Theory and Other Stuff

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Some considerations

What kind of technologies or aspects are involved with magnetic mass drivers?

Why is there so many researchers studying these subject, mainly the military?

Is it possible to someone to build some device that can have nearly the performance obtained by the researchers which have the $$$ available for it?

Why am I doing that?

Where did we came from and where will we go to?

I've always been impressed with new technologies. Sometimes I wonder why. What I realize is that I feel more pleasure when studying and discovering how things works, and reaching the goals I propose to myself than actually "using" the thing that resulted from those mental exercises.

But, let's cut the blah blah blah (some of it) and try getting to the point:

The mass drivers

One of the oldest men dreams is to conquer the outer space. But burning tons of fuel doesn't seems to be so elegant does it? Why not to put together some old ideas with new ones? So we get the principle of a catapult and apply to it some new technologies, we get a mass driver! Let's then put some load inside a big can and throw it out to space using our brand new catapult!!

Some years ago people begun to wonder if is it possible to use big magnetic coils  aligned in sequence, which are one after the other energized in order to accelerate a payload until it reaches earth orbit speeds (something more that 14 Km/s).

It's the same principle of an electric linear motor. But there are some problems to be solved. The amount of energy required to put such a machine to effectively work is astronomical (quite ironic, isn't it?).

And what has been achieved after all the research?

The practical use that has been the closest to a final use is (guess what?) military. Regular weapons have reached a practical limit in launching speeds (about 1 ~ 2 thousand meters per second, maybe some more). With coil guns (and rail guns), the idea is to reach projectile speeds in the field of 5 to 10 thousand m/s or even more! even with smaller projectiles, the kinetic energy that arises with those speeds is really big!

As an example, in the present days a war ship carries a big load of ammunition, is basically a very explosive ship, if it gets hit, the risks of explosions are very big. Now imagine if all that the ship needs to carry as ammo is a lot of projectiles, smaller in size if compared with actual canon bullets, that will be launched in weapons that use electricity as the power, not expanding gases. As the speeds achieved are bigger, the weapons would have more range/power, the ship would become safer and able to carry a bigger load of bullets.

Of course, some other uses have been found; there is some laboratories that made small particle launching systems which are used to test the impact of micrometeorites against ship fuselage. The principle also can be used to propels trains or other vehicles, and the studies about launching spacecraft also continue.

What we need to know to start

But, as common people, far from the huge budgets and the leading technology and resources, here we are trying to have fun, trying to learn (and maybe launch something at ballistic speeds!!!).

The basic principle involved in a coil gun is the generation of magnetic fields that will attract and then release a ferrous projectile. In a practical way, only one coil, some wire and a battery would be enough to test the concept and have some nails jumping about 1 or 2 feet high.

A coil is known in electronics as a "solenoid", an active component with some interesting characteristics: one - it accumulates energy (in certain conditions) and two - it generates a magnetic field, proportional to the current applied to the coil. The generation of the field and the coil energy variation obviously involve basically other aspects: the time the variation of energy takes to occur (depends of the coil inductance) and how many current can be applied, so we won't have a lamp or a bomb instead of a coil. There is also some other interesting aspects involving the construction, relations between sizes, empty spaces between the elements, and so on. With patience, we will get there. When a coil is energized, a piece of iron inside of it (or near one of the coil ends) will be "sucked" inside the coil in a first place, then by inertia it will advance a little passing the middle of the coil, then it will be pulled back again, thus oscillating until it "accommodates" in the middle point of the coil. This way, we can conclude that to accelerate an object using a coil, the effective length of the coil that will be usable is from about on end of the coil until the projectile reaches the middle, when the power should be turned off, so the projectile would continue its movement by inertia. In this case, other coils in the pathway of the projectile would be activated in a precise timing/detection scheme, in order to continuously accelerate the projectile until it would be launched from the last coil at high speeds.

And what about the projectile? What kind of things can be thrown away in such a device? Well, since the coils will produce magnetic fields, we need "magnetically permeable" stuff. In different words, we need a metal that have the property of being attracted by a magnetic field (a nail, screw, a piece of iron, etc.).

The surrounding items, like the circuitry needed to provide power to the coils, the timing logic needed to control it, among other stuff, will be discussed later.

