# Accuracy Analysis of the Measurement of Centre of Gravity and Moment of Inertia with a Swing
## 2 Materials and Methods
### Measurement Procedure  
The swing itself is made of aluminium and has a mass of around 42 kg. This allows it to be safely handled by two trained persons and the crane is not needed. A pallet cart can be used for the installation at the pivot axis at P1 as shown in Figure 1d. For both of the different pivot axis options, shown in Figures 1 and 2, the swing rests on two cutting edges on top of the support structure, which only requires a very small adjustment. As part of the initial installation as well as after each change of the pivot axis, the inertial inclinometer is moved so that it is orientated parallel to the pivot axis. These measurements and the following adjustments ensure that the swing sits level on the support structure. After this, the instrument is brought back to the position shown in Figure 1a to measure the angle around the pivot axis P1 or P2. It is placed on the level P0 (Figure 2) aligned to the side of the swing. After the exact positioning of the device on this plane to reach an initial measurement close to 0\({}^{\circ}\), it is secured with electrical tape to ensure that it stayed in place. With this, the swing is ready for use.  
The specific construction allows for lifting of bigger models into the swing with the crane or investigation of taller models, for example, the floating wind turbine model which can be seen in the background of Figure 1a. The width is limited to 1.3 m; and the other dimensions do not have a hard limit [30]. Ideally, the investigated model is placed so that the swing stays in the zero position, which might be difficult to achieve for a heavier model. This can be corrected with an offset in the calculations introduced in Section 2.4.  
The next steps are dependent on the purpose of the investigation but, typically, the centre of gravity (CG) has to be measured first. Therefore, a rope is attached on the cross profile of the swing, which holds the relevant pivot axis at a distance of 0 to 0.65 m. This rope holds the danger for the calibration weight. The smallest step used here is 50 g. After loading the swing or changing the mass, the oscillation of the swing is damped with the two finger tips of the operating person to introduce a certain amount of damping to achieve a new equilibrium faster. The angle is measured for typically 64 s to ensure that the magnitude of the remaining oscillation was captured and can be averaged out. This is followed by a further change of the mass until the maximum range of 3\({}^{\circ}\) is reached.  
Control measurements with at least one additional distance between rope and pivot axis are advisable. This ensures that potential user errors can be detected. The calculation of the CG is introduced in Sections 2.4 and 3.1 presents the results for the empty swing which is expanded for an example model in Section 3.2.  
The distance of the CG as well as the mass of the object are a constant value and, by oscillating around a point/an axis, the moment of inertia (MI) can be calculated, knowing the period of the oscillation. Section 2.4 provides the requisite mathematical background and Section 3.3 compares the measurement of the empty swing with the theoretical values. For the presented experimental set-up, the initial inclination should be limited to \(\pm 3^{\circ}\) based on the range of the inertial inclinometer. If the changes are too fast, the reading of the instrument is not correct and underestimates the actual angles. This is to be expected given that the device is designed for high accuracy measurements of slow changing objects. The limitations were reached for oscillations around the pivot axis P2. In those cases, the motion capturing system can provide the observation and check with a stopwatch allows a further independent verification.