Saturday, March 28, 2009

What Is (And Is Not) A “Railgun”? (a long rant, intended to educate)

Let's get one thing out of the way right off the bat: In this blog, we are talking about the real thing, not a gamer fantasy. If you’re interested in real-world electromagnetic launchers, whether amateur or military, then read on. If your primary interest is in the man-portable fantasies presented in first-person-shooter computer games, you’re going to be disappointed.

Now then, let’s define “railgun”. There are three things in the field of arms which people call “railguns” today, but only one usage is correct in the modern world.
Railway Guns

Once upon a time, conventional (that is, combustion-propelled) artillery pieces were constructed which were so large that the only practical means of transporting them was on railroads. These were also sometimes called railguns, because they moved on rails. Since the advent of the modern electromagnetic railgun, arms experts prefer to use the term “railway gun” for these obsolete but impressive monsters.

Another modern device, which is frequently (but mistakenly) called a “railgun” by the ignorant, is the coilgun. A coilgun is also an electromagnetic launcher, but its construction and mode of operation is very different from a true railgun. The coilgun has one or more coils of wire or cable, each typically consisting of multiple turns. The projectile is accelerated by either being attracted to, or repelled by, the magnetic fields created by these coils. The projectile itself may have an independent source of an electromagnetic field, although it is more common for them to create repulsion via eddy currents induced in the projectile and the resulting mirror-image magnetic field which pushes against the field created in the working coil(s).

Other names for these devices are “coaxial linear motor”, “gauss gun” and “mass driver”.

In a coilgun, there are no current-carrying “rails”, and the current which passes through the working coils does not pass through the projectile. These devices are typified by high inductance in the coils, lower operating currents, higher complexity due to sequential switching of current to the coils. Their maximum practical muzzle velocity is considerably lower than railguns, although this does not mean that they are impractical. Coilguns are well suited for accelerating high masses to relatively conventional velocities. If your goal is to launch an aircraft from the deck of a carrier, or even to lob conventional-sized exploding projectiles at typical artillery velocities, a coilgun is very likely to fill the bill. A word about the Navy’s research into electromagnetic catapults for aircraft carriers: these devices are linear motors, arguably a form of coilgun. They are NOT railguns!

True Railguns
The true railgun has three essential components:

1. a pair of parallel, conductive rails which line the bore of the launcher. 100% of the operating current passes through these rails.

2. an armature placed between the rails, which is free to slide along their long axis, and which conducts electric current from one rail to the other. 100% of the operating current fo the gun passes through this armature. Note that the armature may be the projectile itself, or in modern military designs, the armature is a sabot which holds the actual projectile (typically a kinetic penetrator dart very similar to those used in conventional APFSDS rounds).

3. A source of enormous electrical current, AKA the pulsed power supply. Note that I did not say “voltage”. We’ll get to that in a bit. Generally speaking, the power supply is connected across the breach end of the two rails. One rare but possible exception is in a case of “augmentation rails”, to be discussed later.

Theory of Operation
Way back on September 18, 1820, a clever fellow named André-Marie Ampère demonstrated before the Royal Academy that two parallel wires carrying current would be attracted to each other or repelled from each other, depending on whether the current passed through the two wires in the same, or opposite directions. This effect was later formally described by Ampere by a formula later called Ampere’s Law in his honor, and also (with different math and for different purposes) by Hendrik Lorentz. The Lorentz Force – crucial to the operation of a railgun, is named after Hendrik Lorentz.

Put simply, the Lorentz Force says that a point of charge (an electron for example) moving through a magnetic field will experience a force that is at right angles to both the axis of the magnetic field and the direction of current flow. See also:Fleming’s Lefthand Rule

In a railgun, the current from the power supply travels down the first rail, through the armature (at right angles to both rails) across to the other rail, and back to the power supply through the second rail. Since all current-carrying conductors create a magnetic field, fields are created by the rails as well as the armature. Because these fields are at right angles to each other, a net force on the armature (and the rails!) is produced. The rails are constrained so they cannot move (because having the gun barrel explode is sub-optimal) but the armature is free to move and if the currents are high enough, move it will, and with alacrity!

