Through much research I found all the Variables that affect the efficiency of a coil gun:
Length to diameter ratio
Number of layers
Thickness of wire
Current Pulse length
Switch bounce and resistance
Capacitor Voltage and Capacitance
Overall wire length and diameter used.
Also there are several ways to increase standard performance using:
Optical, Inductive or Physical Triggering
Step 1: The Plan
I took apart 17 disposable cameras and soldered the capacitors in parallel to form a capacitor bank of 1360uF 330v which using E=1/2CV^2 gives a stored energy of 73J.
I used one of the camera circuits as a charging circuit by removing the flash, removing the trigger switch and soldering the charge switch closed.
I then used an old mains PSU switch as a charging switch although any switch will do. The whole circuit was covered thouroughly in insulation tape and put in the only plastic box of the right size I could find at the time; An empty Bertolli spread box.
I wrapped a coil out of 26AWG enamel coated wire 30mm long and 7 layers thick. This is because the coil should be the same length as the projectile and the projectile should be five times longer than it is wide, hence 5x6=30. The number of layers is dependant on wire thickness and capacitor bank size and voltage. The thinner the wire, the smaller the bank, the less layers. wire too thin will impede flow and maybe burn out. Wire too thick will mean you have less coil density than is potentially attainable.
Simulations ran well after the device was constructed reveal this isn't an optimal design and there is some 'suck back' as you can see on the graph when the turquoise line falls bellow the axis suddenly.
Step 2: The Coil
Get your enamel coated wire and tape it to the tape stopper at one end and start coiling the wire around the tube, when you reach the end use super glue to hold the first layer in place. When it has dried start coiling again, this time the coil will go back to the starting end over the top of the first layer and glue in place. Repeat this process for approximately 7 layers. When the coil is finished put on a layer of insulation tape and your done.
Step 3: The Circuit
Next solder the charge switch closed and add extension wires that you can solder onto your battery holder with an toggle switch. This is your charging switch and should be a switch over toggle so that one side is charge and the other is safety so that you can never fire it while the charge circuit is engaged. Doing so wouldn't damage the coil gun but it's good practice not to, especially when you upgrade to a mains powered coil gun.
Remove the flash tube and capacitor taking care to remember the polarity. Solder in new wires from the circuit where the capacitor was previously connected.
Take your capacitors, essentially you want as many as possible and solder them in parallel so that all the negative legs are connected on a rail and all the positive legs are connected on a separate rail. Solder the wires from the charge circuit to the bank.
Solder on the two thickest wires you can find to go from the capacitor bank to the coil and insulate the whole circuit with heat shrink, insulation tape and hot melt glue. You do not want any chance that you may accidentally electrocute yourself. I will warn you now, it hurts... ALOT... and when you've got a bank of over 50J it can make you feel very ill. Not an enjoyable experience.
Solder in your push switch in line with the positive lead from the cap bank and then to the coil you just wrapped.
Put all this circuitry in a nice safe plastic box and your ready to go!
Step 4: The Projectiles
I've done a separate Instructable on Projectile Design since it is such a big section.
Step 5: The Results
I've designed and built a 50 cal 217J Coilgun.