# Design and Experiment of Discharge Control Methods for Three-Stage Coil Gun Experiments
## 6 Conclusions  
We proposed two discharge methods for reduced multi-stage coil gun systems. Both discharge methods required adjustment of the discharge position for the maximum launch velocity at each stage. The proposed charging device has the advantage of small differences in the charging amount depending on the capacitor used. Based on the justifications provided in this paper, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Stage**} & **Initial Launcher** & **Final Launcher** & **Launcher Velocity** \\  & **Velocity (m/s)** & **Velocity (m/s)** & **Increment (m/s)** \\ \hline
1 & 0 & 31.2 & 31.2 \\
2 & 31.2 & 48.6 & 17.4 \\
3 & 48.6 & 60.8 & 12.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the measurement of launcher velocity of the three-stage coil gun. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Experimental Order**} & **Control by Delay** & **Control by Optical** \\  & **(m/s)** & **Sensor (m/s)** \\ \hline
1 & 60.5 & 60.2 \\
2 & 56.7 & 60.6 \\
3 & 60.5 & 60.8 \\
4 & 56.2 & 59.5 \\
5 & 59.1 & 60.8 \\
6 & 60.8 & 60.7 \\
7 & 60.4 & 60.3 \\
8 & 57.3 & 59.8 \\
9 & 60.7 & 60.8 \\
10 & 59.6 & 60.7 \\ Average & 59.18 & 60.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Final velocities of the three-stage coil guns with control by delay and optical sensor. the charging device can be utilized as the capacitor charging device in a coil gun system with three or more stages. Two methods have been proposed for the discharging circuit, and an appropriate circuit can be selected for the coil gun system of interest based on the characteristics of the two circuits. The optimal discharge positions were obtained using finite element analysis without friction between the projectile and the launch tube. Moreover, in the simulation, there is wind drag, and the projectile is not located at the center of the launch tube, so the mechanical force received from the electromagnetic coil in the experiment may be different than that in the simulation. Furthermore, error arises from the difference in the resistance and inductance values of the solenoid coil designed in the simulation and the prototype of the solenoid coil with an actual coil. Consequently, adjusting the discharge position of the projectile is necessary to obtain the maximum velocity in both discharge methods. Velocity measurements showed that the frequency and magnitude of errors were greater in the delay-based discharge control method than in the photointerrupter-based method. The delay-based method does not require the fabrication of a launch tube, but any errors such as those that occur due to recoil during launch affect the acceleration in the next stage. This results in errors stacking up and an overall decrease in performance as the number of stages increases. The photointerrupter-based method addresses the issue of these errors, but it requires the fabrication of a launch tube to install the sensors as well as space for them. Therefore, the coil gun is longer than one with the delay-based method with the same number of stages. To reduce the resultant errors in the delay-based control system, a controller that sends out control signals that are more precise than those by an Arduino must be used. In a photointerrupter system, the LED light guide must be processed so that the infrared rays entering the photointerrupter are not dispersed, and a phototransistor with a narrower viewing angle than that used in this study is recommended. Moreover, it is important to secure the coil gun model in place to reduce the error due to recoil during firing and fasten the photointerrupter sensor attached to the launch tube in a delay-based control method. In conclusion, the photointerrupter-based control circuit with smaller operation errors is likely to be more fitting for a reduced coil gun system. Moreover, the charging circuit and discharge methods presented are fully capable of being used in a multi-stage coil gun system with more than three stages.