# Calibration of a 3-Component External Balance for MAVs Wind Tunnel Research
## 4 Balance Calibration  
The main objective of the calibration process is to get experimental information for the computation of the matrix \([A]\). The static calibration of the external balance required the design and fabrication of a calibration bench (Figure 6) composed of a structure outside the balance, a central body, pulleys, wires, supports, and weights. The central body is formed by a set of metallic parts located around the balance (Figure 6B). First, 2 circular pieces are placed, one on each side of the symmetry axis of the balance to generate the pitching moment, followed by 2 square pieces to generate the lift and drag. The diameter of the circular pieces was 4 cm based on the expected pitching moment, and the area of the square pieces was 4 \(\times\) 4 cm\({}^{2}\) with a hole inside to house a bearing. Additionally, 4 holes were made, one on each face of the piece, aligned with the symmetry axis of the balance, allowing the application of loads in the lift and drag directions. The outer structure (Figure 6C) was used to fix the pulleys (6 in total), while the weights were placed on top of the supports, which in turn were connected to the central body with wires. Figure 6B shows an example of combined load application (positive drag force, \(+D\), positive lift force, \(+L\), and positive pitching moment, \(M_{y}\)). Figure 6: **(A)** Body, **(B)** 3 directions, and **(C)** components for the calibration process. Since the external balance prototype was designed with the objective of measuring 3 components (\(L\), \(D\), and \(M_{y}\)), loads in 3 different directions must be applied during the calibration process. The selected loads were pure loads (in a single direction) and combined loads (in 2 directions). Figure 7 shows a diagram of the central body with the application load points (12 in total) and the direction of the aerodynamic components based on the balance axes. In the calibration process, a maximum load (\(F_{max}\)) and 2 intermediate loads (\(1/3F_{max}\) and \(2/3F_{max}\)) are selected. Thus, in each loading case, there will be 7 measurement points, corresponding to the loading phase (zero, \(1/3F_{max}\), \(2/3F_{max}\), and \(F_{max}\)) and the unloading phase (\(2/3F_{max}\), \(1/3F_{max}\), and zero). Since the forces expected during the tests with the balance will vary depending on the direction of application, the loads applied in the lift direction (\(Z\)-axis) will be greater than the loads applied in the drag direction (\(Y\)-axis). To evaluate the forces and the moment, weights of 35 g and 77 g are used. For instance, when loads are applied to points 3 and 5, the balance is subjected to a pure force in the \(+Z\) direction, generating a positive lift force (orange arrows in Figure 8). Conversely, when loads are applied to points 7 and 8, the pure force is generated in the \(-Z\) direction (green arrows), creating negative lift. To generate a pure force in the \(\pm X\) direction, the same procedure as before is followed, but 35 g weights are used. By applying a load in the \(+X\) direction, the balance is subjected to a pure positive drag force according to the balance axes (orange arrows in Figure 8). Conversely, if the load is applied in the \(-X\) direction, the pure drag force is negative (green arrows). The following tables show an example of load application for the lift force in the \(+Z\) direction (Table 1), generating a positive force according to the balance axes, and for the aerodynamic drag force in the \(-X\) direction (Table 2), generating a negative force according to the balance axes. Figure 7: Diagram of directions of the measured components. Orange color indicates the positive forces, while the green color indicates negative forces. To generate a pure pitching moment (see Figure 9), loads will be applied to points 9, 10, 11, and 12 of the circular pieces in such a way that a positive or negative moment is generated depending on the applied loads.