Railguns

	Notice:
	Please bear with us. Your ride's still a work in progress.

A railgun is a projectile weapon that uses high electric currents to push a projectile between two rails. The potential advantages of a railgun are high speed projectiles. Disadvantages include rail wear, the need to store large amounts of energy, and the equipment to produce pulses of extreme currents.

Working principles

An electric current creates a magnetic field that circulates around it. If you have two parallel conductors carrying current in opposite directions, they both produce a field that points in the same direction between them, amplifying the field in that direction (likewise, outside the two wires the fields point in opposite directions making the field weaker there and causing it to fall off faster than the field from a single wire).

A magnetic field exerts a force on any electric currents going through it. The force is in the a direction perpendicular to both the magnetic field and the current, and is proportional to both.

The magnetic field (magenta) circulating around a cross sectional plane perpendicular to the direction of an infinite line of current (green).	The magnetic field (magenta) circulating around a cross sectional plane perpendicular to the direction of two infinite line of current in the opposite directions (green).	The force on a current due to a magnetic field.

The basic idea for building a railgun is to take two parallel conductive rails. Short the two rails with a conductive projectile near the breach. Apply a pulse of very high current, that will run down one rail, through the projectile, and back up the other rail. The current-carrying parts of the rail make a high magnetic field between them. This field pushes on the current flowing through the projectile, which launches it down the rail. As long as the projectile shorts the two rails, it experiences the force and is accelerated faster.

A simplified diagram showing the workings of a railgun.

The magnetic field can be enhanced if the railgun uses a ferromagnetic barrel around its rails. This in turn will increase the force on the projectile and improve the railgun efficiency and performance.

The overarching requirement of extreme currents to provide both the magnetic field and propulsive force combined with a largely low resistance design using highly conductive rails and a projectile mean that railguns are engineered to be high current but low voltage devices. A consequence of this is that artistic visions of railguns with electric arcs buzzing between the rails as the weapon charges up will not happen; the gun will never develop the voltage needed to cause these arcs across such a large gap as the rail separation and in general arcs are to be avoided to prevent excess wear on the rails.

Basic electrical engineering and interior ballistics of a railgun

The mechanics of a system of electric currents, its energy and the forces acting on it, are often most conveniently found using the inductance of the system, commonly denoted $L$. For our purposes, the inductance per unit length ${\mathcal {L}}$ will be more convenient. The actual inductance of a particular circuit will likely be computable only numerically, but we can make some useful approximations. The DC inductance per unit length of a transmission line of radius $r$ with wire separation $d$ is known to be

${\mathcal {L}}={\frac {\mu _{0}}{2\pi }}\left({\frac {1}{2}}+\ln \left[{\frac {d}{r}}\right]\right)$

where $\mu _{0}=4\,\pi \times 10^{-7}$ H/m is the permeability of free space. The rails in our railgun approximate this transmission line between the power couplings at the breach and the location of the projectile. While the rails might not be circular in cross section, we can still take $r$ to be some approximate characteristic transverse length scale of the rail cross section (perhaps $r\approx {\sqrt {h\,w}}$ for rectangular rails of height $h$ and width $w$; the logarithmic dependence means the net result is not strongly dependent on the exact value for $d\gg r$). If the rails are enclosed in a permeable material (such as iron or other ferromagnetic substance), $\mu _{0}$ can be approximately replaced by the permeability $\mu$ of the material as long as the current is not so strong as to produce a magnetic field which saturates the material.

The electric force on the projectile with constant current $I$ is

$F_{e}={\frac {1}{2}}\,{\mathcal {L}}\,I^{2}.$

The kinetic energy is the product of the force and the distance over which that force is applied. For a total rail length $l$, this gives

$K_{e}=F_{e}\,l={\frac {1}{2}}\,{\mathcal {L}}\,I^{2}\,l.$

For the projectile at a distance $x$, the total inductance is $L={\mathcal {L}}\,x$. The magnetic energy of the circuit is

$U={\frac {1}{2}}\,L\,I^{2}.$

When the projectile leaves the railgun $x=l$ such that $U=K_{e}$. The total energy is $E=K_{e}+U$, with the result that, ignoring any other losses, the efficiency of a railgun with current fed into the rails only at the breach is never greater than 50%.

