PowerLabs Rail Gun 2.0 Research!

 Project Introduction:

From its conception, the original PowerLabs Linear Magnetic Accelerator (“Rail Gun”, or “Railgun”) was conceived for the primary goal of simply proving that it could be done; on a low budget, with common materials and powered by a never tried before electrolytic capacitor bank.
In that, it was extremely successful: Not only did the gun fire flawlessly over 30 times (it is not uncommon for research rail guns to break down in the first shot), but it also attracted vastly more attention than I could ever have hoped for:
After its page generated hundreds of thousands of hits, the gun was featured on Discovery Channel, TV6, numerous newspaper and magazine articles, and earned me several job offers from the private sector, research institutes, and industry. The highlight of the popularity of this project came in the form of two separate offers from laboratories associated with the department of defense (DoD), which, apparently can’t hire me because I was not born in the USA (someone must have forgotten that the majority of the best scientists and engineers in the world weren’t born here)…
The original railgun design was completely experimental; built, assembled and operated solely by myself, on my first year of engineering school and being entirely based on my knowledge of electricity and magnetism at the time. With the catastrophic failure of the injector casing and the injector/rail assembly during a full power shot, I found the extra motivation I needed to re-design the gun so that my research in this area could continue. Of course, by now, with 3 years of engineering school and extensive research on the subject, I expected even greater successes.

 Project Description and Goals:

 The objective of this project is to successfully design and construct a linear electromagnetic accelerator capable of accelerating a lightweight payload to velocities greater than 1000m/s so that high velocity erosion in the rail/armature interface can be studied and a means for minimizing this erosion be investigated.
 Rail Guns are not by any means a new technology; 50 years ago when the first true rail guns were built and fired it was believed that they would provide a means to accelerate objects to virtually any desired speed, replace conventional weapons and provide cheap orbital launches for small payloads. Today, despite enormous advances in the technology, the maximum muzzle velocities attainable are nowhere near what was once believed possible, and railguns remain confined to the laboratory where some times the rails need to be removed and resurfaced after every shot. The cost of obtaining high acceleration through electrical action between sliding contacts is the rapid destruction of those contacts through arcing and friction. I am not alone in believing that we are very close to a solution to this erosion problem, and it is my belief that once this solution is found it will have profound implications our understanding of materials science, power transmission, high velocity friction, and open new doors to the fields of transportation, defense, manufacturing, and more.
As I embark on this research once again to further my knowledge in various fields of science I hope to make a significant contribution to the field of electromagnetic acceleration, which has fascinated me ever since I first learned about it, and hopefully secure a job offer in this field.

 Theory (a simplified overview):

RailGuns differ from other means of accelerating objects in that the acceleration in the rails occurs purely by magnetic repulsion. This magnetic force is termed a “Lorentz Force“, and it has been shown to be:
F_rg = 1/2*dL/dX * I² [1]. The dL/dX term can also be written as L’, the inductance gradient of the rails. From this equation it can thus be seen that even in a well designed Rail Gun (high inductance gradient), the most predominant factor in determining exit velocity will always be the power supply current.
Thus it follows that in order to produce high muzzle velocities, long rails and/or very high currents must be used. Unfortunately, maintaining a high current through a long pair of rails requires a lot of energy (Current * Voltage * Time), and with high currents high rates of rail erosion have so far been unavoidable.
The exit velocity of a rail gun can be estimated through the equation:

V=u+L’/2m * (integral 0→t) I²dt [1] , where u is the injection velocity.
Although this equation is of limited use unless the exact shape of the current pulse is known, it once again it demonstrates the importance of a high current. It also states the obvious fact that higher exit velocities will be attainable with higher injection velocities. Not easily seen from the equation, but equally important, is the fact that at higher injection velocities the electrical arcing and ohmic heating between the projectile and the rails will not have as much time to heat the rail surfaces to vaporization. Thus, up to a certain point, a higher injection velocity will help minimize  rail damage[10]. It will also prevent rail/projectile spot welding, which can occur at zero injection velocities and low powers on metal/metal contacts. Given the energy expenditure of accelerating the projectile electrically, and the advantages of pre-injection, it makes sense to impart as much initial velocity to the projectile as possible, and only then allow the electric action to do what it is most effective at: attaining velocities that would not be feasible with a gas injection mechanism alone.
Resistive losses in a Rail Gun are given by:
W_r= R₀(integral 0→t)i²dt = 2R₀(mv)/L’ . With mv being the momentum of the projectile, it can be seen that energy loss in a railgun is proportional to projectile momentum (not kinetic energy, as might be expected), and can be minimized by increasing the induction gradient. This would imply that rail guns are most efficient at accelerating light payloads, which would steer research towards smaller bores; however it has been shown experimentally [9] that with very small calibers (<18mm)  the efficiency of a railgun decreases with smaller size bores. Clearly other factors are involved, some of which still unknown.
For the sake of simplicity and clarity I will limit myself to these and only a few more equations on this write up. The interested reader is invited to seek further knowledge by reading the sources cited at the bottom of the page (as opposed to creating yet another copy of my design, like so many others seemingly incapable of creative thought and engineering design)

