# Accuracy Analysis of the Measurement of Centre of Gravity and Moment of Inertia with a Swing
## 3 Results
### Centre of Gravity (CG)--Example  
The centre of gravity (CG) for the swing is investigated in Section 3.1 based on Equation (3). In a next step, an example model is investigated, which is part of a research project at FloWave. Figure 8 shows this part of a floating structure, which is based on a hexagonal ground with a side length of 280 mm and a total height of 277 mm. The wall and bottom thickness is 12 mm. The total mass of the structure is 11.27 kg and the theoretical CG lays in the centre in the height of 100.273 mm in relation to the bottom. This example was chosen because it has a typical size and comparable simple geometry for which the theoretical value should be very accurate.  
Table 4 provides an overview of the conducted three measurement series with three different distances \(d_{W}\) of the added calibration weights. The analysis base on Equation (2) but also includes the additional constant offset, which was introduced in Equation (11). This value \(d(2)\) is relatively small (range of \(10^{-4}\) degrees) but allows a far better fitting result. Two of the three measurement series provide a very good agreement but the C2 series is not as good. A detailed investigation of the individual time series do not indicate any obvious mistake as well as the analysis similar to Figure 4. This leads to the conclusion that a single measurement series with only one distance \(d_{W}\) is not enough and can potentially lead to an error, which is hard to identify. The guidance should be to use multiple distances for the added calibration weights.  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Case** & \(d_{W}\) & \begin{tabular}{c} **Max** \\ **F\({}_{W}\)** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **max** \(i\) \\ **(kg)** \\ \end{tabular} & \begin{tabular}{c} **Pivot** \\ **Point** \\ \end{tabular} & \begin{tabular}{c} \(d_{MPI}\) \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **d\({}_{MPI}\)+** \\ **Mean(d\({}_{MPI}\))** \\ \end{tabular} & \begin{tabular}{c} **d(2)** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **d\({}_{MPI}\)** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **d\({}_{MPI}\)** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **d\({}_{MPI}\)** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **d\({}_{MPI}\)** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **d\({}_{MPI}\)** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **d\({}_{MPI}\)** \\ **(mm)** \\ \end{tabular} \\ \hline C1 & 0.64 & 1.0 & 17 & P1 & 837.6 & 2.1 & \(-\)0.00039 & 100.4 & 0.1 & 0.11\% \\ C2 & 0.40 & 1.0 & 11 & P1 & 829.3 & \(-\)6.3 & \(-\)0.00036 & 108.7 & 8.4 & 8.42\% \\ C3 & 0.20 & 1.1 & 6 & P1 & 883.8 & 3.2 & \(-\)0.00043 & 99.3 & \(-\)1.0 & \(-\)1.02\% \\ C4 & \(\Sigma\) & 34 & P1 & 836.6 & 1.0 & \(-\)0.00037 & 101.4 & 1.2 & 1.17\% \\ Mean & & & & 835.6 & 0.0 & 102.5 & 2.2 & 2.17\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Overview of the investigated cases for the example geometry presented in Figure 7—Data fitted based on Equation (2) similarly to the approach shown in Equation (11).  
Figure 8: Example model on the swing with support structure (1), swing (2), inclinometer (3) and calibration weights including the rope highlighted with a red line (4) as well as the used pivot axis P1: (**a**) overview, (**b**) detail from the back of the swing (**c**) and the knife edge pivot.