Making Music with a Coil Gun, Part 3
Turns out that lots of folks have thought about modeling solenoids. Just hop over to Google for a quick search and you’ll turn up dozens of hits. They all make for very interesting reading, but as for me I’d rather not reinvent the wheel.
So, after perusing the literature for awhile, I came to a few conclusions about what dimensions might be appropriate for my coilgun coil. One rule of thumb suggests that the length of the solenoid barrel need not be longer than the diameter of projectile. My previous simulation seems to bear this out, with the acceleration on the ball dropping off quite rapidly once the ball had entered the barrel. The next step in my investigation would therefore be a test of this theory.
I created a new simulation, with the solenoid barrel length being about equal to
the diameter of the ball. The coil is almost a square in cross section, constrained to the barrel length. Granted, this is a much smaller coil size than I was using before. Here is a thumbnail which links to the full size animated GIF.
Due to the smaller coil size, overall magnetic forces are smaller. But all in all, the 
simulation bears out my expectations. If you plot the force on the ball as it moves through the coil you’ll find that the force drops to zero at the center or the barrel. To the left is a thumbnail of a closeup of that instant. Take a look at the full size image, and you’ll notice how the flux lines entering and leaving the ball appear to be “in balance”. This accounts for the net force on the iron ball being nearly zero at this point. As the ball continues past this point then the forces begin to drag the ball back into the coil. If you’re talking about a coilgun, this is negative acceleration on your projectile, and your overall velocity is going to drop.
Incidentally, you might wonder where is the point at which the ball is experiencing the maximum acceleration. According to the output of the 
simulation, that point occurs when about half of the ball has entered the throat of the barrel. The thumbnail on the left depicts that point. Note how the flux lines from the halfway point on the ball to the back of the ball do not mesh with the barrel of the coil itself.
This has been a fun exercise, and gives me another data point for designing the first prototypes. If you’ve got any good ideas then I’d love to hear a comment!
MirthMaker
