# An Electromagnetic Circuit Design to Improve a Multi-Stage Coil-Gun's Energy Conversion Efficiency
## 7 Conclusions  
In this study, we added the diameter of the copper wire used to manufacture a coil gun's solenoid coil as a design variable. Subsequently, the respective designed models of coil gun systems with varying copper wire diameters were simulated to compare the circuit's acceleration performance and energy conversion efficiency. First, for the efficient conversion of the electromagnetic force generated in the circuit into kinetic energy, at least 70% of it should be transmitted to the projectile in the launch direction to reduce the force transmitted to it in the reverse direction after passing through the coil's center. The period of the RLC function with the energy distribution shape suitable for the projectile's initial  
Figure 9: (**a**) Projectile velocity by stage (**b**) Projectile velocity increment by stage. velocity should be set by comparing the function's shape and the projectile's acceleration shape. Additionally, the electromagnetic force generated in the solenoid coil is proportional to the coil's winding shape and the supplied current's magnitude. Therefore, we can use two methods to increase the magnitude of the coil's generated electromagnetic force. The first method is designing a low-capacitance coil using a small-diameter copper wire to increase the winding density and number of turns. The second is using a large-diameter copper wire to increase the capacitance by reducing the number of turns to increase the supplied current's magnitude, thereby increasing the magnitude of the coil's electromagnetic force. When we configured the coil gun system using a 1.3 mm diameter copper wire based on the experimented projectile in this study, the solenoid coil's resistance and inductance were high. Therefore, a capacitance of 3000 uF, which is a capacity less than half of that of a coil gun system configured using a 1.7 mm diameter copper wire, was used to match the RLC period. However, the magnetic flux density transferred from the coil gun's solenoid coil to the projectile increased. Thus, there was no significant velocity difference. When configuring the coil gun circuit using a small-diameter copper wire, we can increase the magnetic flux density by increasing the number of turns for the same volume of the solenoid coil. However, we should use a low-capacitance capacitor to set the RLC function's period due to the coil's high inductance and resistance. In the case of a multi-stage coil gun, setting this period is limited by the number of turns and capacitance because the acceleration time depends on the projectile's initial velocity. This adjustment may be good for energy conversion efficiency because the circuit can be configured with a low-capacitance capacitor. On the other hand, when a coil gun circuit is configured using a large diameter copper wire, if the number of turns increases, the entire coil's size increases compared to that of the projectile. This may decrease the efficiency of the electromagnetic force transmission to the projectile. Therefore, we should design a multi-stage coil gun to match the RLC function's period using a high-capacitance capacitor and by increasing the supplied current's magnitude. In this study, we identified the acceleration performance degradation in the five-stage and higher-stage coil gun systems. Despite optimally designing the values, acceleration performance degradation and increases in the number of stages were observable in the simulation. This was mainly because the solenoid coil's generated electromagnetic force decreased proportionally to the reduction in the number of turns, even though we optimized the values by reducing the RLC function's period by reducing the number of turns. Therefore, if one's purpose is to improve the acceleration efficiency more than that in this study, the solenoid coil should be designed using a copper wire with a diameter larger than 1.5 mm to optimize the five-stage and higher-stage coil gun systems.