## 4 Results and Discussion
### Accuracy of Interpolation  
Figure 8a compares a representative \(C_{p}\) profile of original smooth wall data with that of the interpolated profile. The flight experimental conditions for the presented case were a flight Mach number (\(M_{\infty}\)) of 0.65, a 2\({}^{\circ}\) angle of attack (\(\alpha\)), total ambient pressure (\(P_{\infty}\)) of 22.4 kPa, and total ambient temperature (\(T_{\infty}\)) of 235.0 K. Note that the reconstructed interpolated curve for this reference case should be identical to the original distribution since the same dataset was used for the interpolation. Therefore, the difference (i.e., maximum difference) between the original and interpolated curves is an uncertainty (\(\epsilon\)) arising from the interpolation. This maximum uncertainty caused by interpolation using the response surface model for reconstructing the profile will be described in detail later in this section. Figure 7: Data interpolation using the response surface model reconstructed based on flight Mach number and total pressure (original experimental data are superimposed for comparison): (**a**) probe No. = 5; (**b**) probe No. = 45. Figure 8b plots the maximum uncertainty expressed by the maximum difference between the original and interpolated profiles for all measured points in percentage for all test cases. The maximum uncertainty by the reconstruction using the response surface model stays within approximately 4.43 \(\times\) 10\({}^{-9}\)%. Therefore, \(\varepsilon\)\(\leq\) 4.43 \(\times\) 10\({}^{-9}\)%. The maximum uncertainty by using the 2 nd-degree response surface model was approximately 0.23% for the same calculation condition used for the 3 rd-degree response surface model. Thus, with this level of uncertainty, the interpolation method using the 3 rd-degree response surface model reconstructs the boundary layer profile on the aircraft fuselage well. Figure 9 compares the profiles of \(C_{p}\) (Figure 9a) and \(U\)-velocity (Figure 9b) between two smooth wall cases obtained at different flights under the same premised \(s^{+}\) condition (where 'Ref' denotes a flight condition with \(M_{\infty}\) = 0.65, \(\alpha\) = 2.68\({}^{\circ}\), \(s^{+}\) = 23.8, and 'Com' denotes a flight condition with \(M_{\infty}\) = 0.65, \(\alpha\) = 2.59\({}^{\circ}\), \(s^{+}\) = 23.0). 'Original' and 'interpolated' profiles denote the raw profile and interpolated profile, respectively. For example, in Figure 9a, Ref (Original) represents the original boundary layer profile data for the reference case; and Ref (Interpolated) represents the interpolated data for the reference case. The same rule is applied to the other dataset. The 2 nd-degree response surface model with two variables: \(x_{1}\) = \(P_{0\infty}\) and \(x_{2}\) = \(M_{\infty}\) was employed here. As seen in Figure 9a, discrepancy between the original and interpolated profiles is evident around the probe height in the region of 20-30 mm. This region approximately corresponds to an inflection point of the boundary layer profile exists. Therefore, qualitatively, the 2 nd-degree response surface model can roughly interpolate the profile though it involves some error as seen in Figure 9. The maximum discrepancy between the reference and compared cases in their interpolated profiles was found to be approximately 0.1% for \(C_{p}\) and approximately 2.6% for \(U\)-velocity. Figure 8: (**a**) Example case (\(M_{\infty}\) = 0.65, \(\alpha\) = 2\({}^{\circ}\), \(P_{\infty}\) = 22.4 kPa, \(T_{\infty}\) = 235.0 K) of the original \(C_{p}\) profile superimposed with the interpolated profile; and (**b**) maximum uncertainty presented in percentage among all pitot-probes for all measured flight cases caused by interpolation, along with flight experimental data for smooth wall cases. Figure 10 compares the profiles of \(C_{p}\) (Figure 10a) and \(U\)-velocity (Figure 10b) between two smooth wall cases as presented in Figure 9. The 3 rd-degree response surface model with two variables: \(x_{1}=P_{0\infty}\) and \(x_{2}=M_{\infty}\) was employed here.