# Maximizing force of magnetic mass accelerator

I am planning to build a coil gun to fire small neodymium magnets out of a pipe. For this I am planning to use a large 400 Farad 2.7 Volt capacitor. I am wondering how many coils of wire I should make to launch the projectile. I know that the more coils the stronger the magnetic field, however I am unsure at what point the resistance will lower the current enough to limit the strength of the magnet. The capacitor has an internal resistance of 3.2 mOhms. In addition, I was wondering whether the electromagnet should have a ferrite core. While I know that this will increase the strength of the electromagnet I was not sure if it would slow the projectile down as it passed the ferrite because of its attraction to it. Finally, I was wondering what diode I should use to protect the capacitor from voltage generated be the magnetic field. Please tell me if this will not be strong enough to accomplish my needs. I do not need the projectile to travel very fast however I would like the projectile to be able to travel through the a little bit for proof of concept.

• Hmm how exactly does it work? (I've seen rail guns with conductors with current perpendicular to a constant B field.) (I also would worry about using fragile expensive magnets as the projectiles.) – George Herold Nov 19 '14 at 22:15
• I was planning to send a temporary current through a coil to set the magnet in motion and then quickly shut the current off before the magnet can reach the coil. I plan to have soft object to absorb the impact. – popgalop Nov 19 '14 at 22:18
• OK, the force on the magnet will depend on the magnetic field gradient. So maybe two Helmholtz coils wired in opposition. The time for the field to be on will be a function of the force, magnet mass and coil separation. – George Herold Nov 19 '14 at 22:26
• @GeorgeHerold: Does Wikipedia: coil gun explain how a coil gun works? – davidcary Nov 21 '14 at 3:34
• I've never built one but researched coil guns to an extent in the past. From the sound of things, you are building a single stage gun? To maximize the force, you should ideally have multiple stages. For a coil gun, the two most important aspects of it's operation are multiple stages, each with a coil that is wound enough to maximize it's magnetic field while being small enough to be responsive... as the second important aspect is proper timing of each stage. A stronger field will indeed give you more acceleration, but you'll achieve more with multiple small stages instead. – Jarrod Christman Nov 22 '14 at 21:01

Firstly, I do not think you can use a neodymium magnet as a projectile.

## Coilgun

A coilgun (or Gauss gun, in reference to Carl Friedrich Gauss, who formulated mathematical descriptions of the magnetic effect used by magnetic accelerators) is a type of projectile accelerator consisting of one or more coils used as electromagnets in the configuration of a linear motor that accelerate a ferromagnetic or conducting projectile to high velocity.

And you should be more focused on the kinetic energy of the projectile as it leaves the tube. A 400 farad 2.7 v capacitor stores 1450 joules of energy, which given a efficiency of 1 percent translates to 14.5 joules of projectile energy. Plugging this in to the kinetic energy equation $$\E = \frac{1}{2}mv^2\$$, gives us a muzzle velocity of 170 m/s for a 1 gram projectile.

Now let's come to the question of force. The force depends on how much power you can pump through the coil. And this minimum force will be huge, because the projectile must reach muzzle velocity by the middle of the coil. (The coil must also be discharged by this time, or the projectile will slow down) For a one gram projectile, this will be 729 newtons or 73 kgs of force, assuming a coil length of 4 cm. (You can calculate acceleration from this equation - $$\ a = \frac{v^2}{s}\$$ where s is the barrel length and v is velocity)

And what does this mean? You need a strong projectile, definitely. And your capacitor must provide a vast amount of power. Taking the above parameters, the time before the projectile hits the middle of the barrel is 0.23 milliseconds, which you can calculate using the kinematic equation $$\x = \frac{1}{2}at^2\$$. Dividing the total energy by the time gives us a power requirement of 6.5 MW to be discharged. That's right. 6.5 MW.

With a 2.7 volt capacitor, the resistance must be below 1 micro-ohm. Definitely not possible. With a 400 volt capacitor, the minimum will be 24 milliohms. This is possible.

Now, your question specifies you are not interested in maximizing velocity. In that case, you can go through these calculations for your specific use case. The wire gauge depends on the current going through the wire and the voltage. Once you have that you can calculate the number of turns needed, and that gives you the resistance of the coil. You can add this to the resistance of the capacitor and the diode to give you the total resistance. This must be lower than the minimum resistance you calculated.

And of course, exercise caution. 1500 joules is a lot of energy.