# Calibration of a 3-Component External Balance for MAVs Wind Tunnel Research
## 4 Balance Calibration
### Verification  
The verification process of the external balance involved determining the force matrix \([F]\) measured by the balance using two methods. First, an initial verification was conducted using the same output signals \([U]\) from the calibration (Figures 10A, 11A and 12A), allowing for the calculation of the calibration residual to ensure that it is minimal. Next, a second verification was carried out by applying known loads different from those used during calibration. This approach assesses the balance's accuracy from a global perspective as a \"black box\" sensor, where the balance is subjected to input loads and responds with output digital signals. In this case, a total of five loads were selected, including both pure and combined loads (Figures 10B, 11B and 12B). Figure 10 shows the real lift data, that is, the force matrix \([F]\) with the applied and known loads (blue points) and the lift values measured with the external balance (data in red). It can be observed that the real values are almost identical to the values measured by the external balance in the verification with calibration loads (Figure 10A). However, in the verification with 5 selected loads, there is a small deviation between the real load and the load measured by the balance for the 3 and the 5 load points (1, 3, and 5). Figures 11 and 12 show the real aerodynamic drag data and pitching moment, respectively, that is, the force matrix \([F]\) with the applied and known loads (blue points) and the values measured with the external balance (data in red). As in the previous case, the real values are practically the same as the values measured by the external balance in the two verifications. Since these components present rather lower values compared to the lift force,  
Figure 11: Verification of aerodynamic drag with calibration loads (**A**) and 5 selected loads (**B**). Figure 10: Verification of lift with calibration loads (**A**) and 5 selected loads (**B**). it can be concluded that the deviation is in the allowable range of measurement, and thus the calibration matrix \([A]\) results to be valid for future wind tunnel tests. Table 8 shows the force and moment values that constitute the matrix \([F]\) of real values, that is, the 5 selected load cases, the force, and moment values measured with the balance. The absolute error in the measurement of each component \(|\Delta F_{i}|\) is calculated as follows:  
\[|\Delta F_{i}|=|F_{i\_real}-F_{i\_balance}| \tag{32}\]  
where \(i\) represents each measured force or moment in each load case. The relative error of each component in percentage \(\epsilon_{F_{i}}(\%)\) is defined as follows:  
\[\epsilon_{F_{i}}(\%)=\frac{|\Delta F_{i}|}{|F_{i}|}\cdot 100 \tag{33}\]  
Table 9 shows the errors in the measurement of each component and the non-dimensional values according to the full scale (FS). Figure 12: Verification of pitching moment with calibration loads (**A**) and 5 selected loads (**B**). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(N^{\circ}\) & \multicolumn{3}{c}{\(F_{i\_real}\)} & \multicolumn{3}{c}{\(F_{i\_balance}\)} \\ \hline
**Case** & \(L(g)\) & \(D(g)\) & \(My(g\cdot m)\) & \(L(g)\) & \(D(g)\) & \(My(g\cdot m)\) \\ \hline
**1** & 225.175 & 0 & 0 & 215.152 & 0.407 & 0.001 \\ \hline
**2** & 0 & 154.816 & 0 & \(-\)2.380 & 156.048 & \(-\)0.004 \\ \hline
**3** & 225.175 & \(-\)154.368 & 0 & 216.895 & \(-\)154.840 & 0.077 \\ \hline
**4** & \(-\)295.46 & 154.816 & 3.0798 & \(-\)299.313 & 156.284 & 3.075 \\ \hline
**5** & \(-\)140.644 & 0 & 3.0798 & \(-\)151.302 & 0.425 & 3.109 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Verification with the 5 selected loads.