Power Supply and pulse shaping:

The Lorenz force decreases drastically with a reduction in current, and below a minimum current the accelerating force drops below the projectile frictional force and thus power is dissipated with no extra kinetic energy being imparted into the projectile. In order to counter this loss, the ideal railgun electrical pulse shape is a square wave with rapidly increasing pulse current, a high plateau, and a fast current decay. Such a pulse shape can be approximated through a Pulse Forming Network (PFN).
As with the previous Rail Gun, this power supply consists of Cornell-Dubilier Inverter Grade capacitors, each rated at 6300uF and 400V (450V Surge). Operating Temperature is -40C to +95C. These capacitors utilize the latest technology in electrolytic capacitor construction to store 640J each in a can measuring only 3″ dia. x 5.63″ length and weighting 900grams each. Each individual capacitor has a 50KOhm 10W wire wound resistor for charge equalization and also to serve as a bleeder to prevent unwanted charge buildup when power is switched off. They are charged through a 900Ohm current limiting resistor and can be safely discharged through a 6.25kOhm resistor bank mounted inside the bank.
In order to counter skin effect related losses the capacitors are inter connected by very large surface area (30in^2) oxygen free copper strips each 0.064″ thick (1.6mm). The bank is internally fitted with a Fluke 80K6 6-kV probe for voltage monitoring.
The capacitors in the power supply for this railgun has been generously donated by S. Parler of Cornell-Dubilier Electronics.

Rails and Rail Enclosure Design:

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 = u₀I/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 (4π*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 magnetizable 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.

 

 Injector:

 I would like to publicly thank Calumet Machine for assisting in the manufacture of the injector gas system; their expertise was critical in choosing and locating the components necessary for the safe realization of this high pressure system. It was a pleasure working with you guys and I am still amazed that you managed to make a paintball tank-steel hydraulic coupler-brass pipe fitting adaptor!

If full power was to be applied to a static armature the rails and whatever was between them would instantaneously melt under the intense localized heat produced by Ohmic heating as 100thousand amperes tried to make it through the contact resistance. In order to prevent the Rail Gun from becoming a spot welder it is necessary that the armature be moving with some initial speed prior to electromagnetic acceleration. Furthermore, there is no point in wasting valuable electrical energy stored in expensive capacitor banks to accelerate the projectile during the first couple hundred meters per second; compressed gas is a far more efficient and economical way of pre-accelerating the projectile until it starts moving at speeds where electrical acceleration makes more sense. Finally, with increasing injection velocities, there is a corresponding decrease in rail erosion, as the projectile spends less time at any given spot on the rails and thus produces less heating and associated material loss.

 With this in mind a new injector was designed to provide the highest injection velocity possible. The primary design constraint was the solenoid valve; the highest pressure attainable for a reasonably priced rapid dump high flow solenoid valve was 1200PSI working pressure. As such, the entire injector has been designed around this component. The 1200PSI will place a force just shy of 200pounds on the projectile, accelerating it at at over 20thousand “Gs”. Consequently, it will also place a large amount of force on the gun breech, which is why 1/2 thick Aluminum 6061 was chosen as the support material. The mating surfaces were polished to a mirror shine and silicone gasket maker was used throughout in order to ensure everything is gas tight. Ideally this injector should be able to achieve Mach 1 compared to the old design which was only able to push 150m/s at 500PSI.

Armature Design:

