Kinetic Energy

How many capacitors of some given size will result in what velocity? How is potential energy related to kinetic energy in a coilgun?

The Energy Budget

The amount of potential energy stored in a capacitor depends on the voltage:
                PE = ½ C V2
                Where C is capacitance in farads, and V is voltage

The total potential energy needed depends on the efficiency you can build, and what velocity you want to achieve. A conservative guess at coilgun efficiency is 1% or, in a highly tuned coilgun, it might reach 2%.

The kinetic energy that corresponds to a desired velocity is:
                KE = ½ m v2
                Where m is mass in kilograms, and v is velocity in meters/second

Now the exercise that I leave to the reader is to use algebra to confirm this equation that gives velocity as a function of everything else, assuming 1% efficiency. Start with KE = PE*efficiency to arrive at these results.
                v = V * sqrt(C/m) / 10
                where v is velocity in m/s, V is voltage, C is capacitance in farads, and m is mass in kilograms

With this equation you can try substitute your various numbers and see what sort of results you might get.