


Fig. 1:  Schematic of the rail gun with block magnets.


Fig. 2:  Schematic of the rail gun with the magnetic field lines from the current in the rails.

design 1 - operation

Figure 1 shows a schematic of the rail gun arrangement. An electric current runs down one rail, through the metal rod and back along the second rail. Underneath the rod is a set of block magnets with their north poles facing up, producing the magnetic field indicated by the blue arrows. As the current flows through the rod, it produces a magnetic field, which in turn interacts with the magnetic field from the block magnets and gives rise to forces between the rod and the magnets in the same way that two magnets push or pull on each other. The force that the current-carrying rod feels in the magnetic field is called a Lorentz force, which is perpendicular to both the magnetic field and the current. (See A Survey of Simple Electric Motors for more on the Lorentz force.) For any conducting rod or wire, it's easiest just to remember that the force is always sideways (perpendicular) to the conductor.

To calculate the exact direction of the Lorentz force, we use the right hand rule mnemonic. Place the extended fingers of your right hand in the direction of the current flow and orient your palm in the direction of the magnetic field. (Remember that the  conventional positive current is defined to be opposite the flow of electrons, and remember that the magnetic field points away from the north pole of a magnet.) Your extended right thumb now points in the direction of the Lorentz force. In figure 1, the magnetic field is upwards, the (positive) current flows horizontally through the rod from left to right, and the force on the rod is in the forward direction (green arrow). The rod will accelerate in that direction. A long enough track will get the rod up to very high speeds, which is probably why it's called a rail gun.

In principle, the rail gun can work even without the ceramic magnets. Earth's magnetic field is always present, and generally has a component of the field perpendicular to the Earth's surface.1 In Antarctica, the field would look the same as the field in figure 1. The issue is that the Earth's magnetic field is tens of thousands of times weaker than the field near a strong ceramic magnet. To get the same propulsion using the Earth's field, we would need to put tens of thousands of amps of current through the system, and the metal would probably melt.

The Earth is not the only source of magnetic field in this experiment, however. The rails themselves produce a magnetic field due to the current flowing in them. According to Ampere's law, which describes the relation between the current and the magnetic field produced, the magnetic field lines form circles around the rails, as shown in figure 2. In this figure, the field lines point down on the outside of the rails, and up on the inside of the rails. The rod on the inside sees an upward pointing magnetic field much like in figure 1, and the force on the rod is once again in the forward direction (green arrow). Unfortunately, for a small battery-powered experiment, the magnetic field is still only a few times stronger than the Earth's magnetic field, too weak to do much good. However, as we increase the current, both the magnetic field from the rod and the magnetic field from the rails increases, so that the strength of the push goes up like the square of the current. To achieve the same propulsion as we saw with the ceramic magnets, we would need hundreds of amps of current (not tens of thousands of amps). This current may still be too much for a thin wire to take without melting its insulation, but it can be suitable for larger setups. For even larger currents, some rail guns replace the conducting rod with an ionized plasma, which also conducts electricity. One of the earliest such "plasma guns" was the Marshall Gun,2 developed at Los Alamos Laboratories in 1960, and which could accelerate a hydrogen plasma to 150 km/s.

design 2 - materials

Simon Quellen Field has made an extremely clever variation on our simple rail gun by using magnetic wheels. His instructions can be found at http://sci-toys.com/scitoys/scitoys/electro/railgun/railgun.html . You will need:

  • stiff cardboard
  • aluminum foil
  • a 9 V battery
  • alligator leads
  • a coat hanger
  • 2 neodymium disk magnets

The magnets should be fairly small, 3 to 8 mm in diameter and 1 to 5mm thick works well, so that they stick securely to the coathanger and can't be knocked off easily. WARNING: Neodymium magnets are very strong and must be kept away from electonics chips and credit cards. They are very brittle and will shatter when dropped.


Fig. 3:  Schematic of a rail gun with magnetic wheels.


Fig. 4:  Lorentz forces on a wheel in design 2.

design 2 - operation

A schematic of Field's design is given in figure 3. The current travels from the battery up one rail, through one magnet from edge to center, across the conducting axle, through the other magnet from center to edge, and back through the other rail to the battery (red path). There are forces between the magnetic wheel assembly and the magnetic field produced by the current in the rails that push the wheels along the rails.