Perhaps the single most important factor determining Rail Gun efficiency is the degree of contact between the rails and the armature. Ideally a perfect electrical contact would exist between the two and cause resistive losses to be virtually negligible when compared to the rest of the circuit. These low resistive losses would make for a very low voltage drop across the rails, which would cause very little resistive heating, zero arcing and almost no rail erosion. Unfortunately, maintaining perfect electrical contact between two metallic surfaces that are very small and move at extremely high speeds relative to one another has so far eluded most Rail Gun designers. Solid Armature Rail Guns start off as such and quickly become transitional or hybrid as the metallic contact breaks down and arcing begins at 1.5km/s+[2] forming a plasma interface. Above 4000m/s rail guns are almost exclusively of the plasma type [3], but secondary arcing tends to limit their performance by lowering efficiency as longer barrels are made [4]. Currently there are 3 approaches to armature design: Solid armatures employing a V-notched or U-shaped tail, which is forced against the rails under the high currents present in firing (most common), brush armatures which utilize hundreds of small metallic wires to maintain some degree of contact with the rails despite small irregularities (such as with the French PEGASUS design[]), and plasma armatures, which allow arcing to occur in a controlled fashion behind the projectile and utilize that arc to propel a non conductive projectile down the barrel, despite heavy rail erosion and resistive losses. These were at some point in time believed to be the only means of obtaining velocities above 5km/s, although advances in rail and armature design have made it possible for solid armature designs to perform at similar levels.
In the new PowerLabs design a completely novel armature will be employed which has never before been fired from a rail gun; through advances in materials science a special copper / carbon composite has been made which will retain its dimensional stability due to the extreme heat resistance of carbon, while at the same time not causing excessive resistive losses thanks to a high degree of copper imbedded in it. Other advantages of this material include low residue, the inherent lubricating properties of carbon, ease of machining (can be machined with HSS tools), and the fact that it can never weld itself to the rails. On this photo the compound can be seen being heated with an oxygen acetylene cutting torch. The 5000F flame leaves the carbon virtually unharmed even after several minutes, and copper can be seen evolving from inside the compound, coloring the flame. Much like composite materials have made it possible to construct strong lightweight rail enclosures, different composites should also make it possible to construct a lightweight armature that will withstand the stresses of electromagnetic firing and accelerate payloads with superior performance. Other composites will be tried, as well as conventional armature materials such as aluminum and plasma.
The machined rounds weight 4.27grams

A more conventional armature was also produced from pure, electrical grade aluminum (Al1100). Aluminum has conventionally been the preferred armature material for both research and military railguns. There are various reasons for this:

• Aluminum has one of the lowest resistances per unit weight of any material,
• It has a lower melting point than the rails, reducing rail erosion somewhat,
• It has a low density, so when used as a sabot not a lot of energy is wasted accelerating it,
• It is easily available and easy to machine.

 Al1100 was also the material of choice for my original railgun. I found, as others did, that when using any solid armature the rail/armature interface must be perfect; should the sliding armature lose contact with the rails for just an instant, it will automatically start an arc which then consumes very large amounts of power and metal.

 Plasma armatures propelling composite projectiles were planned, but not attempted at this time.

 Charger:

For the rapid, safe, controlled charging of the capacitor bank and the safe firing of the gun the following charger was devised:
Current limited, 2kW, 0 – 4kV variable voltage, 1A output current.
The charger feeds two microwave oven transformers in series through a Variac, and then charges the capacitor bank through an ammeter, to monitor current. The voltmeter in the charging supply monitors a Fluke� High Voltage probe within the capacitor bank itself. For safety power is controlled by a key, and the main switch routes power through a relay so that the gun can not be fired whilst charging. This is particularly important due to the massive back EMF that occurs when the gun fires; this has literally exploded diodes in the past.
Firing is performed by routing power to a 110V outlet within the charger which energizes the solenoid on the gas injector. The fire switch is, of course, a big red button…

 Completed Device:

 Here are some shots of the gun right before it was fired for the first time. You will notice a very large inductor next to the barrel; this was necessary to slow the electrical pulse down to a level where the current no longer cratered the rails at the point of initial contact.

Feed lines are: Argon Gas (Top right hose into gas injector)
Power (two white cables on the right)
Fluke Voltage Divider for charge level monitoring (left)
Injector solenoid power (cable from top)

 Results!

Railgun 2.0 was originally fired on the summer of 2006 for a film crew filming an episode of a Discovery Channel show. For those tests, the Carbon/Copper sintered powder composite was utilized.
This armature, much to my dismay, EXPLODED inside the barrel, creating an incredible blast and a shower of fragments from the muzzle.
Since the gun was designed to withstand over ten thousand PSI, no damage of any sort occurred and filming went on as planned. The exploding armatures looked spectacular on camera, but didn’t do much more electrical efficiency. After several shots were fired carbon vapor deposited itself on the insulators and created a rail-to-rail flashover condition.

A further analysis revealed redeposited copper vapor all over the rail channel. It appears as though the carbon/copper composite was too resistive for the particular currents encountered in this gun and localized heating lead the copper within it to vaporize, causing it to fracture from within. It may still prove to be an excellent projectile for rail guns, but only so long as a low current density and limited energy level are adhered to.

The second round of tests occurred in September 2007, again for television. This time aluminum armatures were utilized and these, despite being deformed by the intense magnetic forces within the gun, held together and accelerated inside the gun to a high speed.

Again the chronograph did not work so velocity readings were unavailable. It is not known if the problem relates to muzzle flash, plasma, or EMP. More research is needed in this area.

After several shots the gun’s efficiency decreased markedly. It was found that the insulator covering the first inch of rails had been blown off and now the armatures were making contact with the first inch of rails, before the power feed. This meant that the Lorenz force was actually slowing the projectile down. Tests were then stopped.

More to come!

 Parts List and Construction Pictures: