## 2 Flight Test Bed, Measurement System and Equipment, and Test Conditions
### Test Conditions  
Since the flight experiment was conducted as part of the FINE project's study of the effectiveness of riblets in reducing skin friction drag, test conditions were determined based on certain physical parameters related to evaluating skin friction drag. The primary condition is expressed as Equation (1), which is a non-dimensional riblet width and essentially a Reynolds number based on the riblet width and friction velocity. This parameter was used to determine the flight Mach number, altitude, and other flight conditions.  
\[s^{+}=\frac{u_{\tau}\cdot s}{\
u}=\frac{s}{\
u}\sqrt{\frac{1}{2}\cdot c_{f} \cdot\overline{U^{2}}} \tag{1}\]  
\[c_{f}=0.0592\cdot Re_{x}^{-\frac{1}{5}} \tag{2}\]  
\[Re_{u_{\infty}}=\frac{\rho_{\infty}\cdot\mathcal{U}_{\infty}}{\mu_{\infty}}= \frac{\rho_{\infty}}{\mu_{\infty}}\cdot M_{\infty}\cdot\sqrt{\gamma_{\infty} \cdot R_{\infty}\cdot T_{\infty}} \tag{3}\]  
Figure 1: **(a)** Japan Aerospace Exploration Agency (JAXA) flight test bed and riblet surface attached on the aircraft surface; and (b) schematic of pitot-rake attached on outer surface of an aircraft.  
The effectiveness of the riblet in reducing skin friction depends on the turbulent eddy size in the boundary layer and the riblet valley width; therefore, the effectiveness is strongly related to the Reynolds number. The Mach number dependence is generally small [39]. The unit Reynolds number based on the flight conditions is expressed as Equation (3) and the relationship between \(s^{+}\) and \(Re_{u\infty}\) (or \(Re_{flight}\)) is presented in Figure 2. As seen in Figure 2, \(s^{+}\) has a linear relationship with \(Re_{u\infty}\). The \(R^{2}\) value is 0.99 for those variables. In order to realize a wide range of flight conditions, the Reynolds number was varied by the variance of the flight Mach number and the flight altitude. The resultant flight altitude range was approximately 8900 ft. to 47,000 ft. with the unit Reynolds numbers of approximately 2.9-9.1 \(\times\) 10\({}^{6}\) (as presented in Figure 2) and the flight Mach numbers of 0.5-0.78. In total, six flights were performed during the flight test campaign.  
Figure 3 shows the representative flight history conducted at a single flight in case of \(M_{\infty}\) = 0.65. Each flight involved several cruise conditions at a premised \(s^{+}\) condition for a duration of at least 60 s.  
Figure 4 presents the relationships between certain variables and flight test conditions. Each data point is an averaged value made for a 60-s duration at each targeted cruise condition. The errorbar is the standard deviation (1\(\sigma\)) for the averaging duration. The Mach number and altitude ranges were mentioned before. Figure 4a shows the relationship between \(s^{+}\) and the flight altitude. As can be seen, the \(s^{+}\) value decreases nearly linearly with increasing flight altitude. Additionally, \(s^{+}\) distribution drastically changes across its value of 40 or the flight altitude range across approximately 4-8 km from sea level. Figure 4b shows the relationship between the flight Mach number and \(s^{+}\). While the flight  
Figure 3: Representative flight history showing flight Mach numbers and altitudes.  
Figure 2: Relationship between \(s^{+}\) and unit Reynolds number.  
Figure 5 plots the sensitivities of other variables (i.e., angle of attack, yaw angle, pressure, temperature) to \(s^{+}\). In each plot, a fitting curve is superimposed to identify the overall trend of the distribution. While the yaw angle has less sensitivity to \(s^{+}\), angles of attack, pressures, and temperatures clearly show a dependence on \(s^{+}\) to some extent. Among those property variables, the variables having an influence on interpolation postprocessing will be discussed in a later section, along with the response surface methodology.  
Figure 4: Relationship between each variable and test conditions: (a) flight altitude and \(s^{+}\); (b) Mach number and \(s^{+}\).  
Figure 5: _Cont._