Note for geeks:

In this case, the forces between the magnetic wheels and the rails are a little more subtle than in our first design. Figure 3 shows the north poles of the wheel magnets facing inward. The magnetic field lines in the vertical plane are drawn for reference. Of course there are also magnetic field lines all the way around the wheels, they're just not shown.

Now let's look more closely at the interaction between one wheel and the rail it is sitting on. We notice that at points along the rail, the magnetic field lines are pointing to the outside of the rail. Therefore, the right hand rule for the Lorentz force indicates that the force on the rail is downward (this statement is true for either rail). This fact tells us that the rail and the wheel are repelling each other; the wheel pushes the rail downward and the rail pushes the wheel upward. Based on this analysis, one might expect the wheel to jump up off the rail, and indeed the magnetic force is lifting up somewhat, but gravity still holds it down. The tricky part is understanding why the wheel rolls forward. Figure 4 shows how this works. The rail repels all parts of the wheel upward, but not equally. The back end of the wheel, which is closer to the current in the rail, feels a stronger force. The front end of the wheel, which is farther from the current, feels a weaker force. The force on the back of the wheel tries to turn the wheel counterclockwise, while the force on the front of the wheel tries to resist by turning the wheel clockwise, but the force on the back of the wheel wins and the wheel rolls forward.

questions to ponder

  • In design 1, what happens if we turn the magnets over or reverse the leads on the battery?

Naturally, if we turn the magnets over, we reverse the direction of the magnetic field lines. If we reverse the leads on the battery, we reverse the direction of current flow. In either case, we reverse the direction of the force on the rod. The rod will move in the opposite direction.

  • In design 2, what happens if the magnetic poles are not both facing inward; if one north pole is facing inward and the other north pole is facing outward?

In this case, one wheel will move forwards and the other wheel will move backwards, which has the net effect of turning the axle in place. For good entertainment, make the gap between foil rails very small and see if you can get the wheels to turn back and forth as they move from one rail to the other.

  • What do we do to get more speed out of these trains?

There are only a few options to gain more speed. To make the train accelerate faster, we need either more current or a higher field strength. Higher voltage (using more or different batteries) is one way to push more current through the system and increase the acceleration. That's why we chose 9 volt batteries to start with, rather than 1.5 volt D cells. Choosing a power source with the same voltage, but a smaller internal resistance (like the car battery in the video) is another way of increasing current. Alternatively, the same current and field strength can produce a higher final velocity if we let it run farther. The longer the track, the faster the final speed, up to a point.3

teaching notes

Younger students can enjoy experimenting with this demo to see what happens when they orient magnets in different directions or reverse battery leads.

More sophisticated students can be encouraged to predict the force direction based on an application of the right hand rule. In this endeavor, it helps if they have some prior experience with magnetic fields, and know how to use a compass to determine which end of a magnet is the north pole. See the lesson on Iron and Magnets for ideas along these lines.

For a good time, try using the rail gun as a launch pad to send the axle off the edge of a table. Let students experiment to see what launch angle corresponds to the largest range. If students already know about projectile motion, have them calculate the "muzzle velocity" based on the range of the projectile. Then change the launch angle and have them predict the new range of the projectile. Alternatively, lay a target on the floor to see if they can adjust the launch angle to hit it.

further resources

There's an interesting article at How Stuff Works showing some of the history and applications of rail guns, but beware that the force equation there is a little confused.

  • 1. The National Oceanic and Atmospheric Association hosts a magnetic field calculator that shows the inclination angle of the earth's field at any given location on the globe: http://www.ngdc.noaa.gov/geomag-web/?id=igrfwmmFormId#igrfwmm
  • 2. Marshall, J. "Performance of a Hydromagnetic Plasma Gun" Physics of Fluids 3 (1960): 134-135.
  • 3. Note for geeks: as the axle moves faster, the induced voltage drop ("back EMF") increases, and the current goes down. Ultimately, the current delivered to the motor is just enough to balance the force of friction. At that point, the axle quits accelerating and reaches a steady maximum velocity.


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