We must be aware about some difficulties that may slow down or discourage the efforts on the project; a little study about the physics, the dynamic and the control and mechanical aspects involved can show us that in order to achieve high speeds, we need to know some basic points, and a little calculations should help to understand; so, lets use a coil gun made of just 1 coil (its important to remember that this is a theoretical study, because there are some aspects like efficiency of the system, inductance, resistance, circuitry needed, $$$$, among others and is quite probable that I may have forgotten some detail. If anyone find anything wrong about it, please let me know):

Some physics: the dynamics

as we know, s = s0 + at, where s stands for speed, a equals acceleration, t is time.
the other interesting formula to know is d = d0 + s0t + at2/ 2, where d is distance.
lets now assume a hypothetical case where we want a projectile speed of 100 m/s. We also have a coil about 20 cm length. As we know the usable portion is about half this length, we would have:

distance where the force will be applicable: 0.1m; (we are not considering the distribution of the force along this distance)

final speed of the projectile: 100 m/s; (something like a 4.5 mm compressed air gun projectile speed)

time: seconds;

acceleration: meters per second.

so, 100 = 0 + at; that means t = 100/a.;

now, 0.1 = 0 + 0 + a (100 / a)2/ 2

0.1 = 10,000 / 2a         a = 10,000 / 0.2        a = 50,000 m / s2

That's quite an interesting number, uh? With these numbers at hand, lets calculate for how many time the energy pulse will be applied in our system:

d = d0 + s0t + at2/ 2;            so, 0.1 = 25,000 t2

t2= 0.1 / 25,000

t = 2ms

The energy

Now we can move to the part that involves the energy:

f = ma, where f = force (in Newton, the force needed to accelerate 1 Kg of mass by 1m / s2; m = mass (Kg).

now, the mass of the projectile begins to show its relevance, lets say, for example, 1g (0.001 Kg):

f = 0.001 * 50,000;      

f = 50 N; roughly, 5 Kg of force (assuming gravity = 10 m / s2, to simplify a little)

now that we have a force estimate, lets try to find the energy, remembering that the energy we will find here will be applied to the system (during the dt = 2ms):

e = mv2/ 2, e = kinetic energy, in Joules (in terms of work: 1 Newton * 1 Meter = 1 Joule):

e = 0.001 * 10,000 / 2,

e = 5J;

(or, work: w = f d,       w = 50N * 0,1m = 5J) too.

Just to make a little comparison between these values and the energy stored in a capacitor circuit, which usually is utilized to discharge the energy on a system like ours, considering also that Power P = w/t, where w = work (in our case, the same amount as the energy): P = 5J / 0.002s; P = 2,500W (2.5KW) ( Wow! ). And remember that we will never be able (at least nowadays) to deliver all that energy to the projectile!

The electronics

The power dissipated by an electric circuit is P = I U, where I = current (Amperes) and U = tension (Volts):

2,500 = I U; now is an interesting time we can start to make some choices, like What voltage will we work with? Or maybe we start deciding what current will we be able to handle? For instance, if we use 12V (a car battery, or other):

I = 2,500 / 12; I = 208 Amps; maybe we can use 1 car battery and some IGBTs, and hope that the coil or some part of the system do not explode (just kidding).

Well, but in electronics, we are not that stuck, we can build a capacitor bank that can hold some energy and have a big shot discharge. Also, some electronic power drivers can handle something more that its nominal steady state ranges.

When we talk about capacitors, we talk about a component that behaves something like a coil, and it can accumulate energy. If we charge a capacitor and open the circuit it holds its charge (well, it really slowly loses it), and the coil don't. But let's to the point:

The energy stored in a capacitor system is e = cv2/2 (sounds familiar?). Well, lets find what kind of capacitor bank do we need to supply our system, using 12V: 5 = c*144/2, 5 = c*72, c = 0.07 Farads (ok, 70,000 F). Is very interesting to note, also, that the exponential part of this equation is the voltage, so we could use, for instance, 48V, thus achieving:

5 = c * 2,304, and: c = 0.002 F (2,000 F) using 4 times our original voltage, we could now use a capacitor with 35 times less capacity.

Now is a good time to remember that if we expect an efficiency of about 5% in the transfer of energy from the circuit to the projectile, then we would need 20 times these values in energy delivered to the system in order to achieve the results expected. This would lead us to use 48V and a capacitor bank of 40,000 F.

Conclusions about the physics and electronics

Putting it all together, we need a pulse of 2.5 kW (maybe 50KW), to be applied to the coil for about 2ms, carefully controlled to avoid waste of power; to deliver this energy, we can use a bank of 40,000uF capacitors rated to about 60V and charged to 48~50V. Now, we can think about how to switch these power to the coil, what lead us to high power silicon devices, like power transistors, IGBTs, power FETs, among others. Some considerations about the coil inductance can be seen at Specifics in the title inductance.

And remember, this is a situation where all parts of the system behaves in a somewhat linear fashion; in other words, all that would be great if the projectile never reach magnetic saturation (there is a point where is useless to increase the field in order to increase the force upon the projectile), also if the coil wire hasn't a limit of current before it melts, electrical resistance that limits the current. And, of course, we reach a situation where is difficult to calculate the best solenoid, because of the factors: more turns, more field, but more resistance; thicker wire, less resistance but less turns in the same space; also, maybe there is a limit in the total thickness of the coil (fat coils). My friend Barry (see the links page) is trying to reach to some conclusive point about this matter, and he suggested me to try to find some answers about it too. Finally, my thanks for his help reviewing these calculations.

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This page was last updated on 05/18/99. 1999 by Lissandro