## 1 Introduction
As part of the FINE project, flight experiments have been conducted using the flight test bed owned by JAXA to study the effectiveness of the designed riblet in reducing skin friction drag in an actual flight environment. The boundary layer profiles on the aircraft surface were measured using pitot-rakes attached on the outer surface of the aircraft fuselage. A major concern arising from the boundary layer measurements at several different flights is that the velocity profiles in the boundary layer measured at different flights could differ, albeit the same flight condition was premised due to a slight difference in atmospheric air conditions and flight attitudes such as angle of attack and absolute flight velocity. Because the pitot-rake measurement is sensitive to these flight environmental conditions, this concern evidently appears, resulting in different boundary layer profiles in terms of shape and absolute velocity values. Therefore, the boundary layer profile can be altered by the flight conditional difference and by employing the riblets. Thus, this concern leads to difficulty in properly evaluating the effectiveness of riblets in reducing skin friction drag since the magnitude of reduction would be on the order of several percent as mentioned above. In most testing scenarios, boundary layer profiles with and without riblets would be obtained at different flights. Therefore, it is vital to eliminate the influence of the flight conditional difference on the change of the boundary layer profile. Toward this end, it is expected that efforts will be made to explore a method of interpolating the boundary layer velocity profile obtained at a flight to that at the other flight under the same premised flight conditions by removing the individual flight conditional influence, such as the angle of attack or slight discrepancy in flight conditions due to atmospheric conditions. In this study, an approach using an interpolation method based on response surface methodology (RSM) was implemented to interpolate the velocity profile in the boundary layer on the aircraft surface measured in flight by removing the flight conditional influence, so that the velocity profiles in the boundary layer measured at different flights under the same premised flight condition can be compared equivalently. The RSM has been applied to aerodynamic optimization studies and data fitting to reduce errors in the data acquired in flight conditions [24; 25; 26; 27; 28; 29]. [PERSON] et al. [24] and [PERSON] et al. [25] applied the RSM to design the wing geometry of aircraft. [PERSON] et al. [26] applied the RSM to a coupling problem between the shape optimization and flow control in order to improve the performance of the wings and blades. [PERSON] et al. [27] applied the RSM to reduce both noise and modeling errors for designing a high-speed civil transport wing structure, and successfully demonstrated reduced error inherent in the modeling and optimizing the wing geometry and structure [27]. The RSM can also be used to estimate a geometry of interest which is being optimized [28]. [PERSON] et al. [29] used a multiple regression analysis to fit data obtained at flight conditions to estimate the data trend by reducing measurement uncertainty [29]. This method is similar to the data interpolation method based on the RSM. Thus, the response surface methodology has been widely applied to aerodynamic optimization studies and data fitting to obtain the data trend by reducing uncertainty. In this study, based on the measured _U_-velocity using the pitot-rakes in the boundary layer region on the aircraft surface in flight conditions, the accuracy of the proposed interpolation method based on the response surface methodology applied to the flight experimental data was evaluated and is herein reported.