Is there a mathematical relationship between the spacing of the magnets across each stage in a Gauss rifle, and the velocity of the final ball bearing that is fired from it?
If so, what is this relationship?

Asked Andy

The answer is being prepared and will be posted soon.

A Gauss Rifle (also known as a gauss gun or a coil gun) is a Magnetic Linear Accelerator. In a Gauss Rifle, the barrel is a solenoid: essentially a big coil of wire. If you send a current through a coil of wire, it creates a magnetic field in the middle of the coil. This magnetic field is used to accelerate a magnetic projectile, essentially pulling it along the barrel of the gun.