## 4 Results and Discussion
### Quantitative Evaluation of Reduction of Skin Friction Drag  
The total uncertainty inherent in evaluating the skin friction drag reduction given by Equation (13) was considered to be the cumulative uncertainty of independently propagating sources of uncertainty. When solving Equation (13), the uncertainty (\(q_{5}\)) is considered to be the difference of the calculated values in the freestream region from 0, because the skin friction drag in the freestream region should be 0. The total uncertainty is given by Equation (37), considering \(n\) measurement points and that each uncertainty propagates independently. For this calculation, \(n=5\), which corresponds to the number of measurement points in the freestream region (\(z=12\)-\(20\) mm):  
\[q_{total}[\%]=\sqrt{\left(q_{total\_1}\right)^{2}+q_{5}^{2}}=\sqrt{\left(1.83 \over 100\right)^{2}+\left(0.68\over 100\right)^{2}}\times 100=1.95\%. \tag{37}\]  
Thus, the total uncertainty can be estimated at 2.0% for \(n=5\) (the number of measurement points in the freestream region) for evaluating the skin friction drag reduction. It should be noted that the uncertainty is governed by the uncertainty associated with the integration of the autocorrelation function as shown in Table 2, so the total uncertainty can be lowered further by reducing the uncertainty in integrating the autocorrelation function using smaller increments of \(\Delta t\).  
The reduction of the skin friction coefficient at \(z=1.0\) mm (above the riblet peak) was calculated at 2.8% using Equation (13), based on the hot-wire anemometry and the proposed method described in Section 3.4. Accounting for the total uncertainty of 2.0%, the effect of skin friction drag reduction by use of the paint-based riblet was demonstrated.  
In order to support this evaluation, the skin friction drag reduction was compared to that obtained by the pitot-rake measurement [19] by applying the momentum integration method based on the \(U\) velocity profile in the boundary layer based on the pitot-rake measurement. First, the momentum thickness was calculated by Equation (2) based on the \(U\) velocity profile, then the total skin friction coefficient was calculated using Equation (22) [3], which can be applied to a two-dimensional flat plate surface with a zero-pressure gradient. The height ranged from 1.3 to 50.3 mm where the pitot-probe measurement was conducted. The control surface for calculating the total skin friction was from the virtual origin (\(x=20\) mm) where the disk roughness was placed at \(x=600\) mm where the pitot-probe measurement was done. The boundary layer was considered to be turbulent downstream from the virtual origin. By calculating the total skin friction coefficients from Equation (22) for the smooth wall and for the riblet wall, and by assuming that the local skin friction coefficient is proportional to the total skin friction coefficient, the skin friction drag reduction was obtained using Equation (13). Resultant skin friction drag reduction based on Equation (13) using the pitot-rake measurement was 2.9%. Although a slight difference between the pitot-tube-derived value and that obtained by the proposed method is seen (i.e., 0.1%), the derived value of the skin friction drag reduction by the proposed method is consistent with that by the pitot-rake data. Thus, the proposed method is appropriate.