In addition to inefficiencies due to the loss of magnetic energy once the projectile leaves the barrel and the circuit is broken, there will be frictional and resistance losses. Contact with the rails will produce a frictional force $F_{f}$ on the projectile. The work done by the force against this friction is

$W_{f}=F_{f}\,l.$

The actual kinetic energy of the projectile will be the net force times the length of the rails, such that

$K=K_{e}-W_{f}.$

The projectile speed $v$ will be

$v={\sqrt {2\,K/m}}.$

If the projectile has a resistance $R_{P}$ and the rails have a resistance per unit length $\rho$, the total resistance of the system when the projectile is at a distance $x$ from the breach will be

$R=R_{p}+x\,\rho .$

The resistive power loss is

$P=I^{2}\,R.$

Under constant force, the position as a function of time $t$ is

$x={\frac {1}{2}}{\frac {F_{e}-F_{f}}{m}}t^{2}$

for projectile mass $m$ The time to reach the end of the rails $\tau$ is thus

$\tau ={\sqrt {2\,l\,m/(F_{e}-F_{f})}}.$

If we integrate the resistive power over time to find the total resistive energy loss,

$E_{R}=E_{p}+E_{r}$

where $E_{p}$ is the resistive energy dissipated across the projectile

$E_{p}=I^{2}\,R_{p}\,\tau$

and $E_{r}$ is the resistive energy dissipated into the rails

$E_{r}={\frac {1}{3}}\,I^{2}\,\rho \,l\,\tau .$

The total efficiency therefore becomes

$e={\frac {K_{e}-W_{f}}{U+K_{e}+E_{p}+E_{r}}}.$

For well-engineered real systems, this often takes values on the order of 30%.

More sophisticated design can increase the efficiency, at the expense of increased complexity. For example, multiple energy storage units distributed along the rails that are triggered as the projectile passes would reduce the stored magnetic energy $U$ in the rails at the time the projectile leaves. However, discussing the engineering of these more complicated systems is beyond the scope of this work. In addition, the additional complexity such a system would incur reduces the railgun's attractiveness compared to coilguns, which have similar timing and switching considerations but also can eliminate the rail friction by using a levitated projectile.

Self forces

The same interaction between the magnetic field and the current that pushes the projectile also acts on the current flowing through the rails. This produces a strong force that acts to push the rails apart. If this happens, electrical contact with the projectile will be broken and the rails might get permanently damaged if they are warped beyond their elastic limit. A consequence of this is that railguns will not have bare exposed rails. Instead, the rails will be contained within a strong barrel structure that can support the forces pushing on the rails to minimize strain on the rails and keep the gun from bursting or warping. Sadly, common artistic interpretations of railguns with a pair of exposed unsupported rails will not work.

If you are using the engineering analysis from above, the force per unit length pushing the rails apart is

${\frac {F_{r}}{x}}={\frac {1}{2}}\,I^{2}\,{\frac {\partial {\mathcal {L}}}{\partial d}}.$

Recoil

The circuit containing the current in the rails and projectile must be closed on the other end of the current loop. The magnetic forces push on this just as much as they do on the projectile, producing recoil in accordance with Newton's second law of motion. The total recoil impulse (momentum transfer) will be the mass of the projectile that is launched out the end of the barrel times the speed of the projectile as it is launched. In math-speak, the recoil impulse will be $-{\vec {p}}$, where ${\vec {p}}=m\,{\vec {v}}$ is the momentum of the projectile with $m$ the projectile mass and ${\vec {v}}$ the projectile velocity.

This will be similar in magnitude to the recoil produced by a chemical propellant firearm, with one important difference. A considerable portion of the recoil from a chemical propellant firearm comes from the hot gases jetting out of the barrel, acting like a rocket. The amount differs depending on the interior ballistics of the firearm but a contribution of very roughly 30% to the recoil is typical. The railgun will lack these propellant gases, so that the recoil will be somewhat less than that of an unmodified firearm. However, the same reason it lacks this additional recoil does not allow a railgun to use a muzzle brake, which can reduce the recoil of a firearm even further.

Safety

One advantage suggested for railguns is that without the need for reactive propellants, ships and ammunition storage warehouses will be significantly less hazardous if hit by enemy fire. In operation, a railgun might only store enough energy for one shot in volatile fast-discharge energy storage devices such as capacitors. The fast discharge energy storage would be recharged by a generator between shots. On a vehicle, this could be the same generator used for electric traction, thus allowing a unified power supply system for the drive train and weapons. While hits to the fuel or generator are still possible, this hazard is inherent to the operation of the vehicle and is present whether the vehicle is armed with a railgun or not.

