The Physics Behind the Rail Gun

Magnets and Magnetic Fields:
Magnets are well known for their ability to repel and attract other magnets and various pieces of metal, but what people seldom understand are the physics at work that cause such occurrences.
Magnets are everywhere, from within TV's and cellphones, to the Earth itself, and they are all producing magnetic fields. For a particle, a magnetic field can be defined to be "a vector quantity that is directed along the zero- force axis" with a magnitude equal to the dividend of the magnetic force and the product of the particle's charge and speed, and for a bar magnet, the field is best demonstrated as arcs going from one pole to the other. With that said, magnetic fields can also be created; the basic principle of electromagnetism is that the movement of electrons through a conductor produces a magnetic field in the region around the conductor. This is the fundamental principle behind the workings of the rail gun.


Unlike a bar magnet, a conductor does not have any poles, and consequently, rather than arching from one pole to another, the magnetic field produced by a conductor is best visualized as a series of circular, concentric field lines around the wire segment. The direction of the field can be determined by another version on the right-hand rule: by pointing your thumb in the direction of the current through the conductor, your fingers will curl in the direction of the magnetic fields that are created by it. Using the magnetic field, you can then determine the force that the conductor exerts on an external object, which, in the case of a rail gun, is also a conducting, parallel current. This is important because parallel currents attract each other (the derivation of which can be found below) and consequently, they create a net force between them. This force is the main propellant of the projectile of the rail gun.



The Railgun:


As shown in the picture, the main body of a rail gun consists of two parallel, conducting rails (typically made of copper) with current running in one and out the other. It also needs a projectile and a conducting element that will act as a fuse and bridge the gap between the two rails. For the projectile to be fired, it needs to be on the side of the conducting element that will position the net magnetic force in the direction of the projectile. When the time comes to fire the projectile, the current is turned on, vaporizing the conducting element and creating a conducting gas that is expelled outward, along with the projectile, with the net force that is induced when the current runs through the parallel rails. This force is known as the Lorentz force, and it is directed perpendicular to the magnetic field. The magnitude of this accelerating force is proportional to the square of the current driven through the system, and the launch velocity of the projectile is dependent upon the geometry of the barrel and the materials used for the barrel, projectile, and conducting fuse element. However, since longer barrels typically lead to problems, most rail guns optimize the velocity of the projectile with strong currents (around 1 million amps).
The use of magnetic force to propel a projectile rather than chemicals is advantageous for several reasons. First, the speed of projectiles propelled by chemical propellants are hindered due to the sound speed of the propellants in the barrel, and this, in turn, limits the distance that the projectile can travel. The muzzle velocity of projectiles launched by gunpowder typically peaks at around 4,000 ft/sec with a maximum range of 12 miles. A rail gun, on the other hand, can fire its projectile at a speed of up to 52,493 ft/sec with a range of 100 miles. Moreover, a railgun relies on electricity alone as its power source, and this is a much safer alternative to store (railguns are being developed for Navy destroyers) than the energetic and explosive materials used as propellants and projectiles with typical weapons.

Additional Tidbits:

• Projectiles are made of tungsten, a rare metal with the highest melting point of all elements and are known as one of the toughest things found in nature. 
• A possible application for a rail gun is launching satellites and or space shuttles into the upper atmosphere. 
• Rail guns could be used in space, unlike traditional weaponry, because chemical propellants require air to function. 
• EM railguns fire projectiles with a force of 32 megajoules. "The Navy describes a megajoule as the equivalent of a "one-ton vehicle moving at 100 mph". 
• The equivalent speed of some railguns is 1.2 miles/second

Force Between Two Parallel Currents:
Each wire exerts a force on the other; the current running through wire b creates a magnetic field at wire a and the current running through wire a creates a magnetic field at wire b. Using the equation for the magnetic field due to a long straight wire, you can find the magnitude of the field that is created at each wire.






Using the RHR, it can be determined that the direction of the magnetic field at each wire is down, and, with the field, you can determine the force that each wire exerts on the other.





Since the same magnitude would be derived if computing the force on the wire a due to the current in b, you can show that the two wires attract each other.

Here is a video displaying a railgun in action:

 3:23The Science Behind Electromagnetic Railgun Weaponry - Videos