A deceptively simple-looking formula exists to describe the force acting on the armature for a given amount of gun inductance and current:

Frg = 1/2 * dL/dX * I2

Where F is the force acting on the armature and rails, and the dL/dX term is the change in inductance vs. change in distance, and I is the current. The dL/dX term can be simplified as L‘ to summarize the inductance gradient of the entire gun.

Now we come to the chief difficulty of railguns: that L number is the inductance in the gun. Inductance of a current path is determined by the magnetic permeability of the enclosed medium (in this case, air or some gas), its area, the number of turns around that area, and the axial length of the windings.

In a railgun, we have just one turn. And the area isn’t much at all. The axial length (along the axis of the magnetic field) of the enclosed area of the current path is nearly none – just the width of the rails. The permeability of gases (as opposed to say, iron) is very low. So the inductance of our gun is vanishingly small. Since the force acting on the projectile is the product of the inductance and the current, this means we have to have ENORMOUS currents passing through the rails and the armature to get any accelerating force at all.

Currents in full scale military railguns are in the millions of amps. Currents in “bench top” (ie; amateur) scale railguns will easily be in the hundreds of thousands of amps. Furthermore, with a bit of math, we can see that even a well-designed amateur device with a reasonable bore and size cannot outperform – in terms of muzzle energy vs. mass and size of the device – a typical high powered rifle. It’s tough to beat chemical energy storage until you are pushing the boundaries of what physical laws allow.

Which leads us to the question: Why?

Why build railguns at all?
There are two reasons for anyone to build a railgun.

Reason #1: to outperform a conventional projectile weapon. Conventional projectile weapons are powered by expanding gas, typically the product of combustion. This is very practical because chemical energy storage density (the amount of energy storage per unit mass the storing method) is very high. But there are fundamental limits on their performance. The most important limiting factor for expanding gas guns is this:

The projectile can only be pushed as fast as the gas can expand, and the gas cannot expand faster than the speed of sound in the compressed medium. Now admittedly, the speed of sound in a highly compressed gas can be very, very high. That’s why bullets from firearms routinely exceed the speed of sound in the ambient air outside the muzzle. But nevertheless, there does come a point at which no matter how much powder is stuffed into the breach of a gun, the projectile will not accelerate any faster than some finite number of g’s. Modern artillery has already reached this point. If higher velocities are desired, the only way to accomplish them is to increase the acceleration time, ie; the barrel length. This gets ungainly fast.

Consider the Soviet-era 2S7 “Pion” self-propelled 203mm artillery gun, which holds a maximum range record for modern artillery of just over 47kM. Its barrel is over 11 meters long, whereas the vehicle which carries it is only 10.5 meters long. That range was only achieved using rocket-boosted artillery shells. But to achieve maximum range with any artillery, one must fire the projectile at an elevation angle of about 45 degrees, creating a parabolic trajectory which requires a long time to for the projectile to follow. Time to target is another important issue, especially in today’s battlefield where threats move very quickly. The faster the muzzle velocity, the shorter the time to target.

2. Because they’re cool. Look, even well-funded amateurs have no hope of exceeding the performance of chemical propellants using electromagnetic launcher. They just do not scale down that way. Can’t be done with modern technology. Not even the Army is putting any serious effort into man-portable electromagnetic guns because the storage devices required just aren’t small or light enough. But lots of other mad scientist type hobby projects have no practical reason to exist either- think Tesla coils, coin and can crushers, and so on. But they’re a lot of fun to play with.

The moment we start to design a practical railgun, we quickly run into tough questions, such as:

1. how do I source 100 or even thousands of kilo-amperes into the gun?

2. how do I switch or control all that power?

3. Ohm’s Law says I’m going to lose a LOT of my power just to resistive losses in the rails. What – if anything – can I do about it?

4. The environment inside the gun during a launch is like Hell’s own arc welder. How does one make rails, armature, and bore lining materials that will stand up to that?

Okay, one thing at a time…

1. Power source.
To drive a railgun, you need a lot of electrical energy. Even if they were 100% efficient, the amount of kinetic energy contained in a high powered rifle bullet is thousands of joules. The kinetic energy of a long range artillery shell is in the millions or tens of millions of joules, and much more than that must be put into the gun system because of losses. Well-designed modern railguns have typical efficiencies around 30%, and smaller guns are more like 3% – 10%, so we can already see we need a tremendous amount of stored energy.

