# Accuracy Analysis of the Measurement of Centre of Gravity and Moment of Inertia with a Swing
## 2 Materials and Methods
### Measurement Instrument  
Two different measurement systems are deployed to observe the inclination and the oscillation of the swing: (a) inertial inclinometer and (b) the motion capturing system. The latter is included as a verification instrument and covers oscillation for which the chosen inclinometer is not fast enough. It would not be required for routine deployment of the swing. A laser level helps to reduce the effort in the installation phase especially when an additional model is loaded in the swing.  
The inclination of the swing is measured with a gravity referenced inclinometer provided by Sherborne (model LOCS 3) [31]. Such an instrument is typically used in industrial applications including bore-hole mapping, pipeline levelling and observation of big structures such as dams, ships or barges as well as bridge deformation [32] and medical applications for precise alignment of imaging systems [33]. The measurement range of the inertial inclinometer covers \(\pm 3^{\circ}\) resulting in a full range output (FRO) of \(6^{\circ}\). Based  
Figure 2: Drawing of the swing (all length in mm) and different pivot axis and reverences heights P0, P1 and P2: (**a,b**) Axonometric projection and overview. (**c**) Front view and (**d**) top view including dimensions.  
on the manufacturer's information [31], the non-linearity (NL) of 0.05% of FRO and the non-repeatability (NR) 0.02% of FRO, which results in a \(\epsilon_{NL}\) of 0.003\({}^{\circ}\) and \(e_{NR}\) of 0.0012\({}^{\circ}\). 0.2 arc seconds is the resolution of the instrument, which is equal to 5.5\({}^{\circ}\)  10\({}^{-5}\). The output voltage is captured by a National Instruments NI9220 differential voltage acquisition module operating with a measurement frequency of 256 Hz.  
Beside the primary instrument, namely, the highly accurate gravity-referenced inclinometer, additional measurements are conducted with the motion capturing system provided by Qualisys. In this particular case the smaller system with four Oqus 300+ cameras is used [29]. The four Oqus 300+ are arranged in an approximate semicircle on one side of the swing and captures the motion of markers with a very high accuracy less than 1 mm. The measurement frequency is set to 256 Hz, which is identical to the inertial inclinometer.  
The deployment of the Qualisys motion capturing system brings an additional benefit for models, which are investigated in the wave and current tank and are thus typically already fitted with the necessary markers. Based on this the centre of gravity can be measured with a high accuracy in relation to the rigid body definition. For this current paper the swing itself is in the focus and hence additional markers are placed on the structure. The aim of the comparison is to provide an independent verification of the inclinometer and capture oscillations which are too fast for the instrument. A synchronisation of both systems was not conducted with a trigger signal but started manually at the same time, which is acceptable for the specific application. The comparison of the two instruments showed that the difference between the two measured inclination angles is smaller than or in the range of the remaining observed oscillation of the angle in a close to steady position of the swing.