*2.3. Aerodynamic Measurements*

With the balance already calibrated, the procedure for the aerodynamic measurements is as follows. The offset signals *S*<sup>0</sup> can be equal to *SLC*<sup>0</sup> or not, depending on the chosen zero-load state of reference. This aspect is especially relevant when a given pitching angle *α* is fixed for the prototype–balance assembly because *S*<sup>0</sup> must be measured for every particular pitch. In addition, to obtain the forces *FDLz* in the wind coordinate system (drag and lift, see Figure 3), a base–change matrix, *MBC*, must be applied in the following way:

$$M\_{BC} = \begin{pmatrix} \cos a & -\sin a & 0 \\ \sin a & \cos a & 0 \\ 0 & 0 & 1 \end{pmatrix} \tag{7}$$

$$F\_{DLz} = F\_{xyz} \cdot M\_{BC} \tag{8}$$

**Figure 3.** Diagram of the set-up with the variables and the different coordinate systems involved in the measuring procedure.

The aerodynamic coefficients can be finally obtained if the measured forces are made non-dimensional with the upstream dynamic pressure expressed as a force exerted on the prototype:

$$F\_{\infty} = \frac{1}{2} \rho v\_{\infty}^2 cL \tag{9}$$

leading to:

$$\mathbb{C}\_{DLM} = F\_{DL} \cdot \begin{pmatrix} 1/F\_{\infty} & 0 & 0 \\ 0 & 1/F\_{\infty} & 0 \\ 0 & 0 & 1/F\_{\infty} \varepsilon \end{pmatrix} \tag{10}$$

where *ρ* is the air density, *v*∞ the reference wind velocity, *c* is the chord/width of the prototype and *L* its span. The moment component must also be divided by the chord/width again to produce the non-dimensional moment coefficient. Hence, from Equation (10), the drag, lift and moment coefficients are retrieved directly.

The three aforementioned prototypes were tested following this procedure. Particularly, both flat plates were tested at a Reynolds number (*Rec* = *v*∞*c*/*ν*, where *ν* is the air kinematic viscosity) of 130,000 from 0◦ to 90◦ of the pitching angle using a constant angular step of 10◦. Complementarily, the airfoil was tested at a Reynolds number of 200,000, going from −20◦ to 20◦ with a variable angular step, for a better characterization of the aerodynamic forces during the airfoil stall. The three gauge signals were recorded during almost 15 s at a typical acquiring rate of 20 kHz, which assured a sufficient number of points to guarantee correct repeatability and accuracy in the results.