Furthermore, since the whole point to a railgun is to achieve very high accelerations and muzzle velocities, we need to be able to release all that stored energy in a very short period of time, because (if all goes well) the armature isn’t going to be in the barrel for more than a few thousandths of a second at most.

Electricity, as a means of storing energy, stinks in comparison to other means (such as chemical energy storage). A sophisticated high voltage capacitor weighing one pound might be expected to store 1,000 joules or 1kJ. A pound of TNT stores 1,899,536 joules, or nearly 2MJ. So we already know we’re going to be exploring exotic means of electrical energy storage.

It gets worse. Not only do we have to overcome the electrical resistance of the gun, but any rapid change in current is resisted by the inductance of the circuit. The sum of these two numbers (called the impedance) may be quite low, but when the goal is 100,000 amps or more, even the lowest impedance that is practically attainable will still require a fairly high voltage to overcome. This is established by a derivative of Ohm’s Law, which states that the current (at any instantaneous point in time) is equal to the voltage divided by the impedance.

Early railgun experiments in the 1970s tended to use large banks of high voltage capacitors specially designed to deliver very high currents in very short periods of time, but it rapidly became apparent that capacitors would never, ever achieve the storage densities required to field practical weapons on mobile platforms (such as tanks or naval vessels). During the 1980s and ’90s, new electromechanical devices which store energy in a combination of an intense magnetic field and rotating masses were developed.

The first of these was the Homopolar Generator, or HPG. The HPG is a DC generator device similar in working principle to Faraday’s Disk. HPGs achieve many orders of magnitude higher energy density than capacitors, and are capable of currents higher than required by railguns. Unfortunately, HPGs inherently have an output voltage that is so low (a few volts) that it cannot achieve high currents into a practical railgun load, so to use an HPG with a railgun requires a series of exotic pulse-forming devices which shorten the pulse length but increase the pulse amplitude (voltage) to something that a railgun can use. The technologies available for pulse-shaping megampere-regime pulses include things like sacrificial fuses and explosive-driven switches, which must be replaced after each shot. Acceptable for research in the lab, but not practical for a fieldable weapon.

After the HPG, the Compensated Pulsed Alternator, or compulsator, or just CPA, was developed. The compulsator has several advantages over the HPG. Its output voltage is much higher, up to several kilovolts. It is an alternating current device whose output is presented in pulses, potentially making switching of current to the gun much simpler. Most railgun experts believe that compulsators will be a crucial part of any practical weaponized railgun.

Unfortunately, HPGs and CPAs are complex, massive, expensive, precise devices. The construction of an HPG or CPA capable of driving even a small benchtop device would required the resources of a small government or a large university or corporation. They are beyond the reach of any amateur, even an amateur with a rich and very generous uncle.

That leaves the amateur with high voltage capacitor banks. These aren’t cheap either, but they can be had, especially if one is very lucky or very savvy about obtaining surplus exotic hardware.

2. switching all those zoobs
Trick question: Let us suppose we have a capacitor bank capable of delivering 134,444 amps at 9,000 volts (for those who are paying attention, yes, that is 1.21 gigawatts peak power).

What will happen when we connect a heavy duty industrial switch – the biggest, beefiest sort we can find- between this power source and our railgun… and turn it on?  Hints: you’ll never find any pieces of that switch much bigger than a marble, and you’ll probably lose your hand, if the shrapnel doesn’t dismantle your face.

So what sort of switch can handle these sorts of voltages and currents?

Answer: a triggered spark gap switch. Getting into the details of how these work is beyond the scope of this post, but suffice it to say that you can buy them (expensive!) or you can build them. Doing it right is more complex and finicky than it seems, but it is within reach of an amateur who A) has machining  resources and B) does enough homework.

3. power losses and efficiency
Ohm’s law says that resistive losses in the current carrying conductors (rails, cables, everything) of our railgun increase linearly with increasing resistance, but go up as the square of the current! We have a LOT of current. Uh-oh. Short of unobtainable superconductors, the best we can hope for is to use oxygen-free high conductivity copper (AKA alloy 101) for all of our conductors and possibly the rails as well. We must keep all connections and current paths as short as possible.