High speed

In a conventional firearm, the propulsion of a projectile becomes increasingly inefficient as the projectile moves at speeds close to the speed of sound in the propellant gas. A railgun, lacking propellant gas, does not have this problem. As long as the projectile maintains electrical contact with the rails the projectile can be accelerated. This makes railguns a contender for launching high speed projectiles, potentially attaining speeds that would otherwise require an exotic and complicated chemical propellant firearm like a light gas gun. For comparison, artillery will tend to get to around 0.6 to 1 km/s and a tank firing an anti-tank APFSDS dart might reach speeds approaching 2 km/s. Meanwhile, a recent program developing a railgun for the U.S. Navy could launch projectiles at up to about 3.3 km/s (CITE, check if true, other reports say only Mach 6 ~= 2 km/s. NEED TO FIND PRIMARY DOCUMENTS HERE!!!).

At around 3 km/s, the kinetic energy of a projectile will match the energy released by the detonation of the same mass of TNT. This means that a separate warhead is un-needed. The energy liberated by the projectile slamming into a target at more than 3 km/s will produce a bigger explosion than if it were filled with explosives – particularly because artillery shells need to be built extra sturdy to survive launch leaving relatively little space for the warhead. It is worthwhile to note that penetration doesn't increase when speeds get over 2 km/s. A faster speed can flatten a larger area but if your goal is punching through armor any energy used getting faster than 2 km/s at the target is energy wasted. Note that this is speed at the target. Because a projectile launched in atmosphere will suffer from aerodynamic drag in flight, when shooting at distant targets you may need higher speeds at the muzzle to get the desired terminal performance.

The usual expression for the kinetic energy is $K=1/2\,m\,v^{2}$. Using ${\vec {p}}=m\,{\vec {v}}$ we can express the kinetic energy as $K=1/2\,{\vec {p}}\cdot {\vec {v}}=p\,v/2$. We can now see another benefit of high speed – for constant kinetic energy, the magnitude of the recoil impulse is $p=2\,K/v$. So the faster the projectile is launched, the less recoil will be produced (however, we again must caution that the terminal effects of the projectile depend on more than just kinetic energy and it is a mistake to think that two projectiles with the same $K$ but different $m$ and $v$ will have the same effect on target).

In order to maintain electrical contact with the rails the projectile must either keep a sliding physical contact with the rails or strike an electric arc to the rails. An electric arc is arguably the worse of the two options, as each shot will be arc-welding the rails and will produce excessive rail wear. A sliding contact is no worse than any conventional firearm with the bullet maintaining a sliding pressure seal with the barrel. But as speeds get higher and higher, a sliding contact produces more and more barrel wear. A high speed projectile can be expected to significantly reduce rail life compared to the barrel life of a modern firearm. (CITE navy railgun, ~100 shots per barrel & not all that high speed compared to modern artillery, not clear if these were all full power shots) (Disposable rails? Liquid metal rail contacts?)

High speed wear on the rails and projectile will produce vaporized material that are ejected from the barrel on launch, producing a loud muzzle blast and muzzle flash. Much like modern firearms, this will indicate to observers that the weapon was fired and can help to localize its location, either directly by the flash or from dust and debris kicked up by the blast.

As current flows through the projectile, electrical resistance will heat it up. Thus, some fraction of the energy delivered for the discharge will go into raising the temperature of the projectile. At high enough speeds, this inefficiency will deposit so much heat that the projectile will be affected, either warping, partially or fully melting, or vaporizing. Warping or partial melting will adversely affect accuracy, complete melting or vaporization will prevent the projectile from reaching its target. (CITE likely upper achievable speed due to melting, EMRG paper?) Using the terminology of the electrical engineering and interior ballistics section, above, the maximum speed is given when the resistive energy dissipated across the projectile $E_{p}$ exceeds the heat energy needed to damage the projectile to the point that it no longer functions.

Shot consistentcy

In modern artillery, variance in timing of ignition and burning rate of the powder can produce differences in muzzle speed and delays of launch of the projectile. This can result in decreased accuracy. These will not be present in a railgun, resulting in more consistent exterior ballistics and improved accuracy.

power supply, pulse forming network, lack of casing & propellant & primer

efficiency of navy's electromagnetic rail gun ~30% (CITE this)

helical railguns

hybrid railguns-coilguns (using electromagnets to increase the B field)

plasma railguns

plasma rails & why they don't work