## 4 Experiments and Results
### Part B--Hot Gas Propulsion
The upper temperature limitation was due to the solenoid valve material sensitivity, which was 125 \({}^{\circ}\)C. As regards the experiment, of special interest was the total impulse obtained at  
Figure 14: (a) Impulses for the hot and cold gas for \(\Delta t=0.3\) s and warming from 26 \({}^{\circ}\)C to 80 \({}^{\circ}\)C; and (b) cold gas force for \(\Delta t=0.3\) fs and valve recoil. Figure 13: The influence of the valve recoil on the impulse. different initial temperatures of the buffer tank, at a valve opening time of 0.4 s. This opening time was determined as optimal for a 50 bar total pressure drop from the main tank (which corresponds to a 114 g discharged mass). By integrating the force related to time, in the necessary interval of 50 bar, a total impulse was obtained in accordance with Table 2.  
Through extrapolating these results for the entire temperature interval, using the functions from Figure 16, a significant percentage increase (Table 3) can be obtained. Two laws of extrapolation were considered, one linear and the other one polynomial of second degree. Usually, the pressure and temperature vary proportionally, with respect to the ideal gas law, by taking into consideration no gas loss from the tank. The experimental data present a semi-linear pressure evolution with respect to the temperature in the 25-125 \({}^{\circ}\)C interval. The evolution will not be 100% linear given the fact that heat will be lost in space through radiation. The radiation loss is not linear, it varies with T4, where T is the tank temperature. If the radiation is not taken into account, the evolution is linear. If it is desired to take the radiation into consideration, it must be determined how the p-T variation drifts away from the curve. A balancing between the incoming radiation flux from the sun, the radiation given to the tank and the heat lost through the radiation must be made. The data extrapolation is presented in Figure 16.  
It can be noticed that two extrapolation types were taken into account: a linear extrapolation, which is closer to the intuited value from the start of the project (a 2.5\(\times\) increase in the total impulse at maximum temperature) and a polynomial extrapolation. It is impossible to specify an exact value due to the experimental conditions given by the solenoid valve. The fact that a potential 2.7\(\times\) growth can \begin{table}
\begin{tabular}{c c c} \hline
**Temperature (\({}^{\circ}\)C)** & **Total Impulse (Ns)** & **Related Impulse (Ns/bar)** \\ \hline
22 & 63.559 & 1.27118 \\ \hline
60 & 70.37 & 1.4074 \\ \hline
100 & 83.643 & 1.67286 \\ \hline
125 & 89.105 & 1.7821 \\ \hline \end{tabular}
\end{table} 
Table 2: Total impulse value at \(\Delta t=0.4\) s and different temperatures of the buffer tank. Figure 15: Pressure variation with the temperature warming from 26 \({}^{\circ}\)C to 80 \({}^{\circ}\)C (experiment from Figure 12). be obtained at a temperature of 450 \({}^{\circ}\)C (temperature which can be reached at Earth's low orbit) is not to be neglected. The polynomial extrapolation is more optimistic (it approximates a 640% increase), although more precise results can be obtained using a more dedicated valve. Given the mission of the satellite, the propellant mass onboard can vary from satellite to satellite. As a comparison value, the propellant mass is 1/5 the mass of the nano-satellite Adelis-SAMSON,  
Figure 16: Experimentally obtained impulse using N\({}_{2}\) at 50 bar and extrapolation from 125 \({}^{\circ}\)C to 450 \({}^{\circ}\)C at \(\Delta t\) = 0.4 s and different buffer tank temperatures.