“Stray” inductance, that is, inductance created by the area enclosed by the entire current path from source terminal to source terminal but excluding the inductance inside the gun, is “wasted” inductance – that is, it does not contribute to the force on the armature, yet as all inductance does, it impedes any change in current, slowing down the rate of rise of voltage and current in our system. Since this is obviously undesirable, we’ll want to keep all of our conductors as close to each other as possible, without letting them short-circuit. The classic way of doing this is with a “parallel plate transmission line”, that is, a pair of flat, parallel conductors, closely spaced and separated by a thin layer of insulation. Don’t forget that Lorentz force is acting on all the conductors in the circuit. If you don’t clamp all the high current conductors together with strong clamps, bolts, and insulating materials, they will tend to fly apart instead of your railgun shooting its armature down the bore.

4. The gun environment
Fact: at least half of the total power put into a railgun is lost to ohmic heating of the rails and the plasma armature if we’re using one (let’s not – more on that later). If we manage to keep the pulse nice and short (the way we want it) and the peak current nice and high (the way we want it) and the voltage drop across the gun high enough, then we’re going to be dissipating at least several million watts inside our gun in the space of a millisecond or less. Everything is going to get very hot, very fast. Furthermore, the armature is supposed to remain in electrical contact with the rails while it’s sliding down the barrel at Warp Factor 9000. And then there’s the physical force created by the magnetic field which, in the places where it can’t act directly on the armature, such as between the rails, is also trying to tear the gun apart.

In the early days of railgun research, efforts focused on plasma armatures, that is, an arc was formed behind an insulating projectile, and as the arc moved forward, the projectile rode on the shockwave formed by the arc. But it turned out that plasma armatures (which by their very nature are really hot) tended to melt the surface of the copper rails, causing severe erosion. In some cases, a single set of rails were ruined after only one shot.

Later developments focused on armatures with swept-back fingers designed to maintain a high pressure contact with the rail surface so that no arcing would (hopefully) occur. Since this is a relatively recent development (last decade or two) and apparently a successful one since all the labs show pictures of very similar contact armatures, it is still hard to find solid data on how this is best achieved, but pictures of recent armature designs discoverable in open media give us plenty of clues.

Various exotic materials for the rails have been proposed in the past, but in all of the materials proposed so far, the disadvantage of higher electrical resistance far outweighed the advantages of higher melting points or harder surface modulus. This would seem to explain why so many papers have come out researching armature design, looking for ways to maintain good contact with the rails, and so few have come out discussing exotic rail materials.

Remember, the bore of our railgun is square. There are two sides occupied by the copper rails, and two others sides which simply provide physical enclosure and guidance for the projectile.

Those remaining two sides must be made from a material having good electrical insulating properties, low friction, high strength, and high heat resistance.

The experts appear to have nearly solved this problem now, but it’s very hard to find out much information about what they’re using in the latest devices.

For lab-scale railguns, Delrin (AKA acetal resin) has been used with a fair amount of success. This is good news, because Delrin is readily available from industrial sources and is relatively affordable even by amateurs. There are two varieties: acetal homopolymer and acetal copolymer. For our purposes, the homopolymer is better, because it exhibits higher mechanical strength, stiffness, hardness and creep resistance as well as a lower thermal expansion rate and better wear resistance.

Outside the rails and bore sidewalls, we’re going to need a very strong enclosure indeed, since we are, after all, building a cannon. One interesting thing about our cannon is that nearly all of the force on the barrel containment is in a straight line between the rails. Since we also know we’ll probably have to disassemble the thing after each shot to clean it and inspect and/or refurbish the rails and bore liner, this suggests a housing construction style built from slabs of some strong non-conducting material such as fiberglass or other fiber-reinforced plastic, held together with bolts. And lo, that is exactly how everybody – from professionals to amateurs-with-a-clue do it.

It is how my first gun was built, although I did something strange and wrong with the physical design, but it hardly mattered since I didn’t have enough stored energy or gun inductance to do anything more than make loud noises.

In some future article, I will write about my first railgun, constructed in 1989, why it was a dismal failure, and what I learned from the attempt.

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