@Kulverstukas:
Mostly just shooting cans and cats. It's not strong enough for anything else.
@p_2001:
I didn't do any calculations, the coil discharges before it gets stuck in the tube. This is because it's so weak and uses just one 330uf capacitor.
For the second part, you are correct. A setup like you mentioned is called a multi-stage coil gun. You will need to use solid-state-relays for the switching. As for timing when to fire the coils, you could use a clock, but I've had the idea of using optical sensors to fire them. Kinda like a laser and photocell.
There is math involved, like the length of the tube, thickness of the wire and coils, power of the capacitors, etc... I never got into it enough to learn all of it, but there is a lot of write-ups on the methods of doing it.
There is also what's known as a rail gun, that uses two plates of metal, and shoots bolt and plasma.
Also,
here is an index of quite a few coil guns.
