# How to chose the right voltage and coil(s) for coilgun?

Coilgun is a simple canon which attracts piece of metal into the core of the coil and then, when the piece of metal reaches midpoint of the coil, removes the power and leaves metal at it's accelerated speed.

I've seen people making these and it seems to me as a safer alternative of railgun, though still very dangerous.

I'd like to ask how to reach good balance between different aspects of the design. There are three things that are kinda in conflict and all have positive and negative effect:

• Voltage - Higher voltage means higher current through the coil and much more energy delivered. But it also increases risk of fatal injury and requires thicker wire insulation.
• Wire thickness - Thicker wire heats less and has lower resistance, but limits feastible amount of turns the coil has. Also up from certain thickness, manufacturing of the coil is not very easy process.
• Number of turns - AFAIK, number of turns boosts magnetic field strength quite well. However, the more turns the higher resistance AND inductance. And the coil must charge fast, so inductance is a Bad Thing.

Is there a simple way to calculate or guess optimal parameters? I intend to make a gun that is safe enough to make at home with precautions but also powerful enough to shoot objects off a table.

I think you need to understand at what point the magnetic field needs to begin collapsing in order to prevent the projectile decelerating and hence losing built-up momentum. I have done a simulation of a 44 mm long 10 mm radius air cored solenoid to enable to concepts to be more clearly seen. I have made it this shape just for my convenience in answering and I have no-idea if this is shape is useful in the real thing. Below is a picture of the flux density inside and outside the solenoid along with the gradient of said flux density: -

Regard the blue trace - flux density (for a given current) rises as you approach either side of the solenoid. At 22 mm either side of the centre line is the aperture of the solenoid. As you enter the aperture it can be seen that the flux density rises to an almost constant value - by this I mean that if the solenoid were really quite long then maximum flux density would be constant for most of the central length of the solenoid. This is important to realize because when the gradient of flux density is zero there can be no mechanical force exerted (such as in the centre).

So, it's important to look at the gradient (red line). If the projectile enters from the right, the force that accelerates it is maximum as it enters the solenoid (for a typically small projectile). After it has entered it will still accelerate but to a lesser degree until it reaches the solenoid centre. At this point it will start to decelerate (not wanted).

The upshot here is that you need to start turning the mag field off somewhere between the projectile entering and reaching dead centre. This is impossible to do instantaneously because of the solenoid's inductance but given that you can measure the inductance at least you can begin to calculate when to start the process (noting that any magnetic field remaining as the projectile passes dead centre is going to slow it down).

Here are a few extra formula and observations that might help.

The force exerted by a solenoid on a ferromagnetic object is: -

Force = $\dfrac{(N.I)^2\mu_0.A}{2g^2}$

Where N is number of turns, A is cross sectional area of solenoid, I is the applied currents, g is the gap from the end of the solenoid to the object and $\mu_0$ is $4\pi\times 10^{-7}$.

Also, for a solenoid, inductance can be calculated thus: -

Inductance = $\dfrac{\mu_0.N^2.A}{l}$

Where $\mu_0$, N and A are as before and $l$ is length of solenoid.

So, making the inductance bigger makes the force bigger and, to keep turns as low as possible you want the length of the solenoid to be a short as possible.

However, with a bigger inductance it takes longer for the current to ramp up to maximum and this will reduce the effectiveness of a coil-gun due to not being able to accelerate the bullet to sufficient speed.

• The equations you gave seem to imply a solenoid with a closed flux path, while most hobbyist coilguns I have seen use air cored coils (no ferromagnetic materials beside the projectile itself). – jms Sep 26 '16 at 13:47
• @jms $\mu_0$ is used in the equations hence the relative permeability of air is implied. A closed flux path doesn't exist for a solenoid else it wouldn't attract anything but the ferromagnetic materials in that closed loop path i.e. no external force because it becomes a toroid. I'm not 100% sure on this so if you have a link to a different formula then please donate here. – Andy aka Sep 26 '16 at 14:10