## 3 Launch Test and Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Time**} & \multicolumn{2}{c}{**GPS**} & \multicolumn{2}{c}{**Atmospheric Pressure**} & \multicolumn{2}{c}{**Forced Separation**} \\ \cline{2-7}  & **24 ch** & **31 ch** & **38 ch** & **45 ch** & **52 ch** & **59 ch** \\ \hline
5:40 & \(\bigcirc\) & \(\times\) & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \hline
6:00 & & & & & & \\ (before & \(\bigcirc\) & \(\times\) & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ launch) & & & & & & \\ \hline
6:00 & & & & & & \\ (on & \(\times\) & \(\times\) & \(\times\) & \(\bigcirc\) & \(\times\) & \(\times\) \\ launch) & & & & & & \\ \hline \end{tabular} Note: \(\bigcirc\) denotes normally work, \(\times\) denotes signal stopped.  
\end{table} 
Table 4: Telemetry condition of the launch test. Altitude was estimated using the height measurement formula (Equation (1)) derived from the ICAO (International Civil Aviation Organization) standard atmosphere [32]. Note that the subscript 0 means the ground value. As a result of calculation using the pre-launch pressure \(p_{0}\) = 1014.42 hPa, temperature \(T_{0}\) = 13 \({}^{\circ}\)C, and the minimum measured atmospheric pressure \(p_{0}\) = 256.85 hPa, the maximum attainable altitude was calculated to be 10,124 m. This means the flight broke the previous altitude record of 8.3 km (estimated value) held by CAMUI-500P. \[H=\frac{\left\{1-\left(\frac{p}{p_{0}}\right)^{\frac{1}{5.261}}\right\}(T_{0} +273.15)}{0.0065} \tag{1}\]  
Figure 6 also shows the altitude simulation results. The altitude simulation method was based on 6-degree-of-freedom equation of motion using measured thrust, a predicted wind velocity 3 h before the launch, and the drag coefficient (\(C_{d}\)) change by Mach number. The data after the apex show ballistic fall (fall without streamer and parachute deployed) and deceleration fall (fall with streamer and parachute deployed). Considering this result and the fact that the separation signal could not be received, it is thought that the first stage did not separate normally and fell, landing on the water before the planned (timer set) second-stage separation time. As a result of subsequent investigations, the cause was determined to be that a forced separation circuit failure occurred due to dew condensation and a drop in temperature at high altitudes. In addition, the failed rocket recovery prevents clarification of the cause of the failure of the first-stage separation. To achieve the clarification of the cause of the failures, an additional launch is required with improvements in the forced separation circuit regarding vibration and dew condensation, and improvements in separation signal generation for deviations in flight time. Velocities were also evaluated by the altitude simulation results and numerical differentiation of the measured height. The numerical differentiation is second-ordered, using three measured points, shown in Equation (2). \[y^{\prime}_{\ I\ (2)}=\frac{1}{1+n}\left\{\frac{y_{3}-y_{2}}{x_{3}-x_{2}}+n \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right\};\ n=\frac{x_{3}-x_{2}}{x_{2}-x_{1}} \tag{2}\]  
Figure 7 shows the measured and simulated velocity. The maximum velocities of height direction are 309 m/s (measured) and 290 m/s (simulated). The possible cause of the difference is the prediction accuracy of the \(C_{d}\) of the rocket. The \(C_{d}\) was predicted by the following step. We calculated the subsonic \(C_{d}\) (Mach = 0.8) and then predicted the \(C_{d}\) change by Mach number (Mach-\(C_{d}\)) using data from a similar rocket. Thus, the  
Figure 6: Pressure and altitude. measured around Mach = 1 has less accuracy. Improvement of the Mach-\(C_{d}\) is intended for future work.