The magnetic field produced by the rails can be estimated by the Biot-Savart Law, which calculates the field of a current carrying long straight wire; B = u 0 I/2pir. The plot on the right shows how the magnetic field around a wire rises linearly with current. The wire in this case has a radius of 0.00635m and its length is dimensionless. Notice how one Tesla is not achieved until 35000amperes flow through the wire: Producing a strong field in a straight wire requires vast amounts of current, and there are several more efficient ways to achieve these high field strength values without resorting to several tens of thousands of amperes. Some of these methods are to be explored in another, future Railgun design.

The plot on the left illustrates how the magnetic field strength drops with distance between the rails and increases with decreasing rail width. Both relationships are exponential. Seeing as the acceleration is a product of the force created by the magnetic field strength acting on the mass of the armature, it can be seen that ideally, for the highest possible field strength a rail gun would have very thin rails, very close together (not surprisingly, this translates into a large L' value), running a very high current. Unfortunately these two parameters limit the mass that can be launched, and also exacerbate the rail erosion problem, as thinner rails have less surface to dissipate the heat produced during firing.

Ultimately, as is the case with virtually every other engineering design, a practical Rail Gun design represents a compromise of several factors where rail life, muzzle velocity and payload mass are carefully balanced to meet the requirements of what is expected from the gun.

In my previous Railgun design I utilized two flat parallel rails facing with their broad sides; this provided the greatest amount of surface area for the rail/projectile contact interface so as to minimize arcing and arc damage while at the same time maintaining the rails very close to one another, thus maximizing the magnetic field strength. Other research rail designs include flat rails with narrow sides facing, square rails, round bores, multiple symmetrical rails, and others. According to [5] the ideal rail geometry is plate like, with a Width/Height ratio of >2. This provides a high L' value, although as indicated by the Lorenz force calculation, a high inductance gradient is not required nor does it guarantee a successful design.

For this design I will attempt a square bore. There is good evidence to its superiority to a round bore design[], and, contrasting with the previous rectangular bore design I employed, the larger rail spacing will allow for a greater variety of projectiles to be tried (at the cost of less magnetic force, however).

The repulsive force between the two rails of an electromagnetic accelerator can be approximated by [7]

K=-�(I2/16π)*(L/D)

�= Magnetic Permeability in Vs/Am ( 4 π *10-7)H m-1[8]

I= Current through rails in Amperes

L= Length of rails in meters

D= Distance between rails in meters Taking into account a rail length of 60cm, rail separation of 1cm and a peak current of 100kA the maximum repulsive force between the rails becomes 15KN. This amounts to 3372lbs. The mean pressure on the rails is thus 238PSI. Rail repulsive force becomes 10500lbs with the addition of a 500PSI injector. This load is assumed to be shared equally by the 28 bolts holding the structure together, thus requiring the bolts to clamp a 374 pound force each. By pre-tensioning the bolts to a pre determined torque it is possible to preload the entire structure to a force greater than the total repulsive force of the rails during firing, and in this way ensure that no rail deflection occurs, maintaining barrel integrity, seals, and ensuring continuous contact between the armature and the rails.

This does not, however, apply to plasma armatures; as experience from the original RailGun demonstrated, the actual pressure inside the bore during a plasma armature firing will be vastly more than this (enough some times to shatter the enclosure). Peak pressures of over 55000PSI can be obtained with plasma armatures The final design addressed the weak spot where the injector met the gun itself by eliminating it, making the entire gun a single 24 inch long barrel divided equally between the 12" rails and a 12" channel through which pneumatic acceleration takes place. The rails themselves were milled from a large piece of copper, thus eliminating the need for any welding or brazing.

On these pictures the "ears" created by milling the rails in an "L" shape can be seen. Also seen below, behind the bottom rail, is the garolite G-11 "fake rail" where the projectile rides during the initial pneumatic acceleration stage. Below the spot where power is fed into the gun can be seen more clearly. This had to be milled very accurately since that is the point of highest plasma pressure in this particular design. Material choices on this gun were as follows: The enclosure is constructed of 1/2" thick Garolite G9, one of the strongest composites currently available. G9 is both extremely strong, very stiff, non conductive and non magnetic.

The rail spacers are a 1/8" thick strip of Garolite G11 laid over the G9 enclosure. G11 has similar properties to G9, however during tests [] it showed the lowest electrical ablation rate of any non ceramic tested. The low ablation rate means the gun should be able to fire several shots before these need to be replaced.

Rails are oxygen free copper, 3/4" wide, 1/8" thick, 1ft long.

Bolts, nuts and washers are 18-8 Stainless Steel, the highest grade SS available. Stainless was chosen because it is non magnetic; a magnetizeable material around the rail will carry with it magnetization losses. Ideally a small performance gain could be obtained by having non conductive bolts, but there are no such bolts available today which would be strong enough for this application.