## 2 Experimental Methodology
### Test Conditions  
In this experiment, three typical temperatures were selected to simulate glaze ice (\(-7\)\({}^{\circ}\)C), mixed ice (\(-10\)\({}^{\circ}\)C) and rime ice (\(-15\)\({}^{\circ}\)C) at a speed of 90 m/s. The other icing cloud parameters selected were MVD 20, 30 and 40 um, combined with LWC 0.5, 1, 1.3 and 1.5 g/m3. These parameters represent the typical icing conditions outlined in 14 CFR parts 25, Appendix C ([[https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C/part-25/appendix-Appendix%20C%20](https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C/part-25/appendix-Appendix%20C%20) to%20 Part%2025]([https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C/part-25/appendix-Appendix%20C%20](https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C/part-25/appendix-Appendix%20C%20) to%20 Part%2025) (accessed on 23 March 2023)). Heating sheet area was designed using the numerical simulation method under the speed of 90 m/s, an angle of attack ranging from 0\({}^{\circ}\) to 4\({}^{\circ}\), MVD 20 um and a static temperature of \(-7\)\({}^{\circ}\)C. Pre-tests were conducted indicating that a minimum power density of 5 kW/m\({}^{2}\) was required to prevent ice forming on the leading edge with a coating. The test was divided into two parts. The first part (shown in Table 3) explored the sensitivities of a designed superhydrophobic coating range, heating range and power of IPS to icing environmental parameters. The purpose was to evaluate the performance when IPS encountered an icing environment beyond the system's designated capabilities. Each case maintained the same velocity of 90 m/s, angle of attack of 0\({}^{\circ}\) and a testing time of 180 s, while varying MVD, LWC and environmental temperature. Sheets A, B and C were powered on and were covered with superhydrophobic coating, as a basic configuration. The second part studied the performance of various IPS parameters such as coating ranges, heating ranges and powers dealing with a fixed icing environment parameter. The purpose was to explore the potential for further power reduction through optimization. Four types of IPS layout were examined (Figure 5). Type (1) represented the baseline configuration with both the heating sheet range and superhydrophobic coating range identical to the droplet impingement area. It was expected that supercooled droplets impacting the coating would immediately fall off and there w  
Figure 4: Superhydrophobic coating. (**a**) Coating appearance. (**b**) SEM-images of the coating. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **MVD** & **LWC** & **Temperature** & **Heating Power Density** \\  & \(\upmu\)**m** & **g/m3** & \({}^{\circ}\)**C** & **kW/m2** \\ \hline
1 & 20 & 1 & \(-7\) & 5 \\
2 & 30 & 1 & \(-7\) & 5 \\
3 & 40 & 1.3 & \(-7\) & 5 \\
4 & 20 & 0.5 & \(-7\) & 5 \\
5 & 20 & 1.5 & \(-7\) & 5 \\
6 & 20 & 1.5 & \(-10\) & 5 \& 7.5 \\
7 & 20 & 1.5 & \(-15\) & 10 \& 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test condition for part 1.  
after the heating protection area. Type (2) decreased the range of heating area, expecting an increase in heating power density but the reduced heating area would reduce the total heating power consumption. Type (3) increased both the range of heating area and superhydrophobic coating area equally, intending to reduce the total heating power consumption with increased protection area but less power. Type (4) examined whether the water would fall off after the heating protection area. The superhydrophobic coating was positioned after the droplet impingement area with high heating power supplied to ensure the water temperature on the coating remained above freezing point. Type (1)-(3) targeted ways to reduce power consumption. As shown in Equation (1), type (2) decreased heating area but increased heating power density slightly trying to finish heating power compared with type (1).