The solenoid coil is one of the most important design component for electromagnetic induction type coil gun
system. When the voltage and current are applied across the coil, a uniform magnetic field is generated inside
the coil and that is proportional to the number of coil windings, and the high-density magnetic field generated
by the coil can be converted to mechanical energy by applying the strong electromagnetic force to a ferromagnetic
material. At this time, the interaction between the current and magnetic field of the solenoid coil generates
a strong electromagnetic expansive force between each coil wire. In this paper, we introduced a four-stage
induction coil gun as the launcher system using high voltage pulsed power source. Also, we proposed both the
method and formula to calculate the electromagnetic expansion force acting on the multi-winding layer solenoid
coil gun by using energy transfer equations. When the current flows a solenoid coil, the expansion force is
generated in the radial direction of the coil. The mathematical calculation results were verified by simulated
ones.