# Design and Experiment of Discharge Control Methods for Three-Stage Coil Gun Experiments
## 2 Coil Gun Circuit Design  
To design the coil gun circuit, the shape of the projectile must first be determined. As the weight of the projectile decreases, the magnitude of the mechanical force essential to accelerate the projectile also decreases. The force acting on the projectile decreases with the decrease in its volume, but the magnitude of the electromagnetic force to accelerate the projectile increases. Conversely, as the weight of the projectile increases, the electromagnetic force received by the projectile increases, and the magnitude of the electromagnetic force required for acceleration also increases. Therefore, a coil gun circuit must be designed to fit the shape and acceleration of the projectile based on the capacitance, coil winding, the diameter of the copper wire used to fabricate the solenoid coil, and the mass of the projectile. The projectile was made of 1010 steel and weighed 11.35 g. Figure 1 shows the projectile used for the simulation and experiment. Following the selection of the projectile, the coil gun circuit was designed. The coil gun circuit primarily comprises a solenoid coil and a DC power supply, for which a capacitor is used to instantaneously apply a large current. To use a capacitor, a circuit for charging it and a DC power supply are needed. Moreover, during discharge from the capacitor, a current as high as over 400 A flows through the solenoid coil. Therefore, devices such as SCRs are required to control the high voltage and current generated during operation of the coil gun circuit. Figure 2 shows the circuit diagram of a single-stage coil gun, including a charging circuit and a discharge circuit with an SCR. In the coil gun circuit, the position of the projectile and the distance between the solenoid coils are key design factors, in addition to the electrical components of the coil gun, such as capacitor capacitance, charging voltage, and coil winding. This is because force is applied in the direction opposite to the direction in which the projectile is launched when the projectile's center of gravity moves over the center of the solenoid coil due to the characteristics of the coil gun circuit with the solenoid coil. Moreover, the electric current profile through the electromagnetic coil is not constant, and the greatness of the force acting on the projectile in accordance with its position constantly changes when the coil gun circuit includes a capacitor. Therefore, the shape and weight of the projectile must be considered when the capacitance and the shape of the solenoid coil are designed for efficient acceleration of the projectile. The electromagnetic force generated in the solenoid coil is proportional to the magnitude of the current flowing through the coil, whose shape resembles that of an underdamped system. It is important to design the system so that the majority of the electromagnetic force generated by the coil gun circuit is exerted on the projectile in the launch direction while comparing the RLC function waveform to the velocity of the projectile. The electromagnetic force experienced by the projectile changes with the position of the projectile, whereas the electromagnetic force changes in magnitude with time. Because  
Figure 1: Projectile for experiment. Figure 2: Circuit diagram of a single-stage coil gun. of the difficulty when directly calculating the launch velocity, it is recommended to use a computer program. In this study, the capacitance and shape of the solenoid coil for the one-, two-, and three-stage coil sums were determined through the design experiments [12]. Figure 3 presents the projectile velocity and electromagnetic force on the projectile simulated with respect to the distance between the projectile and solenoid coil. The coil gun model used in the simulations is as described for the one-stage coil gun in Table 1. The results were simulated for the distances from 1 mm to 7 mm in 2 mm increments. As shown in Figure 3A, the smaller the distance, the greater the decrease in velocity.