Gauss Gun Theory

Gauss Gun Design (breaks down into

Gauss Gun Projects: Look here for pictures, videos, and explanations of my 3 coil guns.

I believe most of us science types have played with solenoids (coils of wire forming an air cored electromagnet) when we were kids. I remember being particularly interested in them when I was about 7 years old, and sure enough it did not take long for me to realize that if a solenoid could pull metal into its core, it could also shoot that metal metal out if the field was turned off at just the right time…

It would be many years until I came back to that concept, but when I was working in Holland 1998 with a high energy capacitor bank the idea re-occurred to me and I decided to put it to work. After several tries and some very interesting results I have decided to share some my acquired knowledge on the web. Partly because many people have asked me to, but also because the few information that is out there is either incomplete, or inaccurate, and the gauss guns on display are (in my humble opinion) too weak to be of any real interest. After several years investing money on energy storage and switching systems, and researching the underlying principles of these devices, POWERLABS was able to develop linear electromagnetic mass accelerators which are now capable of matching muzzle energies of small caliber firearms. This page is dedicated to showcase the latest advances in those accelerators and their development. But first **a warning: The devices described on this page deal with energy storage systems that are easily capable of delivering LETHAL electric shocks, and can fire projectiles capable of causing serious injury of even death. Do not attempt to replicate any of this research unless you are fully qualified to do so! POWERLABS and its creator assume no responsibility for any damages occurred from experiments derived from this page.
** Also, a quick note: some of the information displayed here is fruit of very extensive (both time and money consuming) research I have done independently. I would appreciate it if you were so kind as to give me credit for any ideas implemented from the knowledge acquired on this page.

Gauss Guns, also known as Coil Guns, derive their name from the Mathematician Gauss, who’s name is a measure of magnetic field strength (and since the propellant force in a gauss gun is a magnetic field, it makes sense to call them by the unit of that field). The scientific definition of a gauss gun is that of an “Asynchronous linear induction motor”. In their most basic level, gauss guns can be described as pulsed solenoids with a moveable core. A solenoid of course being an air cored electromagnet. When power is applied to the coil, it will produce a bipolar magnetic field originating at it’s center and fading in strength as it gets further from the middle. Anything placed in one of it’s extremities will be pulled towards the center. This makes solenoids useful for many applications, such as remotely actuated valves, relays, switches, or control surfaces in airplanes and robotics, in which this pulling motion is used to do any type of mechanical work. However, what differs a gauss gun from just a regular solenoid is that in the gauss gun the core is allowed to move freely into and than THROUGH the solenoid. For the coil must pulsed with a short, but intense electric current, which will form the magnetic field that pulls the core towards the center, but is depleaded by the time the core has reached the middle point of the field; Hence, with nothing to hold it back, the core (which has now become a projectile) exits through the other end… That’s it in simple terms… However, there are problems…

First of all the practical limitations: The complete design of a gauss gun with all of its parameters kept dynamic (I.E. Capacitor, Coil and Projectile parameters chosen at random and matched to achieve maximum efficiency) is a MATHEMATICAL IMPOSSIBILITY! Just like attempting to calculate maximum efficiency for propeller shapes (New Scientist, Nov 99) or calculating dynamic gravitational interaction between several distinct bodies, all of which are allowed to move (typical calculus practice problem), designing a coil gun so that all of its parameters are freely variable an yet match up to provide maximum efficiency in accelerating a projectile is impossible BY DEFINITION.

But this of course does not make it impossible to near perfection to as high a degree of closeness as can be afforded. The reason why the mathematical approach breaks down is due to the fact that not only are there a very large number of variables, but also these variable are infinitely variable within themselves (E.G. There can be any number of turns, any coil length, any capacitor energy storage, any projectile mass that fits the numeric system). So, unless certain variables are fixed, the equation simply becomes unsolvable. In the two other examples mentioned above (the gravitational attraction for multiple dynamically moving masses and the propeller shape vs efficiency) it is possible to reach a solution by finite integrals: The simulation is re-run several number of times with an efficiency result being recorded. As the simulation is run more and more times several high efficiency results are obtained and the largest one is stored for comparison. It is seen that as the number of integrations nears infinity the difference between the highest efficiency values reached with different parameters nears zero. The simulation is stopped when a high enough efficiency value has been reached. I believe it may be possible to design such a program to project any coilgun given a set of values for, say, energy storage and desired projectile mass. However, finite element analysis computer programs are highly specialized and can not be adapted from other tasks. Furthermore, their design is well beyond all of my (admittedly feeble) programming abilities.

Hence, I have developed another approach. First, let us look at the variables:

The final kinetic energy (1/2MV^2) of the projectile will be a direct product of the energy delivered to it times the gun’s overall efficiency loss. Since high energy power supplies are very expensive, dangerous, and difficult to obtain, it follows that one would want to maximize efficiency in order to obtain the best possible results with the least energy possible. Maximizing efficiency also preserves the components of the gun since most energy losses are dissipated in the system as damaging heat or destructive back currents.

In order to maximize the efficiency of the solenoid in pulling the projectile through we must first maximize its force. The force is a direct product of magnetic field strength (**B**), which is in turn given by the equation **B = ï¿½ _{0}NI/L**. We can thus see that the magnetic field of a solenoid is directly proportional to the current and the number of turns. Without going into details on the equation (we will do that on the

Capacitors

The second greatest problem encountered in coilgun design is devising a means to switch the power of the discharge, which very frequently runs in the multi-megawatt range. Because the current leaving the energy storage system are extremely high (thousands to tens of thousands of amperes), any small amount of resistance will generate massive I^2R losses. If a mechanical switch is used to deliver the pulse, the very moment the switch surfaces come into contact microscopic irregularities in the switch material will start to conduct the pulse at a higher resistance, dissipating so much energy as to be vaporized right off. When the switch finally closes in its entirety, these vaporized surfaces and the molten metal beneath them weld together, and the switch is thus ruined. On higher power coil guns, the use of high voltage makes it possible for the impulse to be switched by the means of a spark gap; triggered gaps (trigatrons) are most often the choice as they allow precise control over when the discharge happens. However, any spark occurring at these powers will mean very large (30 – 40%) losses and will be very destructive to the electrodes. Air gaps are unadvisable as the noise levels encountered are excessive. The most efficient way to switch the discharge is through a solid state switch. These can be Thiristors (SCRs), IGBTS, or even some types of MOSFETS and Transistors. SCRs are currently the cheapest and most powerful solid state switches in the market due to mass production arising from the newly implemented DC power grids around the world. This unfortunately does not mean they are cheap, as an SCR capable of reliably switching a coilgun impulse is not a common market device and tends to cost over 100 dollars. However, the gains over spark gaps (1 – 3% losses compared to 30 – 40% for spark dissipation) and the absolute lack of noise, electrode erosion, and maintenance makes them highly attractive and professional on coil guns. The SCR must have an RMS voltage rating equal to or superior to the maximum capacitor charge voltage, and a peak current rating equal to or larger than the peak current encountered on the circuit during a maximum power shot. Furthermore, because they are essentially diodes (SCR = Silicon Controlled Rectifier), the SCRs used have to be protected by a diode wired in reverse across the junction, so as to shunt all cEMF coming back from the inductor (solenoid).

A coil gun projectile must be ferromagnetic (attracted by magnetic field) but also non magnetizeable. The reason for that is because if the projectile was to become magnetized during firing, energy would be lost in the magnetization process which would not contribute to the final kinetic energy. It must have a high magnetic permeability, since the higher the magnetic permeability, the stronger the magnetic field it will concentrate. The use of silicon steel alloys which can not be permanently magnetized (also good because they are dense and very hard, thus making effective projectiles) or ferrites, as are used in high frequency transformers. Ferrite, although being easier to find, makes inferior projectiles for being of lower density, lower magnetic permetivity, and also being very brittle and hard to machine. The second point to be considered in the projectile is its mass: Very light projectiles will accelerate faster and to higher velocities and will therefore require faster pulses. Since faster pulses come with higher amperages, it is very easy to exceed the maximum ratings on the switching system and destroy it. That is the main reason why supersonic coil guns have so far been impossible for amateurs. Finally, the projectile should be as long as possible and not employ a sharp point, as it would add extra weight with very little extra impulse (magnetic coupling). The ideal projectile is cylindrical and has a length that amounts to several times its diameter. The worst possible projectile is spherical, as it concentrates the maximum possible mass on the lowest possible volume, and thus achieves very little acceleration.

Here is where all the components of the gun come together and must match perfectly: The solenoid must provide the greatest amount of magnetic field coupling possible with the projectile, as this determines the pulling force and thus the acceleration. Ideally, it would have the same length as the projectile and have zero wall thickness. Since the windings must be protected from abrasion by the moving projectile, some sort of guiding tube is required; this should be as thin as possible while still having enough structural integrity to withstand the compressive forces encountered as the two poles of the coil attract each other. My first experiments with plastic and glass coils indicate that only metal tubes can be thin enough and yet withstand the forces. Unfortunately, metals inside changing magnetic fields will produce very high eddy losses, which means that the coil form must have a gap across its entire length while inside the coil in order to work. This makes the design rather non-trivial, but is a necessity. The actual length of the solenoid will determine the coupling ratio with the projectile. A 1:1/2 coupling ration would mean that 25% of the energy could be delivered into the projectile (since it starts outside with near 0 coupling and ends up taking up half of the coil, with 50% coupling, the final value is an average of both couplings). That value minus resistive losses gives us the efficiency. The most efficient gun ever developed used a 1:0.8 coupling ratio. Unfortunately, as with the high speed projectile example, the higher the coupling ratio, the shorter the pulse required to accelerate the projectile within such a short distance. This very quickly runs into a power switching barrier (pulse length becomes so short that the current required goes above the switch’s ratings). What is typically done is a realistic coupling ratio is chosen and than the number of turns is varied so as to vary the inductance to obtain the pulse length required to accelerate the projectile right to the middle of the coil while spending all of the energy stored at the capacitors.

PowerLabs 3000-Joule coilgun: Kinetic energies matching a .22 rifle with a single magnetic impulse! Videos up for download.

PowerLabs 7000-Joule Multi Stage GaussGun: 5 stages. The first stage is now complete, and is able to fire the projectile at over 270km/h! Videos available for download.

PowerLabs Advanced Coil Gun Research: My latest and most efficient Coil Gun so far.

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